2110032-Passport-G4-FoundationMax-Maths-FY

Drill Time a) What is the saving of Mona? Write it in words. b) Who has the highest and lowest savings? Write it in words. c) Between Rohan and Varun, who has more savings? Concept 3.2: Compare and Order 5-digit Numbers 7) Compare the numbers: a) 85704, 45910 b) 05814, 41049 c) 75031, 51840 d) 15813, 62104 e) 39520, 39520 8) Arrange the numbers in the ascending and descending orders. a) 51058, 58104, 58104 and 58041 b) 98765, 87659, 76598 and 65987 c) 77654, 77653, 77651 and 77652 d) 65807, 26806, 96905 and 14068 e) 58104, 67104, 71048 and 40328 9) Form the largest and the smallest numbers. a) 5, 2, 6, 1, 0 b) 9, 6, 1, 5, 3 c ) 7, 4, 1, 8, 5 d) 1, 5, 2, 3, 8 e) 6, 9, 1, 5, 0 Concept 3.3: Round off Numbers 10) Round off the numbers to the nearest tens, hundreds, thousands and ten thousands. a) 75917 b) 57141 c) 87610 d) 36104 e) 17501 11) Word problem Rajat went to an electronic shop with his father. They have ` 45000 with them. The cost of a television is ` 54000. Do they have enough money to buy the television? If not, how much more money is needed to buy the television? Numbers 45 Merged File_PPS_Maths_G4_TB_Part 1.indb 45 2/1/2017 3:09:28 PM

Addition and Addition and Subtraction Subtraction I Will Learn Concept 4.1: Add and Subtract 5-digit Numbers Merged File_PPS_Maths_G4_TB_Part 1.indb 46 2/1/2017 3:09:28 PM

Concept 4.1: Add and Subtract 5-digit Numbers I Think In Maths Olympiad, Surbhi solved the problem given: In a town, there were 12456 men, 14567 women and 1567 children. 1200 men, 1200 women and 1200 children went out of the town on 23 March rd 2015. What was the total population of the town on 23 March? What was the rd population on the 22 , if all of them were present in the town that day? nd Can you also solve it? To solve this problem, we need to know addition and subtraction of large numbers. 4.1 I Recall We know the addition and subtraction of 4-digit numbers. Let us recall the steps followed. Step 1: Arrange the numbers one below the other according to their places. For subtraction, ensure that the smaller number is placed below the larger number. Step 2: Start adding or subtracting from the ones place. Step 3: At every stage, see if regrouping is required and then add or subtract. Step 4: Write the answer. Addition and Subtraction 47 Merged File_PPS_Maths_G4_TB_Part 1.indb 47 2/1/2017 3:09:29 PM

Let us use the steps given above to solve the following: a) Th H T O b) Th H T O c) Th H T O 4 2 1 6 1 3 3 5 5 9 8 5 + 1 2 5 9 + 1 2 3 5 + 2 4 5 3 d) Th H T O e) Th H T O f) Th H T O 7 4 5 2 4 3 2 2 6 2 0 0 − 1 3 2 3 − 1 4 7 2 − 4 5 0 0 4.1 I Remember and Understand Addition or subtraction of large numbers is similar to the addition or subtraction of 4-digit numbers. Always begin addition and Let us see an example of addition involving 5-digit numbers. subtraction from the ones Example 1: Add: 48415 + 20098 place. Solution: Steps Solved Solve these Step 1: Arrange the numbers T Th Th H T O in columns, one below the other. 4 8 4 1 5 + 2 0 0 9 8 T Th Th H T O 4 2 3 6 7 Step 2: Add the ones. Write T Th Th H T O + 2 3 4 5 8 the sum under the ones. 1 Regroup if needed. 4 8 4 1 5 + 2 0 0 9 8 3 48 Merged File_PPS_Maths_G4_TB_Part 1.indb 48 2/1/2017 3:09:30 PM

Steps Solved Solve these Step 3: Add the tens and T Th Th H T O T Th Th H T O also the carry forward (if 1 1 any) from the previous step. 4 8 4 1 5 5 7 3 8 3 Write the sum under the + 2 0 0 9 8 + 3 1 3 4 7 tens. Regroup if needed. 1 3 Step 4: Add the hundreds and also the T Th Th H T O carry forward (if any) 1 1 from the previous step. 4 8 4 1 5 T Th Th H T O Write the sum under the + 2 0 0 9 8 hundreds. Regroup if 5 1 3 2 5 3 4 7 needed. + 6 2 5 6 7 Step 5: Add the thousands and also the T Th Th H T O carry forward (if any) 1 1 from the previous step. 4 8 4 1 5 Write the sum under the + 2 0 0 9 8 thousands. Regroup if 8 5 1 3 T Th Th H T O needed. Step 6: Add the ten 3 4 7 6 5 thousands and also the T Th Th H T O + 2 1 1 7 8 carry forward (if any) 1 1 from the previous step. 4 8 4 1 5 Write the sum under the + 2 0 0 9 8 thousands. Thus, 48415 + 6 8 5 1 3 20098 = 68513. We will now learn subtraction of 5-digit numbers. Example 2: Subtract: 56718 – 16754 Addition and Subtraction 49 Merged File_PPS_Maths_G4_TB_Part 1.indb 49 2/1/2017 3:09:30 PM

Solution: Steps Solved Solve these Step 1: Arrange the numbers T Th Th H T O T Th Th H T O in columns, one below the other. 5 6 7 1 8 9 7 0 5 4 − 1 6 7 5 4 − 2 3 5 6 7 Step 2: Subtract the ones T Th Th H T O and write the difference under the ones. 5 6 7 1 8 − 1 6 7 5 4 4 Step 3: Subtract the tens. T Th Th H T O That is, 1 − 5, which is not T Th Th H T O possible. 6 11 5 6 7 1 8 7 5 4 0 0 Regroup the hundreds to − 1 6 7 5 4 − 3 2 6 8 9 ⁄ ⁄ tens, subtract and write the 6 4 difference under the tens. Step 4: Subtract the T Th Th H T O hundreds. That is, 6 − 7, 16 which is not possible. 5 6 11 5 6 7 1 8 ⁄ Regroup the thousands to − 1 6 ⁄ 7 5 ⁄ 4 ⁄ hundreds, subtract and 9 6 4 write the difference under the hundreds. Step 5: Subtract the T Th Th H T O thousands. That is, 5 − 6, 15 16 T Th Th H T O which is not possible. 4 5 ⁄ 6 11 5 6 7 1 8 5 4 6 3 5 ⁄ Regroup the ten thousands − 1 6 7 5 4 − 1 2 7 8 9 ⁄ ⁄ ⁄ to thousands, subtract and 9 9 6 4 write the difference under the thousands. 50 Merged File_PPS_Maths_G4_TB_Part 1.indb 50 2/1/2017 3:09:31 PM

Step 6: Subtract the ten T Th Th H T O thousands, and write the 15 16 T Th Th H T O difference under the ten 4 5 ⁄ 6 ⁄ 11 thousands 5 ⁄ 6 ⁄ 7 ⁄ 1 ⁄ 8 8 9 5 7 6 − 1 6 7 5 4 − 4 5 6 8 9 Thus, 56718 – 16754 = 39964. 3 9 9 6 4 Train My Brain Solve the following: a) 34567 + 27092 b) 45601 + 11419 c) 42363 – 18945 4.1 I Apply Addition and subtraction of 5-digit numbers are useful in our daily life. Here are a few examples. Example 3: Raju had ` 90005 with him. He bought clothes for ` 35289. How much money was left with him? Solution: Amount Raju had = ` 90005 T Th Th H T O Amount Raju spent on buying clothes 8 9 9 9 15 = ` 35289 9 ⁄ 0 0 ⁄ 0 5 − 3 5 2 8 9 ⁄ ⁄ ⁄ Amount left with him 5 4 7 1 6 = ` 90005 – ` 35289 Therefore, the amount left with Raju is ` 54716. Example 4: Preeti drove her car for 26349 km in six weeks and 38614 km in the next eight weeks. How many kilometres in all did she drive in 14 weeks? Solution: Distance Preeti drove in the first six weeks = 26349 km Addition and Subtraction 51 Merged File_PPS_Maths_G4_TB_Part 1.indb 51 2/1/2017 3:09:31 PM

Distance she drove in the next eight weeks = 38614 km The total distance Preeti drove T Th Th H T O 1 1 = 26349 km + 38614 km 2 6 3 4 9 Therefore, the total distance Preeti drove in + 3 8 6 1 4 14 weeks is 64963 km. 6 4 9 6 3 Example 5: 66140 people were living in Village A, out of which 55260 people moved to Village B. How many people are left in Village A? Solution: Number of people living in Village A T Th Th H T O = 66140 10 Number of people who moved to Village B 5 0 ⁄ 14 6 6 1 ⁄ 4 ⁄ 0 = 55260 ⁄ – 5 5 2 6 0 Total number of people left in Village A 1 0 8 8 0 = 66140 – 55260 Therefore, 10880 people are left in Village A. 4.1 I Explore (H.O.T.S.) Let us solve a few more examples of addition and subtraction of 5-digit numbers. Example 6: What is the difference between the greatest 5-digit number and the smallest 5-digit number? Solution: The greatest 5-digit number = 99999 The smallest 5-digit number = 10000 Their difference = 99999 – 10000 = 89999 Example 7: What number must be added to 84890 to get the largest 5-digit number? Solution: The largest 5-digit number is 99999. The number to be added to 84890 to get 99999 is 52 Merged File_PPS_Maths_G4_TB_Part 1.indb 52 2/1/2017 3:09:31 PM

99999 – 84890 = 15109 Therefore, the number to be added is 15109. Maths Munchies Always remember that when we add a number to itself, the sum is 2 3 1 double the original number. If we subtract a number from itself, the difference is zero. For example, 2000 + 2000 = 4000 (which is double of 2000) and 2000 – 2000 = 0 . Connect the Dots Social Studies Fun In 1557, Robert Recorde shortened “ is equal to“ to two long, parallel lines. This gave the presently used equal to sign. He used this to avoid repeating himself 200 times in his book. English Fun ‘Addition’ is a noun. Write the verb, adjective and adverb for this word. Addition and Subtraction 53 Merged File_PPS_Maths_G4_TB_Part 1.indb 53 2/1/2017 3:09:32 PM

A Note to Parent Play this fun game with your child. Shuffle a deck of cards. Draw a card randomly from it. Multiply the number on the card by 100. The number obtained is your score. Note it down on a piece of paper. All those playing the game should do the same. Continue the game for a few rounds or till all the cards are drawn from deck. Add the score obtained by each player. The one with the highest score wins. Drill Time Concept 4.1: Add and Subtract 5-digit Numbers 1) Add the following: a) 56249 + 12121 b) 42584 + 23568 c) 87216 + 11114 d) 65312 + 25842 e) 35216 + 42355 2) Subtract the following: a) 59423 – 12546 b) 86531 – 65372 c) 95361 – 46472 d) 11213 – 11206 e) 34536 – 15623 3) Word problems a) Seeta went to purchase a TV from an electronics shop. The price of the TV was ` 25689. She paid the shopkeeper ` 50000. How much money will she receive as change? b) Rohan collected 12568 beads for a design. Sohan collected 25638 beads for the same design. How many beads did they collect in all? 54 Merged File_PPS_Maths_G4_TB_Part 1.indb 54 2/1/2017 3:09:32 PM

M Multiplicationultiplication I Will Learn Concepts 5.1: Multiplication of 3-digit Numbers and 4-digit Numbers 5.2: Multiply Using Lattice Algorithm 5.3: Multiply by Adding Partial Products Mentally Merged File_PPS_Maths_G4_TB_Part 1.indb 55 2/1/2017 3:09:34 PM

Concept 5.1: Multiplication of 3-digit Numbers and 4-digit Numbers I Think Surbhi went to a the stadium to watch a cricket match with her parents. She observed that the seats are arranged in many rows and columns. All the seats were occupied. She want- ed to guess the total number of people who watched the match that day. How will she be able to do that? To answer this question, we have to learn to multiply a 3-digit number. 5.1 I Recall We have learnt to multiply 2-digit and 3-digit numbers by 1-digit and 2-digit numbers. Let us solve the following to revise the concept of multiplication. a) T O b) H T O c) H T O d) H T O 3 9 2 5 6 5 8 9 8 7 5 × 2 × 3 × 4 × 5 5.1 I Remember and Understand Let us now learn to multiply 3-digit numbers by 3-digit numbers and 4-digit numbers by 1-digit numbers. 56 Merged File_PPS_Maths_G4_TB_Part 1.indb 56 2/1/2017 3:09:36 PM

Multiply a 3-digit Number by a 3-digit Number Multiplying a 3-digit number by a 3-digit number is similar to multiplying a 3-digit number by a 2-digit Standard algorithm is the number. Let us see an example. method of multiplication in which the product is Example 1: Multiply: 159 × 342 regrouped as ones and tens. Solution: To multiply the given numbers, follow these steps. Steps Solved Solve these Step 1: Multiply the Th H T O multiplicand by the ones of the multiplier, 1 1 that is, 159 × 2. 1 5 9 T Th Th H T O Regroup if necessary. × 3 4 2 3 1 8 5 2 6 Step 2: Put a 0 below Th H T O × 2 3 5 ones place of the product obtained in the 2 3 above step. Multiply the 1 1 multiplicand by the tens of the multiplier, that is, 1 5 9 159 × 4. × 3 4 2 Regroup if necessary. 3 1 8 6 3 6 0 Step 3: Put two 0s below T Th Th H T O ones and tens places of T Th Th H T O the product obtained in 1 2 the previous step. Multiply 2 3 the multiplicand by the 4 2 5 hundreds of the multiplier, 1 1 × 1 1 9 that is, 159 × 3. 1 5 9 Regroup if necessary. × 3 4 2 3 1 8 6 3 6 0 4 7 7 0 0 Multiplication 57 Merged File_PPS_Maths_G4_TB_Part 1.indb 57 2/1/2017 3:09:36 PM

Steps Solved Solve these Step 4: Add the products T Th Th H T O from steps 1, 2 and 3. This sum gives the required 1 2 T Th Th H T O product. 2 3 1 1 3 0 1 1 5 9 × 7 6 9 × 3 4 2 3 1 8 + 6 3 6 0 + 4 7 7 0 0 5 4 3 7 8 Multiply a 4-digit Number by a 1-digit Number Multiplying a 4-digit number by a 1-digit number is similar to multiplying a 3-digit number by a 1-digit number. Let us see an example. Example 2: Multiply: 3628 × 7 Solution: T Th Th H T O 4 1 5 3 6 2 8 × 7 2 5 3 9 6 Solve these Th H T O Th H T O Th H T O 2 5 6 8 5 6 8 9 1 2 5 9 × 8 × 2 × 4 Properties of Multiplication Identity Property: For any number ‘a’, a × 1 = 1 × a = a. 1 is called the multiplicative identity. 58 Merged File_PPS_Maths_G4_TB_Part 1.indb 58 2/1/2017 3:09:36 PM

For example, 461 × 1 = 1 × 461 = 461. Zero Property: For any number ‘a’, a × 0 = 0 × a = 0. For example, 568 × 0 = 0 × 568 = 0. Commutative Property: If ‘a’ and ‘b’ are any two numbers then a × b = b × a. For example, 12 × 3 = 36 = 3 × 12. Associative Property: If ‘a’, ‘b’ and ‘c’ are any three numbers then a × (b × c) = (a × b) × c. For example, Distributive Property: 1) If 'a', 'b' and 'c' are any three numbers, then: a × (b + c) = (a × b) + (a × c). For example, 2 × (3 + 5) = (2 × 3) + (2 × 5). 2 × 8 = 6 + 10 16 = 16 Multiplication distributes over addition. 2) If 'a', 'b' and 'c' are any three numbers then: a × (b − c) = (a × b) − (a × c). For example, 2 × (8 − 5) = (2 × 8) − (2 × 5). 2 × 3 = 16 − 10 6 = 6 Multiplication distributes over subtraction. Train My Brain Solve the following: a) 222 × 333 b) 692 × 132 c) 5632 × 4 Multiplication 59 Merged File_PPS_Maths_G4_TB_Part 1.indb 59 2/1/2017 3:09:36 PM

5.1 I Apply Let us see a few real-life examples involving multiplication of 4-digit numbers. Example 3: Neena had 450 pencils in a box. There were 212 such boxes. How many pencils did Neena have in all? T Th Th H T O Solution: Number of pencils in a box = 450 1 Number of such boxes = 212 1 Total number of pencils 4 5 0 × 2 1 2 = 450 × 212 1 9 0 0 = 95400 + 4 5 0 0 + 9 0 0 0 0 Therefore, Neena had 95400 pencils. 9 5 4 0 0 Example 4: 3542 students went to school from each town. There were 4 such towns. How many students went to school? Solution: Number of students who went to school from each town= 3542 Number of towns = 4 T Th Th H T O Total number of students who went to school 2 1 3 5 4 2 = 3542 × 4 × 4 Therefore, 14168 students went to school. 1 4 1 6 8 5.1 I Explore (H.O.T.S.) We know that the smallest 4-digit number is 1000 and the largest 4-digit number is 9999. Let us multiply the largest 4-digit number by the smallest and the largest 1-digit numbers. Example 5: Multiply the largest 4-digit number by the smallest 1-digit number. Solution: The largest 4-digit number = 9999 The smallest 1-digit number = 1 60 Merged File_PPS_Maths_G4_TB_Part 1.indb 60 2/1/2017 3:09:37 PM

We know that the product obtained when any Th H T O number is multiplied by 1 is the number itself. 9 9 9 9 Therefore, 9999 × 1 = 9999. × 1 9 9 9 9 Example 6: Multiply the largest 4-digit number by the largest 1-digit number. T Th Th H T O Solution: The largest 4-digit number = 9999 8 8 8 The largest 1-digit number = 9 9 9 9 9 Therefore, 9999 × 9 = 89991. × 9 8 9 9 9 1 Concept 5.2: Multiply Using Lattice Algorithm I Think Surbhi knows how to multiply a 3-digit number by a 2-digit number. But she makes some mistakes. She wants a simple method for multiplication. Do you know any such method? For this, let us learn multiplication by lattice algorithm. 5.2 I Recall We know multiplication using standard algorithm. Let us recall the standard algorithm of multiplication by solving the following: Multiplication 61 Merged File_PPS_Maths_G4_TB_Part 1.indb 61 2/1/2017 3:09:37 PM

a) b) c) d) H T O Th H T O Th H T O Th H T O 2 2 5 4 2 1 4 2 1 2 4 3 × 6 × 4 × 8 × 2 5.2 I Remember and Understand Let us now learn to multiply 2-digit and 3-digit numbers using lattice algorithm. The important features of the lattice algorithm: • Setting up the lattice before we begin multiplying There are two ways to multiply numbers: • Doing all the multiplications first, followed by additions 1) Standard Algorithm • There is no carry over in the multiplication phase of 2) Lattice Algorithm the algorithm Let us use the lattice algorithm to multiply: 1) a 2-digit number by a 1-digit number and a 2-digit number. 2) a 3-digit number by a 2-digit number. Multiply a 2-digit number by a 1-digit number and a 2-digit number Multiplying a 2-digit number by a 1-digit number and a 2-digit number is similar to multiplying a 1-digit number by a 1-digit number. Let us see an example. Example 7: Multiply: a) 29 × 3 b) 43 × 52 62 Merged File_PPS_Maths_G4_TB_Part 1.indb 62 2/1/2017 3:09:38 PM

Solution: Solved Solved Solve these Steps a) 29 × 3 b) 43 × 52 Step 1: Construct a lattice as shown such that: 3 2 × (a) Number of rows = 4 Number of digits in the multiplier. 2 (b) Number of columns = Number of digits in multiplicand. Step 2: Write the 2 9 × 4 3 × 5 2 × multiplicand along the 3 5 4 top of the lattice and the multiplier along the right, 2 6 one digit for each row or column. Draw diagonals to divide each box into parts as shown. Step 3: Multiply each 4 3 × 6 1 × digit of the multiplicand 2 9 × 2 1 by each digit of the 2 0 5 5 4 multiplier. Write the 7 3 4 products in the cells 2 where the corresponding rows and columns meet. 4 3 × 5 7 × Step 4: If the product is a 2 9 × 2 1 5 3 single digit number, put 0 0 2 0 5 in the tens place. 6 7 3 0 0 2 1 (2 × 3 = 6) = 06 8 6 Multiplication 63 Merged File_PPS_Maths_G4_TB_Part 1.indb 63 2/1/2017 3:09:39 PM

Solved Solved Steps Solve these a) 29 × 3 b) 43 × 52 Step 5: Add the numbers 2 9 × 4 3 × 6 3 × along the diagonals 0 2 3 2 1 5 3 from the right to find 0 6 7 2 0 5 the product. Regroup if 8 7 1 0 0 2 3 needed. Write the sum Therefore, 2 8 6 from left to right. 29 × 3 = 087 3 6 = 87 Therefore, 43 × 52 = 2236. Multiply a 3-digit number by a 2-digit number Multiplying a 3-digit number by a 2-digit number is similar to multiplying a 2-digit number by a 2-digit number. Let us see an example. Example 8: Multiply: 168 × 48 Solution: Solved Steps Solve these 168 × 48 Train My Brain Step 1: Construct a lattice as shown such that: 1 4 2 × (a)Number of rows = Number 4 of digits in the multiplier. 8 (b) Number of columns = Number of digits in multiplicand. 64 Merged File_PPS_Maths_G4_TB_Part 1.indb 64 2/1/2017 3:09:39 PM

Solved Steps Solve these 168 × 48 Step 2: Write the multiplicand 1 6 8 1 7 2 along the top of the lattice. × × Write the multiplier along the 4 4 right, one digit for each row or column. Draw diagonals to 8 2 divide each box into parts as shown. Step 3: Multiply each digit 1 6 8 × 2 6 2 × of the multiplicand by each 0 2 3 4 3 digit of the multiplier. Write the 4 4 2 products in the cells where 8 8 the corresponding rows and columns meet. 1 6 8 × 1 7 1 × Step 4: If the product is a 0 2 3 single digit number, put 0 in 4 4 2 4 3 the tens place. 0 4 6 8 8 4 8 1 1 6 8 × Step 5: Add the numbers along the diagonals to find 0 4 2 3 4 3 4 2 × the product and write the sum 0 4 2 from left to right. 2 0 8 4 8 6 8 3 8 1 4 0 6 4 2 Therefore, 168 × 48 = 8064. Train My Brain Multiply using the lattice method: a) 54 × 3 b) 78 × 21 c) 375 × 27 Multiplication 65 Merged File_PPS_Maths_G4_TB_Part 1.indb 65 2/1/2017 3:09:40 PM

5.2 I Apply Let us now see a few real-life examples involving multiplication of 3-digit numbers. Example 9: There are 345 students in each class. Pooja’s school has 12 such classes. How many students are there in her school? Solution: Number of students in each class = 345 3 4 5 × Number of such classes in Pooja’s 0 0 0 1 school = 12 3 4 5 Total number of students 0 0 1 2 4 6 8 0 = 345 × 12 = 4140 1 4 0 Therefore, there are 4140 students in Pooja’s school. Example 10: 42 people were sitting in a row of a stadium to enjoy a cricket match. How many people would be there in all if there were 35 such rows? Solution: Number of people sitting in one row = 42 4 2 × 1 0 Number of rows = 35 1 2 6 3 Total number of people in 35 rows 2 1 = 42 × 35 = 1470 4 0 0 5 Therefore, there are 1470 people in the 7 0 stadium. 5.2 I Explore (H.O.T.S.) We know how to multiply numbers using lattice algorithm. Let us see if we can analyse and solve the following. 66 Merged File_PPS_Maths_G4_TB_Part 1.indb 66 2/1/2017 3:09:40 PM

Example 11: Find the missing numbers. 2 3 ? × 23___ × 4___= 9954 0 1 n 2 4 0 8 2 8 0 0 1 ? 9 4 6 4 9 5 4 Solution: We can see that the box in the top right corner has the number 28. It is the product of 4 and ?. That is, 4 × ? = 28 4 × 7 = 28 So, 7 is the first unknown number. Similarly, the box in the bottom left corner has 04. It is the product of 2 and?. That is, 2 × ? = 04 2 × 2 = 04 So, the second unknown number is 2. So, the required numbers are 7 and 2 so that 237 × 42 = 9954. Concept 5.3: Multiply by Adding Partial Products Mentally I Think Surbhi’s rose garden has rose plants planted row wise in 7 rows. There are 8 plants in each row. Surbhi wanted to find out the total number of rose plants in her garden. How can she find that mentally? To answer this, we need to learn how to multiply by adding partial products mentally. Multiplication 67 Merged File_PPS_Maths_G4_TB_Part 1.indb 67 2/1/2017 3:09:41 PM

5.3 I Recall To learn how to complete multiplication facts by adding partial products mentally, we must memorise tables from 1 to 5 and 10. For example, we know that 6 × 5 = 30. As 6 = 4 + 2, we have (4 + 2) × 5 = (4 × 5) + (2 × 5) = 20 + 10 = 30. 5.3 I Remember and Understand Let us now understand how to complete multiplication facts by adding partial products mentally. Example 12: Find the answer by adding partial While multiplying two products. numbers mentally, we split the larger number into two 8 × 9 parts. Solution: Solved Solve this Steps 8 × 9 7 × 6 Step 1: Check by how The larger number The larger number is , much the larger number is is 9, and from 5, we and from 5, we count more than 5. count 6, 7, 8 and 9. and . So, is So, 9 is 4 more than 5. more than 5. Step 2: Write the number 5 + 4 = 9 + = as the sum of 5 and another number. 68 Merged File_PPS_Maths_G4_TB_Part 1.indb 68 2/1/2017 3:09:41 PM

Solved Solve this Steps 8 × 9 7 × 6 Step 3: Multiply the 5 × 8 = 40 and 5 × = numbers of the sum by the smaller number. Use 4 × 8 = 32 and memorised tables of 1 to 5 × = and 10 to solve mentally. Step 4: Add both the 40 + 32 = 72 + = products from step 3 to get the final answer. Therefore, Therefore, 7 × 6 = . 8 × 9 = 72. Example 13: Find the answer by adding partial products: 14 × 6 Solution: Solved Solve this Steps 14 × 6 12 × 8 Step 1: Check by how much The larger number is The larger number is the larger number is more than 14, and from 10, we ____, 10. count and from 10 we count 11, 12, 13 and 14. So, and . So is 14 is 4 more than 10. more than 10. Step 2: Write the larger number 10 + 4 = 14 + = as the sum of 10 and another number. Step 3: Multiply the sum in the previous step by the 10 × 6 = 60 and 10 × = and 4 × 6 = 24 smaller number given, using × = memorised tables of 1 to 5 and 10. Multiplication 69 Merged File_PPS_Maths_G4_TB_Part 1.indb 69 2/1/2017 3:09:41 PM

Solved Solve this Steps 14 × 6 12 × 8 Step 4: Add both the products 60 + 24 = 84 + = from step 3 mentally to get the Therefore, 14 × 6 = 84. final answer. Therefore, 12 × 8 = . Train My Brain Find the answer by adding partial products. a) 18 × 7 b) 13 × 4 c) 11 × 6 5.3 I Apply We have learnt some easy ways of completing multiplication facts by adding partial products mentally. Let us now see some examples where we apply this concept. Example 14: Rohit works for 8 hours in a day. He works 6 days in a week. For how many hours does he work in a week? Solution: Number of hours Rohit works in a day = 8 Number of days he works in a week = 6 Total number of hours Rohit works in a week = 8 × 6 The larger number is 8, and it is 3 more than 5. As 8 = 5 + 3, 8 × 6 = (5 × 6) + (3 × 6) = 30 +18 = 48. Therefore, Rohit works for 48 hours in a week. Example 15: Jaya’s father bought 7 boxes of mangoes, which contains 12 mangoes in each box. How many mangoes did Jaya’s father buy in all? Solution: Number of boxes of mangoes Jaya's father bought = 7 Number of mangoes in each box = 12 70 Merged File_PPS_Maths_G4_TB_Part 1.indb 70 2/1/2017 3:09:41 PM

Total number of mangoes = 12 × 7 The larger number is 12, and it is 2 more than 10. So, 12 = 10 + 2. Hence, 12 × 7 = (10 × 7) + (2 × 7) = 70 +14 = 84. Therefore, Jaya’s father bought 84 mangoes in all. 5.3 I Explore (H.O.T.S.) So far, we have seen how to complete multiplication facts by adding partial products, mentally. Let us now see some more examples with larger numbers. Example 15: Find the answer by adding partial products: 17 × 7 Solution: Solved Solve this Steps 17 × 7 19 × 9 Step 1: Check how The larger number is The larger number is , much the larger 17, and from 10 we number is more than count 11, 12, 13, 14, and from 10 we count 10. 15, 16 and 17. So, 17 is , , , , 7 more than10. , , , , and . So, is more than 10. Step 2: Take the Number from step 1 Number from step 1 is , number from step is 7, and from 5, we 1 and check how count 6 and 7. and from 5, we count , much it is more than , and . So, is 5. So, 7 is 2 more than 5. more than 5. Step 3: Write the three numbers whose 10 + 5 + 2 = 17 + + = sum is the larger number. Multiplication 71 Merged File_PPS_Maths_G4_TB_Part 1.indb 71 2/1/2017 3:09:42 PM

Solved Solve this Steps 17 × 7 19 × 9 Step 4: Multiply 10 × = each number of the 5 × = sum in the previous 10 × 7 = 70 step by the smaller 5 × 7 = 35 × = given number. Use memorised tables of 2 × 7 = 14 1 to 5 and 10 to solve mentally. Step 5: Add all the 70 + 35 + 14 = 119 + + = three products from Therefore, 19 × 9 step 4 to get the final Therefore, 17 × 7 = 119. answer. = __. Maths Munchies Chinese method of multiplication 2 3 1 4 × 3 In this example, we multiply 4 × 3. The four pink lines represent 4 and the three green lines represent 3. In order to get the product, we just count the number of orange intersections that the four pink lines and three green lines create. Thus, we get the product 12. 4 × 3 = 12 72 Merged File_PPS_Maths_G4_TB_Part 1.indb 72 2/1/2017 3:09:42 PM

Connect the Dots Social Studies Fun The oldest known multiplication table was found written on bamboo strips in China which are said to be 2300 years old. Modern multiplication tables are said to have been written down by the famous Greek mathematician Pythagoras. It is also called the Table of Pythagoras in many other languages. English Fun The word ‘Lattice’ in ‘lattice’ algorithm is not an English word originally. The word is taken from ‘lattis’, in old French language which itself has been taken from ‘latte’ ‘lath’, old German language of Germany. A Note to Parent Help your child understand and practise the Chinese method of multiplication using straws of different colours. Drill Time Concept 5.1: Multiplication of 3-digit Numbers and 4-digit Numbers 1) Multiply a 3-digit number by a 3-digit number. a) 247 × 567 b) 509 × 121 c) 892 × 469 d) 731 × 691 2) Multiply a 4-digit number by a 1-digit number. a) 6741 × 4 b) 3456 × 8 c) 9258 × 9 d) 5555 × 5 Multiplication 73 Merged File_PPS_Maths_G4_TB_Part 1.indb 73 2/1/2017 3:09:43 PM

Drill Time 3) Word problems a) Pranav makes 253 cotton bags in a day. How many bags will he be able to make in the year 2017? [Hint: 2017 is not a leap year] b) Tanya bought sweaters as Christmas gifts for her 7 cousins. If one sweater costs ` 2734 , then how much money in all did she spend for the gifts? Concept 5.2: Multiply Using Lattice Algorithm 4) Multiply a 2-digit number by a 2-digit number. a) 24 × 32 b) 56 × 15 c) 13 × 39 d) 67 × 51 5) Multiply a 3-digit number by a 2-digit number. a) 158 × 17 b) 451 × 39 c) 651 × 67 d) 721 × 41 6) Word problems a) A movie theatre sold 127 tickets for a movie. Cost of one ticket was ` 85. How much money did the theatre owner earn from that movie? b) There are 47 students in Class 3. Answer sheets were given to each student for Maths exam. If one answer sheet has 15 pages, then how many total sheets of paper were used for the exam? Concept 5.3: Multiply by Adding Partial Products Mentally 7) Multiply the following: a) 9 × 7 b) 9 × 6 c) 11 × 7 d) 14 × 6 e) 13 × 8 8) Word problems a) There are 14 players in a football team. If 8 teams are participating in the district level football tournament, then how many pairs of boots are needed for them? b) Megha eats 8 chappatis daily. How many chappatis does she eat in a week? 74 Merged File_PPS_Maths_G4_TB_Part 1.indb 74 2/1/2017 3:09:43 PM

Ti Timeme I Will Learn Concepts 6.1: Find the Duration 6.2: Estimate Time Merged File_PPS_Maths_G4_TB_Part 1.indb 75 2/1/2017 3:09:44 PM

Concept 6.1: Find the Duration I Think Surbhi and her brother were going to school. When they started from home, the time shown by the clock was . Surbhi’s brother asked her to read the time. She read it easily as 8 o’clock. When they reached the school, the time shown by the clock in the school was Surbhi’s brother again asked her how long it took them to reach the school. She could not answer him. Can you tell? To answer this, we have to learn to find the duration. 6.1 I Recall There are 24 hours in a day. In a clock, the hour hand shows hours and completes one turn in 12 hours. The minute hand shows minutes and takes one turn in one hour. We have learnt to read time to the nearest hour and minutes when the minute hand is on any one of the numbers on the clock. Let us recall the concept by writing the time for the clocks shown below: Read the time shown by the clocks given: 76 Merged File_PPS_Maths_G4_TB_Part 1.indb 76 2/1/2017 3:09:45 PM

6.1 I Remember and Understand Observe this clock. • The long hand is called the minute hand. • The short hand is called the hour hand. • It has numbers 1 to 12 on its face. • Between 12 and 1, there are four lines. Between 1 and 2, there are four lines. They divide the space between two consecutive numbers into five equal parts. • Each division between these consecutive numbers indicates a minute. • Thus, these sixty divisions together make 60 minutes or 1 hour. Example 1: Let us read the time shown by these clocks. One is done for you. a) Read this b) Read this c) Read this Hour hand is on 10 = 10 h Hour hand is on Hour hand is on Minute hand is on the ____________________ ____________________. second divison after 2. Minute hand is on _____. Minute hand is on _____. (2 × 5 + 2) = 12 min The time is _____. The time is _____. The time shown is 10:12. We have learnt to read and write time in 12-hour clock. Now, let us learn to read time in the 24-hour clock. In 12-hour clock time: • The hour hand of the clock goes around the clock face (dial) twice in 24 hours. • To identify morning or evening, we write a.m. or p.m. along with the time. Time 77 Merged File_PPS_Maths_G4_TB_Part 1.indb 77 2/1/2017 3:09:45 PM

In 24-hour clock time: • The time is expressed as a 4-digit number (hhmm) followed by ‘h’ to denote hours. 12-hour clock time 24-hour clock time Read as 4:20 a.m. 0420 h Four twenty hours 11:40 a.m. 1140 h Eleven forty hours 5:30 p.m. 1730 h Seventeen thirty hours 7:35 p.m. 1935 h Nineteen thirty-five hours • Here, the first two digits from the left tell us the hours and the next two digits tell us the minutes. • We do not write a.m. or p.m. • 12 o’clock midnight is written as 0000 h. • 12 o’clock noon is written as 1200 h. Time before noon is written as in a12-hour clock but without a.m. For example, 5:30 a.m. is written as 0530 hours. • Time post noon is written by adding 12 to the number of hours. • When the number of hours is more than12, then the time indicates post noon. For example, 1730 h, 1815 h, 2210 h and so on. a.m.< 12 < p.m. • When the number is 12 and the To convert the time in 24-hour clock minutes are more than 00, the to12-hour clock format, we subtract 12 time is past noon and we write from the number of hours and write p.m. p.m. along with the number. after the difference. For example, 1220 h = 12:20 p.m. To convert time from 12-hour clock into (Here, we do not subtract 12 from 24-hour clock for the time after 12 noon, hours.) we add 12 to the number of hours and omit writing p.m. Do you know? • Railways/Airlines/Armed forces use the 24-hour clock to keep time. • The 24-hour clock is used in digital watches. 78 Merged File_PPS_Maths_G4_TB_Part 1.indb 78 2/1/2017 3:09:46 PM

Example 2: Convert the given time to 12-hour clock time. a) 1320 h b) 0550 h c) 0915 h d) 2105 h e) 1800 h f) 1945 h g) 2355 h h) 0030 h i) 0045 h j) 0312 h Solution: a) (13 – 12):20 = 1: 20 p.m. b) 5:50 a.m. c) 9: 15 a.m. d) (21 – 12): 05 = 9:05 p.m. e) (18 – 12):00 = 6 p.m. f) (19 – 12): 45 = 7:45 p.m. g) (23 – 12):55 = 11:55 p.m. h) (00 + 12):30 = 12: 30 a.m. i) (00 + 12):45 = 12: 45 a.m. j) 3:12 a.m. We have learnt how to read and show time, exact to minutes and hours. Let us now consider an example of finding the length of time between two given times. Example 3: The clocks given show the start time and end time of a Maths class in a school. How long was the Maths class? Solution: The start time is 9:00 and the end time is 9:45. So, the time between is the length of the Maths class = 9:45 – 9:00 = 45 minutes The time between two given times is called the length of time or time duration or time interval. It is given by the difference of end time and start time. Train My Brain Draw the hands of a clock to show the time given: a) 6:12 b) 11: 43 c) 3:32 Time 79 Merged File_PPS_Maths_G4_TB_Part 1.indb 79 2/1/2017 3:09:46 PM

6.1 I Apply Let us see a few real-life examples involving duration of time. Example 4: Neha went to the airport to see off her uncle. There she saw the departure time for Flight 142 to Hyderabad as 1102 h. What was the time of departure of the flight in the 12-hour clock time? Solution: Time of departure of the flight = 1102 h 1102 h is in hhmm form. Since 11 < 12, the given time is a.m. Therefore, the given time in 12-hour clock is 11: 02 a.m. 6.1 I Explore (H.O.T.S.) Let us now see a few more real-life examples involving the duration of time. Example 5: Anil took a flight from Delhi at 10:10 p.m. and reached Hyderabad in 2 hours 5 minutes. At what time did the flight reach Hyderabad? Solution: Start time of the flight = 10:10 p.m. Duration of travel = 2 hours 5 minutes End time = Start time + Duration = 10:10 p.m. + 2 hours 5 minutes = 12:15 a.m. (After 12 midnight, time is taken as a.m.) Example 6: A movie began at 5:35 p.m. Lucky switched on the TV at 6:23 p.m. For how much time did Lucky miss the movie? Solution: Start time of the movie = 5:35 p.m. Time at which Lucky switched on the TV = 6:23 p.m. 5:35 pm to 6 p.m. = 25 minutes 80 Merged File_PPS_Maths_G4_TB_Part 1.indb 80 2/1/2017 3:09:46 PM

6 pm to 6:23 p.m. = 23 minutes Therefore, the time for which Lucky missed the movie = (25 + 23) = 48 minutes Example 7: When Shruti was having her breakfast, it was 7:45 in the clock. What is the time in 12-hour and 24-hour clock formats? Solution: The time when Shruti was having her breakfast = 7:45 This time in 12 hour clock time is 7:45 a.m. In 24-hour clock time, it is 0745 h. Concept 6.2: Estimate Time I Think Surbhi’s father was trying to book flight tickets from Mangalore to Dubai. He asked Surbhi to see the flight timings. He wanted her to find the time it would take for him to reach Dubai. Do you know how to find that? To know that, we have to learn estimation of time. 6.2 I Recall The time from midnight 12 to midday 12 is 12 hours. The time from midday 12 to midnight 12 is 12 hours. Observe this timeline. The time after midnight is written with a.m. after it. The time after midday is written with p.m. after it. So, 4 o’clock in the morning is 4 a.m., and 4 o’clock in the evening Time 81 Merged File_PPS_Maths_G4_TB_Part 1.indb 81 2/1/2017 3:09:47 PM

is 4 p.m. We can show the time in the morning or evening on a clock face. We know how to find the length of the time between two given times. Now, let us see the comparison between different units of time. • A minute is a shorter period of time than an hour. • An hour is shorter than a day. A day is shorter than a week. • A week is shorter than a month. • A month is shorter than a year. Express the following in a.m. or p.m. a) 3:30 in the morning b) 11:45 before noon c) 12:15 at midnight d) 5 in the evening 6.2 I Remember and Understand We have learnt how to find the duration of time with the help of start time and end time. We can also estimate the time taken for an event to happen with the start or the end time and its duration. Let us understand this through a few examples. Example 8: If an event starts at 1:15 p.m. and Duration = End time – Start time it takes 2 hours to get over, then End time = Start time + Duration by what time will the event end? Start time = End time – Duration Solution: The start time of the event = 1:15 p.m. Duration of the event = 2 hours End time of the event = Start Time + Duration = 1:15 p.m. + 2 hours = 3:15 p.m. Therefore, the end time of the event is 3:15 p.m. Example 9: If a dance class ends at 9:20 a.m. and has taken 1 hour 15 minutes to complete, when did it begin? 82 Merged File_PPS_Maths_G4_TB_Part 1.indb 82 2/1/2017 3:09:47 PM

Solution: The end time of the dance class = 9:20 a.m. Duration of the class = 1 hour 15 minutes Start time of the class = End Time – Duration = 9:20 a.m. – 1 hour 15 minutes = 8:05 a.m. Therefore, the dance class began at 8:05 a.m. Example 10: Ravi’s swimming class is for a duration of 1 h 50 min. If the class begins at 10:15 a.m., at what time does it end? Solution: Duration of Ravi’s swimming class = 1 h 15 min The start time of the class = 10:15 a.m. The end time of the class = 10:15 a.m. + 1 h 15 min = (10 + 1)h + (15 + 15) min = 11 h 30 min Therefore, Ravi’s swimming class ends at 11:30 a.m. Example 11: On the Sports day of a school, indoor games competition begins at 11:40 a.m. If the competition goes on for 2 hours, at what time will it end? Solution: Start time of indoor games competition = 11:40 a.m. Duration of competition = 2 hours End time = Start time + Duration = 11:40 a.m. + 2 h = 1:40 p.m. Example 12: Our school’s annual day begins at 5:30 p.m. and would end after 5 h 12 min. At what time does it end? Express the end time in 24-hour clock time. Solution: Start time of our annual day = 5:30 p. m. Duration of the celebration = 5 h 12 min End time = Start time + Duration = 5:30 p.m.+ 5 h 12 min = 10:42 p.m. Time 83 Merged File_PPS_Maths_G4_TB_Part 1.indb 83 2/1/2017 3:09:47 PM

Therefore, the annual day ended at 10:42 p.m. In 24-hour clock time, it is (10 + 12) 42 h = 2242 h. Train My Brain Find the time interval between the following. a) 4:30 a.m. and 2:30 p.m. b) 10:25 a.m. and 4:30 p.m. 6.2 I Apply Let us see a few real-life examples involving estimation of time. Example 13: Radha participated in a drawing competition which was scheduled for one hour starting at 9 a.m. If Radha completes her drawing 15 minutes before the end time, at what time does she complete her drawing? Solution: Drawing competition was for 1 hour, starting at 9 a.m. So, the competition was scheduled to end at 10 a.m. Radha completed her drawing 15 minutes before the end time. That is, she took (60 – 15) minutes that is 45 minutes for the drawing. 45 minutes from 9 a.m. is 9:45 a.m. Therefore, the time at which Radha completed her drawing was 9:45 a.m. Example 14: Leela goes for a dance class at 4:48 p.m. and comes back at 6:45 p.m. How much time does she spend in the class? Solution: Start time of Leela’s dance class is 4:48 p.m. End time of Leela’s dance class is 6:45 p.m. 1 hour 12 minutes 45 minutes 4:48 p.m. ____________ 5 p.m. __________ 6 p.m. __________ 6:45 p.m. Time spent by Leela in the class = 1 hour + 45 minutes + 12 minutes = 1 hour 57 minutes 84 Merged File_PPS_Maths_G4_TB_Part 1.indb 84 2/1/2017 3:09:48 PM

6.2 I Explore (H.O.T.S.) Let us consider another example of estimating time. Example 15: On 12 February, Raju saw the calendar and circled 21 March as his st th father’s birthday. He wanted to buy a gift for his father. How many days were left for him to buy the gift? Solution: Since it is not mentioned as leap year, we take 28 days for the month of February. Days in February = 28 – 11 = 17 Days in March = 21 Total number of days = 17 + 21 = 38 Therefore, there are 38 days from 12 February to 21 March for Raju to st th buy a gift for his father. Maths Munchies 1 When the hour was divided into 60 minutes, consisting of 60 seconds, the 2 3 number 60 was probably chosen for its mathematical convenience. It is divisible by a large number of smaller numbers without a remainder: 2, 3, 4, 5, 6, 10, 12, 15, 20 and 30. Connect the Dots Social Studies Fun The Earth’s rotation about its own axis takes 24 hours. Time 85 Merged File_PPS_Maths_G4_TB_Part 1.indb 85 2/1/2017 3:09:48 PM

Science Fun A sundial is a tool that uses the position of the Sun to measure time, typically involving a shadow cast across a marked surface. A Note to Parent Help your child build his or her own sundial. Go outdoors with your family on a sunny afternoon. Explain your child how shadows are formed and how people in the olden days used to measure time using shadows. Drill Time Concept 6.1: Find the Duration 1) Read the times on the clocks and write them in 12-hour and 24-hour formats. a) b) c) d) e) 2) Find the duration of time from the given start time and end time. a) Start Time = 12:00 and End Time = 02:15 b) Start Time = 15:00 and End Time = 19:00 c) Start Time = 3:15 and End Time = 7:20 d) Start Time = 7:20 and End Time = 10:41 e) Start Time = 5:56 and End Time = 7:57 86 Merged File_PPS_Maths_G4_TB_Part 1.indb 86 2/1/2017 3:09:49 PM

Drill Time 3) Word problems a) Karthik started his running race at 8:20 a.m. and finished it at 8:45 a.m. For how long did he run? b) Shirish was eating his dinner when it was 10:36 in the clock. What is the time in 12-hour and 24-hour clock formats? Concept 6.2: Estimate Time 4) Word problems a) If Ram’s magic show begins at 5:56 p.m. and ends in 2 hours, at what time does his show end? b) Sunny’s karate class lasted for was 4 hours. If it ended at 8:20 p.m., when did it begin? Time 87 Merged File_PPS_Maths_G4_TB_Part 1.indb 87 2/1/2017 3:09:49 PM

D Divisionivision I Will Learn Concept 7.1: Divide Large Numbers Merged File_PPS_Maths_G4_TB_Part 1.indb 88 2/1/2017 3:09:50 PM

Concept 7.1: Divide Large Numbers I Think Surbhi and seven of her friends want to share 3540 papers equally among themselves. Do you think the papers can be divided without some being left over? To answer this question, we must know how to divide large numbers. 7.1 I Recall Recall that we can write two multiplication facts for a division fact. For example, a multiplication fact for 45 ÷ 9 = 5 can be written as 9 × 5 = 45 or 5 × 9 = 45. 45 ÷ 9 = 5 ↓ ↓ ↓ Dividend Divisor Quotient The number that is divided is called the dividend. The number that divides is called the divisor. The number of times the divisor divides the dividend is called the quotient. Factors Factors Multiplicand × Multiplier = Product Multiplicand × Multiplier = Product 9 × 5 = 45 5 × 9 = 45 ↓ ↓ ↓ ↓ ↓ ↓ Divisor Quotient Dividend Divisor Quotient Dividend Division 89 Merged File_PPS_Maths_G4_TB_Part 1.indb 89 2/1/2017 3:09:51 PM

The part of the dividend that remains without being divided is called the remainder. Let us solve the following to revise the concept of division. a) 72 ÷ 9 b) 42 ÷ 3 c) 120 ÷ 5 d) 80 ÷ 4 e) 24 ÷ 1 7.1 I Remember and Understand In class 3, we have learnt that division means equal sharing and equal grouping of things. Let us now understand the division of large numbers. Division and 1) Division of 4-digit numbers by 1-digit numbers multiplication are Dividing a 4-digit number by a 1-digit number is similar to reverse operations. that of a 3-digit number by a 1-digit number. Example 1: Divide: 2065 ÷ 5 Solution: Steps Solved Solve these Step 1: Check if the thousands ) digit of the dividend is greater 52065 than the divisor. If it is not, consider 2 is not greater than 7 ) 3748 the hundreds digit also. 5. So, consider 20. − Step 2: Find the largest number 4 in the multiplication table of the ) divisor that can be subtracted 52065 − from the 2-digit number of the -20 dividend. Write the quotient. Write the product of the quotient and 5 × 4 = 20 − divisor below the dividend. 5 × 5 = 25 25 > 20 Step 3: Subtract and write the Dividend = _____ difference. 4 5 ) 2065 Divisor = ______ -20 Quotient = ____ 0 Remainder = ___ 90 Merged File_PPS_Maths_G4_TB_Part 1.indb 90 2/1/2017 3:10:06 PM

Steps Solved Solve these Step 4: Check if difference < 0 < 5 (True) divisor is true. If it is false, the division is incorrect. 3 ) 2163 Step 5: Bring down the tens 4 − digit of the dividend and write it ) near the remainder. 5 2065 − 20 ↓ − 06 − Step 6: Find the largest number 5 × 1 = 5 in the multiplication table of the 5 × 2 = 10 divisor that can be subtracted 5 < 6 < 10 from the 2-digit number in the So, 5 is the required Dividend = _____ previous step. number. Divisor = ______ Step 7: Write the factor of the 4 1 required number, other than the 5 2 0 6 5 Quotient = ____ ) divisor, as the quotient. − 20 ↓ Remainder = ___ Write the product of the divisor 0 6 and the quotient below the 2-digit − 0 5 number. 0 1 Then subtract them. 5 ) 1555 Step 8: Repeat steps 6 and 7 till 1 < 5 (True) − all the digits of the dividend are 4 1 3 ) brought down. 5 2 0 6 5 Check if remainder < divisor is − 2 0 ↓ − true. 0 6 Stop the division. (If this is false, the − 0 5 division is incorrect.) 0 1 5 − −− 0 1 5 0 0 0 Dividend = _____ Step 9: Write the quotient and the Quotient = 413 remainder. Remainder = 0 Divisor = ______ Quotient = ____ Remainder = ___ Division 91 Merged File_PPS_Maths_G4_TB_Part 1.indb 91 2/1/2017 3:10:10 PM

Steps Solved Solve these Step 10: Check if (Divisor × 5 × 413 + 0 = 2065 Quotient) + Remainder = Dividend 2065 + 0 = 2065 is true. If this is false, the division is 2065 = 2065 (True) incorrect. 2) Division of 3-digit numbers by 2-digit numbers Let us understand the division of 3-digit numbers by 2-digit numbers, through some examples. Example 2: Divide: 414 ÷ 12 Solution: Steps Solved Solve these Step 1: Write the dividend and the divisor as shown. ) 12 414 ) DivisorDividend 14 324 ) Step 2: Guess the quotient by 12 414 − thinking of dividing 41 by 12. ) Find the multiplication fact which 12 × 3 = 36 has the number less than or equal 12 × 4 = 48 − to the dividend and the divisor. 36 < 41 < 48 So, 36 is the number to be subtracted from 41. Step 3: Write the factor other than Write 3 in the quotient Dividend = _____ the dividend and the divisor as and 36 below 41, and the quotient. subtract. Then bring Divisor = ______ down the next number in the dividend. Quotient = ____ 3 Remainder = ___ 12 ) 414 − 36↓ 054 92 Merged File_PPS_Maths_G4_TB_Part 1.indb 92 2/1/2017 3:10:15 PM

Steps Solved Solve these Step 4: Guess the quotient by 12 × 4 = 48 thinking of dividing 54 by 12. 12 × 5 = 60 Find the multiplication fact which 48 < 54 < 60 16 548 ) has the number less than or equal So, 48 is the number to to the dividend and divisor. Write be subtracted from 54. − the factor other than the dividend Write 4 in the quotient and the divisor as the quotient. and 48 below 54, and subtract. − 34 12 ) 414 − 36↓ Dividend = _____ 0 54 Divisor = ______ − 048 Quotient = ____ 6 Quotient = 34 Remainder = ___ Remainder = 6 Checking for the correctness of division: We can check whether our division is correct or not using a multiplication fact of the division. Step 1: Compare the remainder and the divisor. [Note: The remainder must always be less than the divisor.] Step 2: Check if (Quotient × Divisor) + Remainder = Dividend Let us now check if our division in example 2 is correct or not. Steps Checked Step 1: Remainder < Divisor Dividend = 414 Divisor = 12 Quotient = 34 Remainder = 6 6 < 12 (True) Step 2: (Quotient × Divisor) + 34 × 12 + 6 = 414 Remainder = Dividend 408 + 6 = 414 414 = 414 (True) Division 93 Merged File_PPS_Maths_G4_TB_Part 1.indb 93 2/1/2017 3:10:17 PM

Note: a) If remainder > divisor, the division is incorrect. b) If (Quotient × Divisor) + Remainder is not equal to Dividend, the division is incorrect. 3) Dividing a 4-digit number by a 2-digit number Dividing a 4-digit number by a 2-digit number is similar to dividing a 3-digit number by a 2-digit number. Let us understand this through the following example. Example 3: Divide: 2340 ÷ 15 Solution: Steps Solved Solve these Step 1: Check if the thousands 2 is not greater than 15. So, digit of the dividend is greater consider 23. than the divisor. If it is not, 12 ) 5088 consider the hundreds digit 15 ) 2340 − too. Step 2: Guess the quotient by 1 thinking of dividing 23 by 15 2340 − ) 15. − 15 Find the multiplication fact which has a number less than 15 × 1 = 15 − or equal to the dividend and 15 × 2 = 30 the divisor. 15 < 23 < 30 So, 15 is the required number. Dividend = _____ Step 3: Write the factor other Write 1 in the quotient and 15 than the dividend and the below 23, and subtract. Then Divisor = ______ divisor as the quotient. bring down the next number in Quotient = _____ the dividend. 1 Remainder = _____ 15 2340 ) − 15 ↓ 84 94 Merged File_PPS_Maths_G4_TB_Part 1.indb 94 2/1/2017 3:10:21 PM