INTEGRATED TEXTBOOK – Grade 3 Name: _________________________ Section: ________Roll No: _______ School: ________________________
English Contents Class 3 Term 1 R1 Reading Comprehension ������������������������������������������������������������������������������� 19 NR_BGM_9789388751957 MAPLE G01 INTEGRATED TEXTBOOK TERM 1_Text.pdf 4 1/7/2019 1:43:33 PM
R1 Reading Comprehension Passage 1 Read the passage and answer the questions given below. In Amalapuram lives a young shepherd named Ramu. He works for Mani, a farmer. Every morning, Ramu opens the gates of the pen (shed) with a bunch of keys. This is where the sheep are kept. He drives the flock of sheep into the forest where they eat grass. In the forest, Ramu is not alone. He has a dog to help him. ‘My work is impossible without Blackie’, he says. Blackie helps him to control the sheep. Blackie also guards Ramu and the sheep from wild animals. Blackie is a loyal and helpful dog. 1) Who lives in Amalapuram? Ans. 2) Who helps Ramu with his work? Ans. 3) Write the plural forms of the words given below. a) sheep − ________________________ b) key − ________________________ c) dog − ________________________ NR_BGM_9789386663191 MAPLE G03 INTEGRATED TEXTBOOK TERM 1_Text.pdf 23 19 1/7/2019 2:17:38 PM
4) Write the word from the passage that means ‘a large place covered by trees’. Ans. 5) Match the words with their correct meanings. Column A Column B 1) shepherd a) faithful 2) farmer b) a person who looks after sheep 3) loyal c) a person who takes care of a farm Passage 2 Read the passage and answer the questions given below. Once upon a time, a famine broke out in a kingdom. There was very little food. Every day, the children of the city went to a rich man’s house. They went there to get loaves of bread. As soon as the servants brought out the loaves, all the children used to fight to get the biggest loaf. One little girl never fought. She waited patiently for her turn. She always got the smallest loaf, right at the end. One day, as usual, she brought home the smallest loaf. When she cut it, she found two gold coins in it. She went back at once to return the money. The rich man was very pleased with her honesty. He gave her four gold coins as a reward. 1) Why would the children go to the rich man’s house every day? Ans. 2) What did the little girl find in her loaf one day? Ans. 20 NR_BGM_9789386663191 MAPLE G03 INTEGRATED TEXTBOOK TERM 1_Text.pdf 24 1/7/2019 2:17:38 PM
3) Punctuate the following sentences. a) the little girl went to the rich man’s house Ans. b) what are you doing with the small loaf of bread Ans. c) the girl bought a blue and green dress with a gold coin Ans. 4) Write the word from the passage that is the opposite of the word ‘punishment’. Ans. 5) Match the words with their correct meanings. Column A Column B 1) famine a) the quality of telling the truth 2) patiently b) extreme lack of food 3) honesty c) calmly; without anger Reading Comprehension 21 NR_BGM_9789386663191 MAPLE G03 INTEGRATED TEXTBOOK TERM 1_Text.pdf 25 1/7/2019 2:17:38 PM
Mathematics Contents Class 3 Term 1 3 Numbers 3.1 Count by Thousands ..............................................................................17 3.2 Compare 4-digit Numbers .....................................................................23 4 Addition 4.2 Add 3-digit and 4-digit Numbers ..........................................................34 5 Subtraction 5.2 Subtract 3-digit and 4-digit Numbers ...................................................47 NR_BGM_9789386663191 MAPLE G03 INTEGRATED TEXTBOOK TERM 1_Text.pdf 39 1/7/2019 2:17:39 PM
Chapter Numbers 3 Let Us Learn About • writing 4-digit numbers with place value chart. • identifying and forming the greatest and the smallest number. • writing the standard and the expanded forms of the number. • comparing and ordering numbers. Concept 3.1: Count by Thousands Think Farida went to buy one of the toy cars shown. She could not read the price on one of the cars. Can you read the price on ` 1937.00 both the cars and understand what they mean? ` 657.00 Recall We know that 10 ones make a ten. Similarly, 10 tens make a hundred. Let us now count by tens and hundreds as: Counting by 10s: 10, 20, 30, 40, 50, 60, 70, 80 and 90 Counting by 100s: 100, 200, 300, 400, 500, 600, 700, 800 and 900 17 1/7/2019 2:17:40 PM NR_BGM_9789386663191 MAPLE G03 INTEGRATED TEXTBOOK TERM 1_Text.pdf 56
When we multiply a digit by the value of its place, we get its place value. Using place values, we can write a number in its expanded form. Let us answer these to revise the concept. a) The number for two hundred and thirty-four is _____________. b) In 857, there are _______ hundreds, _______ tens and _______ ones. c) The expanded form of 444 is _______________________. d) The place value of 9 in 493 is _____________. e) The number name of 255 is _______________________________________. & Remembering and Understanding To know about 4-digit numbers, we count by thousands using boxes. Suppose shows 1. Ten such boxes show a 10. So, = 10 ones = 1 ten Similarly, 10 such strips show 10 tens or 1 hundred. = 10 tens = 1 hundred Numbers 18 NR_BGM_9789386663191 MAPLE G03 INTEGRATED TEXTBOOK TERM 1_Text.pdf 57 1/7/2019 2:17:40 PM
= 1 hundred = 100 = 2 hundreds = 200 = 3 hundreds = 300 = 4 hundreds = 400 In the same way, we get 5 hundreds = 500, 6 hundreds = 600, 7 hundreds = 700, 8 hundreds = 800 and 9 hundreds = 900. Using a spike abacus and beads of different colours, we represent 999 as shown. 9 blue, 9 green and 9 pink beads on the abacus represent 999. H TO Remove all the beads and Th H T O represent 999 put an orange bead on the represent 1000 next spike. This represents one thousand. We write it as 1000. 1000 is the smallest 4-digit number. Now, we know four places: ones, tens, hundreds and thousands. Let us represent 4732 in the place value chart. 19 1/7/2019 2:17:40 PM NR_BGM_9789386663191 MAPLE G03 INTEGRATED TEXTBOOK TERM 1_Text.pdf 58
Thousands (Th) Hundreds (H) Tens (T) Ones (O) 4 7 32 We count by 1000s as 1000 (one thousand), 2000 (two thousand)... till 9000 (nine thousand). The greatest 4-digit number is 9999. Expanded form of 4-digit numbers The form in which a number is written as the sum of the place values of its digits is called its expanded form. Let us now learn to write the expanded form of 4-digit numbers. Example 1: Expand the following numbers. a) 3746 b) 6307 Solution: Write the digits of the given numbers in the place value chart, as shown. Expanded forms: Th H TO a) 3746 = 3000 + 700 + 40 + 6 a) 3 7 46 b) 6307 = 6000 + 300 + 0 + 7 b) 6 3 0 7 Writing number names of 4-digit numbers Observe the expanded form and place value chart for a 4-digit number, 8015. Th H TO Place values 80 15 5 ones = 5 1 tens = 10 0 hundreds = 0 8 thousands = 8000 We can call 8015 as the standard form of the number. Let us look at an example. Example 2: Write the expanded forms and number names of these numbers. a) 1623 b) 3590 Numbers 20 NR_BGM_9789386663191 MAPLE G03 INTEGRATED TEXTBOOK TERM 1_Text.pdf 59 1/7/2019 2:17:40 PM
Solution: To expand the given numbers, write them in the correct places in the place value chart. Expanded forms: Th H T O a) 1623 = 1000 + 600 + 20 + 3 a) 1 6 2 3 b) 3590 = 3000 + 500 + 90 + 0 b) 3 5 9 0 Writing in words (Number names): a) 1623 = One thousand six hundred and twenty-three b) 3590 = Three thousand five hundred and ninety We can write the standard form of a number from its expanded form. Let us see an example. Example 3: Write the standard form of 3000 + 400 + 60 + 5. Solution: Write the numbers in the place value Th H T O chart in the correct places. Write the 3 46 5 digits one beside the other, starting from the thousands place. 3000 + 400 + 60 + 5 = 3465 So, the standard form of 3000 + 400 + 60 + 5 is written as 3465. 21 1/7/2019 2:17:40 PM NR_BGM_9789386663191 MAPLE G03 INTEGRATED TEXTBOOK TERM 1_Text.pdf 60
Concept 3.2: Compare 4-digit Numbers 1/7/2019 2:17:41 PM Think Farida has 3506 paper clips and her brother has 3605 paper clips. Farida wants to know who has more paper clips. But the numbers appear to be the same, and she is confused. Can you tell who has more number of paper clips? 23 NR_BGM_9789386663191 MAPLE G03 INTEGRATED TEXTBOOK TERM 1_Text.pdf 62
Recall In class 2, we have learnt to compare 3-digit numbers and 2-digit numbers. Let us quickly revise the concept. A 2-digit number is always greater than a 1-digit number. A 3-digit number is always greater than a 2-digit number and a 1-digit number. So, a number with more number of digits is always greater than a number with lesser digits. We use the symbols >, < or = to compare two numbers. & Remembering and Understanding Comparing two 4-digit numbers is similar to comparing two 3-digit numbers. Let us understand the steps to compare through an example. Example 9: Compare: 5382 and 5380 Solution: Follow these steps to compare the given numbers. Steps Solved Solve this Step 1: Compare the number of digits 5382 and 5380 7469 and 7478 Count the number of digits in the given numbers. The number having more number of digits is Both 5382 and greater. 5380 have 4 digits. Step 2: Compare thousands If two numbers have the same number of digits, 5=5 ____ = ____ compare the thousands digits. (If two numbers have an equal number of digits, start comparing 3=3 ____ = ____ from the leftmost digit.) The number with the greater digit in the thousands place is greater. Step 3: Compare hundreds If the digits in the thousands place are the same, compare the digits in the hundreds place. The number with the greater digit in the hundreds place is greater. Numbers 24 NR_BGM_9789386663191 MAPLE G03 INTEGRATED TEXTBOOK TERM 1_Text.pdf 63 1/7/2019 2:17:41 PM
Steps Solved Solve this 5382 and 5380 7469 and 7478 Step 4: Compare tens 8=8 ____ > ____ If the digits in the hundreds place are also same, So, compare the digits in the tens place. The number with the greater digit in the tens place is greater. ____ > ____ Step 5: Compare ones If the digits in the tens place are also the same, 2>0 compare the digits in the ones place. The So, - number with the greater digit in the ones place is greater. When the ones place are the same, the 5382 > 5380 numbers are equal. Note: Once we can decide a greater/smaller number, the steps that follow need not be carried out. 25 1/7/2019 2:17:41 PM NR_BGM_9789386663191 MAPLE G03 INTEGRATED TEXTBOOK TERM 1_Text.pdf 64
Concept 4.2: Add 3-digit and 4-digit Numbers Think Farida’s father bought her a shirt for ` 335 and a skirt for ` 806. Farida wants to find how much her father had spent in all. How do you think she can find that? Recall We can add 2-digit or 3-digit numbers by writing them one below the other. This method of addition is called vertical addition. Let us revise the earlier concept and solve the following. a) 22 + 31 = _________ b) 42 + 52 = _________ c) 82 + 11 = _________ d) 101 + 111 = _________ e) 100 + 200 = _________ f) 122 + 132 = _________ Addition 34 NR_BGM_9789386663191 MAPLE G03 INTEGRATED TEXTBOOK TERM 1_Text.pdf 73 1/7/2019 2:17:41 PM
& Remembering and Understanding Let us now understand the addition of two 3-digit numbers with regrouping. We will also learn to add two 4-digit numbers. Add 3-digit numbers with regrouping Sometimes, the sum of the digits in a place is more than 9. In such cases, we need to regroup the sum. We then carry forward the digit to the next place. Example 8: Add 245 and 578. Solution: Arrange the numbers one below the other. Regroup if the sum of the digits is more than 9. Step 1: Add the ones. Solved Step 3: Add the hundreds. H TO Step 2: Add the tens. H TO 1 11 245 H TO 245 11 +578 245 +578 3 +578 823 23 H TO Solve these H TO H TO 823 171 +197 390 +219 +121 Add 4-digit numbers without regrouping Adding two 4-digit numbers is similar to adding two 3-digit numbers. Let us understand this through an example. Example 9: Add 1352 and 3603. Solution: Arrange the numbers one below the other. 35 NR_BGM_9789386663191 MAPLE G03 INTEGRATED TEXTBOOK TERM 1_Text.pdf 74 1/7/2019 2:17:41 PM
Solved Step 1: Add the ones. Step 2: Add the tens. Th H T O Th H T O 135 2 135 2 +3 6 0 3 +3 6 0 3 5 55 Step 3: Add the hundreds. Step 4: Add the thousands. Th H T O Th H T O 135 2 13 5 2 +3 6 0 3 +3 6 0 3 955 49 5 5 Solve these Th H T O Th H T O Th H T O 41 9 0 20 0 2 11 1 1 +2 0 0 0 +3 0 0 3 +2 2 2 2 Add 4-digit numbers with regrouping We regroup the sum when it is equal to or more than 10. Example 10: Add 1456 and 1546. Solution: Arrange the numbers one below the other. Add and regroup, if necessary. Solved Step 1: Add the ones. Step 2: Add the tens. Th H T O Th H T O 1 11 1456 1456 +1 5 4 6 +1 5 4 6 2 02 Addition 36 NR_BGM_9789386663191 MAPLE G03 INTEGRATED TEXTBOOK TERM 1_Text.pdf 75 1/7/2019 2:17:41 PM
Solved Step 3: Add the hundreds. Step 4: Add the thousands. Th H T O Th H T O 111 111 1456 1456 +1 5 4 6 +1 5 4 6 002 3002 Th H T O Solve these O Th H T O Th H T 175 8 459 2 +5 6 6 2 267 8 +1 4 5 6 +1 3 3 2 37 1/7/2019 2:17:41 PM NR_BGM_9789386663191 MAPLE G03 INTEGRATED TEXTBOOK TERM 1_Text.pdf 76
Concept 5.2: Subtract 3-digit and 4-digit Numbers Think The given grid shows the number of men and women in Farida’s town in the years 2017 and 2018. Years 2017 2018 How can Farida find out how may more Men 2254 2187 men than women lived in her town in the Women 2041 2073 two years. Recall Recall that we can subtract numbers by writing the smaller number below the greater number. A 2-digit number can be subtracted from a larger 2-digit number or a 3-digit number. Similarly, a 3-digit number can be subtracted from a larger 3-digit number. Let us answer these to revise the concept. a) 15 – 0 = _________ b) 37 – 36 = _________ c) 93 – 93 = _________ f) 50 – 45 = _________ d) 18 – 5 = _________ e) 47 – 1 = _________ & Remembering and Understanding We have learnt how to subtract two 3-digit numbers without regrouping. Let us now learn how to subtract them with regrouping. Subtract 3-digit numbers with regrouping When a larger number is to be subtracted from a smaller number, we regroup the next higher place and borrow. And, we always start subtracting from the ones place. Let us understand this with an example. Example 6: Subtract 427 from 586. Solution: To subtract, write the smaller number below the larger number. 47 1/7/2019 2:17:42 PM NR_BGM_9789386663191 MAPLE G03 INTEGRATED TEXTBOOK TERM 1_Text.pdf 86
Step 1: Subtract the ones. But, 6 – 7 is Solved Step 3: Subtract the not possible as 6 < 7. So, regroup the hundreds. digits in the tens place. Step 2: Subtract the tens. 8 tens = 7 tens + 1 tens. Borrow 1 ten to the ones place. Reduce the tens by 1 ten. Now subtract 7 ones from 16 ones. H TO H TO H TO 7 16 7 16 5 5 7 16 –4 8\\ 6\\ 5 \\8 \\6 –4 \\8 \\6 27 –4 2 7 1 9 59 27 59 H TO Solve these H TO H TO 6 23 5 52 4 53 – 3 76 – 2 63 – 2 64 Subtract 4-digit numbers without regrouping Subtracting a 4-digit number from a larger 4-digit number is similar to subtracting a 3-digit number from a larger 3-digit number. The following examples help you understand this better. Example 7: Subtract: 5032 from 7689 Solution: To subtract, write the smaller number below the larger number. Step 1: Subtract the ones. Solved Step 2: Subtract the tens. Th H T O O 76 8 9 Th H T 9 −50 3 2 768 2 7 −503 7 5 Subtraction 48 NR_BGM_9789386663191 MAPLE G03 INTEGRATED TEXTBOOK TERM 1_Text.pdf 87 1/7/2019 2:17:42 PM
Step 3: Subtract the hundreds. Step 4: Subtract the thousands. Th H T O Th H T O 7689 7 68 9 −5032 − 5 03 2 2 65 7 657 Th H T O Solve these Th H T O 2879 8000 –2137 Th H T O –2000 4789 –2475 Subtract 4-digit numbers with regrouping In subtraction of 4-digit numbers, we can regroup the digits in thousands, hundreds and tens places. Let us see an example. Example 8: What is the difference 7437 and 4868? Solution: Write the smaller number below the larger number. Steps Solved Solve these Step 1: Subtract the ones. Th H T O Th H T O But, 7 − 8 is not possible as 1654 74 2 17 −1 2 4 6 7 < 8. So, regroup the tens digit, −4 8 3. 3 tens = 2 tens + 1 ten. Borrow 3\\ \\7 1 ten to the ones place. 6 8 9 Step 2: Subtract the tens. But, Th H TO 12 2 − 6 is not possible as 2 < 6. 7 So, regroup the hundreds digit, −4 3 \\2 17 4. 4 hundreds = 3 hundreds + 4\\ 3\\ \\7 1 hundred. Borrow 1 hundred to 868 the tens place. 69 49 1/7/2019 2:17:42 PM NR_BGM_9789386663191 MAPLE G03 INTEGRATED TEXTBOOK TERM 1_Text.pdf 88
Step 3: Subtract the hundreds. Th H T O Th H T O But, 3 − 8 is not possible. So, 13 12 regroup the thousands digit, 5674 7. 7 thousands = 6 thousands + 6 \\3 \\2 17 −2 3 8 2 1 thousand. Borrow 1 thousand to the hundreds place. \\7 4\\ 3\\ \\7 −4 8 6 8 569 Step 4: Subtract the thousands. Th H T O Th H T O 13 12 7468 6 \\3 \\2 17 −4 8 3 7 \\7 4\\ 3\\ \\7 −4 8 6 8 2569 Subtraction 50 NR_BGM_9789386663191 MAPLE G03 INTEGRATED TEXTBOOK TERM 1_Text.pdf 89 1/7/2019 2:17:42 PM
English Contents Class 3 Term 2 R2 Reading Comprehension ................................................................................. 9 R3 Reading Comprehension ������������������������������������������������������������������������������� 28 NR_BGM_9789388751957 MAPLE G01 INTEGRATED TEXTBOOK TERM 1_Text.pdf 4 1/7/2019 1:43:33 PM
R2 Reading Comprehension Passage 1 Read the passage and answer the questions given below. I saw a potter at a fair. He was making pots with clay. The clay was soft and felt very cool. He had a wheel in front of him that went round and round. He made the pots by placing the clay on the wheel and shaping it with his hands. Then, he placed the pots over a fire and made them hard and strong. I tried making a pot too. It was very exciting to see the clay change form and become something different. The potter gave me a pot to take home. I painted the pot in bright colours. 1) What did the potter use for making pots? Ans. 2) How did the potter make the pots hard and strong? Ans. 3) Change the tense of the given sentences according to the instructions given in brackets. a) I saw a potter. (change to simple future tense) Ans. NR_BGM_9789386663207 MAPLE G03 INTEGRATED TEXTBOOK TERM 2_Text.pdf 11 9 1/7/2019 2:26:04 PM
b) He was making clay pots. (change to present continuous tense) Ans. c) I painted the pot in bright colours. (change to simple present tense) Ans. 4) Write one word from the passage that rhymes with the word ‘got’. Ans. 5) Match the words with their correct meanings. Column A Column B 1) potter a) shiny and cheerful 2) exciting b) a person who makes objects with clay 3) bright c) interesting or thrilling Passage 2 Read the passage and answer the questions given below. A heron lived by the side of a pond that was full of fish. The greedy heron wanted to eat all the fish. So, it told a lie that some fishers were coming to catch the fish. To save the fish, he offered to fly them to another pond. He caught the fish in his mouth. Before he reached the other pond, he ate all of them. One day, a crab climbed into his mouth. The crab realised that something was wrong. He caught the heron’s neck between his claws. He did not let go until the heron promised not to be greedy ever again. ─ Adapted from a Panchatantra story 10 1/7/2019 2:26:04 PM NR_BGM_9789386663207 MAPLE G03 INTEGRATED TEXTBOOK TERM 2_Text.pdf 12
1) Who lived by the side of the pond? Ans. 2) What did the heron offer to do for the fish? Ans. 3) Fill in the blanks with the correct words given in brackets. a) The pond ________________________ a lot of fish. (had/have) b) A fisher ________________________ come to the pond. (has/have) c) The crab and the fish ______________________ left the pond now. (has/have) 4) Which word from the passage is the opposite of the word ‘right’? Ans. 5) Match the words with their correct meanings. Column A Column B 1) heron a) wanting more always 2) greedy b) understood clearly 3) realised c) a large, fish-eating bird with long legs Reading Comprehension 11 NR_BGM_9789386663207 MAPLE G03 INTEGRATED TEXTBOOK TERM 2_Text.pdf 13 1/7/2019 2:26:04 PM
R3 Reading Comprehension Passage 1 Read the passage and answer the questions given below. Once, there lived a blind man in a small town. He carried a lighted lamp in his hand whenever he went out at night. One night, a group of men were walking on the same path. They saw the blind man and made fun of him. They said, ‘O blind man, why do you carry the lamp? You are blind and cannot see anything.’ The blind man politely said, ‘This lamp is not for me but for those who have eyes. You may not see a blind man in your path and may collide with him.’ Upon hearing this, the men felt ashamed and asked for forgiveness. 1) What did the blind man carry when he went out at night? Ans. 2) What did the group of men do when they saw the blind man? Ans. 3) Fill in the blanks with the correct articles (‘a’, ‘an’, ‘the’ ). a) The blind man took ____________ hour to finish his work. b) Bring me _______________ lamp that the blind man is carrying. 28 1/7/2019 2:26:06 PM NR_BGM_9789386663207 MAPLE G03 INTEGRATED TEXTBOOK TERM 2_Text.pdf 30
c) There is _____________ blind man walking in the street. 4) What is an antonym of ‘polite’? Ans. 5) Match the words with their correct meanings. Column A Column B 1) polite a) crash into someone or something 2) ashamed b) well mannered 3) collide c) felt sorry about an action Passage 2 Read the passage and answer the questions given below. Raju was a naughty boy. He enjoyed telling lies. His father told him that lying was a bad habit. But Raju did not stop making up stories. One day, he came running and shouted, ‘Please save me. There is a tiger here.’ All the villagers ran to help him. Raju laughed and said, ‘I tricked you. There is no tiger.’ The villagers were very angry with Raju. After a few days, Raju played the same trick again on the villagers. This time, they decided not to be fooled by him anymore. One day, when Raju was alone, he actually saw a tiger. He shouted for help. However, the villagers thought it was a joke and did not believe him. The tiger attacked Raju. Moral: One should never tell lies and trouble others. 1) What did Raju enjoy doing? Ans. Reading Comprehension 29 NR_BGM_9789386663207 MAPLE G03 INTEGRATED TEXTBOOK TERM 2_Text.pdf 31 1/7/2019 2:26:06 PM
2) What did the villagers decide after Raju tricked them? Ans. 3) Fill in the blanks with the correct words. a) ________________ is Raju. (This/Those) b) ________________ tiger attacked Raju. (These/That) c) ________________ villagers saved Raju. (That/These) 4) Write a word from the passage that is the opposite of the word ‘cried’. Ans. 5) Match the words with their correct meanings. Column A Column B 1) habit a) people who stay in a village 2) tricked b) something that we do a lot 3) villagers c) fooled 30 1/7/2019 2:26:06 PM NR_BGM_9789386663207 MAPLE G03 INTEGRATED TEXTBOOK TERM 2_Text.pdf 32
Mathematics Contents Class Term 2 3 6 Multiplication 1 5 6.1 Multiply 2-digit Numbers 6.2 Multiply 3-digit Numbers by 1-digit and 2-digit Numbers 26 32 8 Division 8.1 Division as Equal Grouping 8.2 Divide 2-digit and 3-digit Numbers by 1-digit Numbers NR_BGM_9789386663207 MAPLE G03 INTEGRATED TEXTBOOK TERM 2_Text.pdf 35 1/7/2019 2:26:06 PM
Chapter Multiplication 6 Let Us Learn About • using repeated addition to construct multiplication tables. • multiplying 2-digit numbers with and without regrouping. • doubling the numbers mentally. Concept 6.1: Multiply 2-digit Numbers Think Farida bought 2 boxes of toffees to distribute among her classmates on her birthday. Each box has 25 toffees inside it. If there are 54 students in her class, do you think she has enough toffees? Recall In Class 2, we have learnt that multiplication is repeated addition. The symbol ‘×’ indicates multiplication. Multiplication means having a certain number of groups of the same size. 1 1/7/2019 2:26:06 PM NR_BGM_9789386663207 MAPLE G03 INTEGRATED TEXTBOOK TERM 2_Text.pdf 36
Let us recall the multiplication tables of numbers from 1 to 6. 1 2 3 1×1=1 2×1=2 3×1=3 1×2=2 2×2=4 3×2=6 1×3=3 2×3=6 3×3=9 1×4=4 2×4=8 3 × 4 = 12 1×5=5 2 × 5 = 10 3 × 5 = 15 1×6=6 2 × 6 = 12 3 × 6 = 18 1×7=7 2 × 7 = 14 3 × 7 = 21 1×8=8 2 × 8 = 16 3 × 8 = 24 1×9=9 2 × 9 = 18 3 × 9 = 27 1 × 10 = 10 2 × 10 = 20 3 × 10 = 30 4 5 6 4×1=4 5×1=5 6×1=6 4×2=8 5 × 2 = 10 6 × 2 = 12 4 × 3 = 12 5 × 3 = 15 6 × 3 = 18 4 × 4 = 16 5 × 4 = 20 6 × 4 = 24 4 × 5 = 20 5 × 5 = 25 6 × 5 = 30 4 × 6 = 24 5 × 6 = 30 6 × 6 = 36 4 × 7 = 28 5 × 7 = 35 6 × 7 = 42 4 × 8 = 32 5 × 8 = 40 6 × 8 = 48 4 × 9 = 36 5 × 9 = 45 6 × 9 = 54 4 × 10 = 40 5 × 10 = 50 6 × 10 = 60 Let us now construct multiplication tables of 7, 8 and 9. We can then learn to multiply 2-digit numbers. & Remembering and Understanding In multiplication of two numbers: • The number written to the left of the ‘×’ sign is called the multiplicand. • The number written to the right of the ‘×’ sign is called the multiplier. • The number written to the right of the ‘=’ sign is called the product. Multiplication 2 NR_BGM_9789386663207 MAPLE G03 INTEGRATED TEXTBOOK TERM 2_Text.pdf 37 1/7/2019 2:26:06 PM
Multiplication Fact ↓↓ ↓ Multiplicand Multiplier Product Note: (a) Representing the multiplicand, multiplier and product using the symbols ‘×’ and ‘=’ is called a multiplication fact. (b) The multiplicand and the multiplier are also called the factors of the product. (c) The product is also called the multiple of both the multiplicand and the multiplier. For example, 2 × 7 = 14 = 7 × 2; 4 × 5 = 20 = 5 × 4 and so on. Order Property: Changing the order in which the numbers are multiplied does not change the product. This is called order property of multiplication. Using multiplication facts and order property, let us now construct the multiplication tables of 7, 8 and 9. 7 8 9 7×1=7 8×1=8 9×1=9 7 × 2 = 14 8 × 2 = 16 9 × 2 = 18 7 × 3 = 21 8 × 3 = 24 9 × 3 = 27 7 × 4 = 28 8 × 4 = 32 9 × 4 = 36 7 × 5 = 35 8 × 5 = 40 9 × 5 = 45 7 × 6 = 42 8 × 6 = 48 9 × 6 = 54 7 × 7 = 49 8 × 7 = 56 9 × 7 = 63 7 × 8 = 56 8 × 8 = 64 9 × 8 = 72 7 × 9 = 63 8 × 9 = 72 9 × 9 = 81 7 × 10 = 70 8 × 10 = 80 9 × 10 = 90 Multiply 2-digit numbers by 1-digit numbers Now, let us learn to multiply a 2-digit number by a 1-digit number. Consider the following example. 3 1/7/2019 2:26:06 PM NR_BGM_9789386663207 MAPLE G03 INTEGRATED TEXTBOOK TERM 2_Text.pdf 38
Example 1: Find the product: 23 × 7 Solution: Follow these steps to find the product. Steps Solved Solve these Step 1: Multiply the ones. 3 × 7 = 21 H TO Step 2: Regroup the product. 21 ones = 2 tens and 1 ones 17 Step 3: Write the ones digit of ×9 the product in the product TO and carry over the tens digit 2 H TO to the tens place. 23 15 ×7 ×4 Step 4: Multiply the tens. Step 5: Add the carry over 1 from step 3 to the product. Step 6: Write the sum in the 2 × 7 = 14 tens place. 14 + 2 = 16 H TO 2 23 ×7 161 Multiplication 4 NR_BGM_9789386663207 MAPLE G03 INTEGRATED TEXTBOOK TERM 2_Text.pdf 39 1/7/2019 2:26:06 PM
Concept 6.2: Multiply 3-digit Numbers by 1-digit and 2-digit Numbers Think Farida collected some shells and put them into 9 bags. If each bag has 110 shells, how many shells did she collect? Recall We have learnt to multiply a 2-digit number with a 1-digit number. We have also learnt to regroup the ones in multiplication. 5 1/7/2019 2:26:06 PM NR_BGM_9789386663207 MAPLE G03 INTEGRATED TEXTBOOK TERM 2_Text.pdf 40
Let us answer these to revise the concept. a) 22 × 2 = _________ d) 33 × 4 = _________ b) 42 × 1 = _________ e) 50 × 2 = _________ c) 11 × 7 = _________ f) 45 × 3 = _________ & Remembering and Understanding We multiply 3-digit numbers just as we multiply 2-digit numbers. Multiply 3-digit numbers by 1-digit numbers without regrouping Let us understand the step-by-step procedure through a few examples. Example 6: Multiply: 401 × 3 Solution: Follow these steps to multiply the given numbers. Step 1: Multiply the ones Solved Step 3: Multiply the hundreds Step 2: Multiply the tens H TO Th H T O 401 H TO 401 401 ×3 ×3 3 ×3 1203 03 H TO Solve these H TO 220 232 HTO ×4 13 0 ×3 ×2 Multiply 3-digit numbers by 1-digit numbers with regrouping We always start multiplying the ones of the multiplicand by the ones of the multiplier. When a 3-digit number is multiplied by a 1-digit number, we may get a 2-digit product in any or all of the places. We regroup these products and carry over the tens digit of the product to the next place. Let us understand this better through an example. Multiplication 6 NR_BGM_9789386663207 MAPLE G03 INTEGRATED TEXTBOOK TERM 2_Text.pdf 41 1/7/2019 2:26:06 PM
Example 7: Multiply: 513 × 5 Solution: Follow these steps to multiply the given numbers. Steps Solved Solve these H TO Step 1: Multiply the ones and write the H TO product under ones. Regroup if the 444 product has two or more digits. 1 3 ×8 5 51 5 × Step 2: Multiply the tens. Add the carry H TO H TO over (if any) to the product. Write the sum under tens. 1 342 ×5 Regroup if the product has two or more 513 digits. ×5 65 Step 3: Multiply the hundreds. Add the Th H T O H TO carry over (if any) to the product and write the sum under hundreds. Regroup if 1 635 the product has two or more digits. ×7 513 ×5 2 565 Multiply 3-digit numbers by 2-digit numbers Multiplication of 3-digit numbers by 2-digit numbers may sometimes involve regrouping too. Let us understand this concept through step-by-step procedure. Consider the following examples. Example 8: Multiply: 243 × 34 Solution: Follow these steps to multiply the given numbers. 7 1/7/2019 2:26:06 PM NR_BGM_9789386663207 MAPLE G03 INTEGRATED TEXTBOOK TERM 2_Text.pdf 42
Steps Solved Solve these Step 1: Arrange the numbers in columns, H TO as shown. H TO 141 243 ×22 Step 2: Multiply the ones of the ×34 multiplicand by the ones digit of the H TO multiplier. 3 × 4 = 12 H TO 1 453 Write 2 in the ones place of the product. ×13 Write 1 in the tens place as the carry over. 243 ×34 H TO Step 3: Multiply the tens by the ones digit of the multiplier. 4 × 4 = 16 2 263 ×23 Add the carry over from the previous H TO step. So, 16 + 1 = 17. Write 7 in the tens 11 place of the product and 1 in the 243 hundreds place as the carry over. ×34 Step 4: Multiply the hundreds by the ones digit of the multiplier. 2 × 4 = 8 72 Add the carry over from the previous H TO step. So, 8 + 1 = 9. Write 9 in the hundreds 11 place of the product. 243 ×34 Step 5: Write 0 in the ones place. 972 Multiply the ones of the multiplicand by HTO the tens digit of the multiplier. Write the 11 product under the tens place. 243 ×3 4 3×3=9 972 Step 6: Multiply the tens by the tens digit 90 of the multiplier. H TO 4 × 3 = 12 1 Write 2 in the hundreds place of the 11 product and 1 in hundreds place of the 243 multiplicand as the carry over. ×34 972 290 Multiplication 8 NR_BGM_9789386663207 MAPLE G03 INTEGRATED TEXTBOOK TERM 2_Text.pdf 43 1/7/2019 2:26:06 PM
Steps Solved Solve these Step 7: Multiply the hundreds by the tens digit of the multiplier. Th H T O H TO 2×3=6 Add the carry over from the previous 1 352 step. So, 6 + 1 = 7. Write 7 in the thousands ×23 place of the multiplicand. 11 243 Step 8: Add the products and write the ×34 sum. The sum is the required product. 972 7290 Th H T O 1 11 243 ×34 972 7290 8262 9 1/7/2019 2:26:07 PM NR_BGM_9789386663207 MAPLE G03 INTEGRATED TEXTBOOK TERM 2_Text.pdf 44
Chapter Division 8 Let Us Learn About • equal grouping and sharing. • repeated subtraction and division facts. • dividing 2-digit number by 1-digit number. • checking the correctness of division. Concept 8.1: Division as Equal Grouping Think Farida and Piyush got a chocolate bar with 14 pieces for Christmas. Piyush divided it and gave Farida 6 pieces. Do you think Farida got an equal share? How can we find out? Recall In the previous chapter, we have learnt multiplication. Multiplication is finding the total number of objects that have been grouped equally. Let us use this to distribute objects equally in groups. Consider 12 bars of chocolate. The different ways in which they can be distributed are as follows. NR_BGM_9789386663207 MAPLE G03 INTEGRATED TEXTBOOK TERM 2_Text.pdf 61 26 1/7/2019 2:26:07 PM
Distributing in 1 group: 1 × 12 = 12 Distributing in 2 groups: 2 × 6 = 12 Distributing in 3 groups: 3 × 4 = 12 Distributing in 4 groups: 4 × 3 = 12 Distributing in 6 groups: 6 × 2 = 12 Distributing in 12 groups: 12 × 1 = 12 Distributing a given number of objects into equal groups is called division. We can understand division better by using equal sharing and equal grouping. & Remembering and Understanding Equal sharing means having equal number of objects or things in a group. We use division to find the number of things in a group and the number of groups. 27 1/7/2019 2:26:07 PM NR_BGM_9789386663207 MAPLE G03 INTEGRATED TEXTBOOK TERM 2_Text.pdf 62
Suppose 9 balloons are to be shared 1st round: 1 balloon is taken by each equally among 3 friends. Let us use friend. repeated subtraction to distribute the balloons. 9 – 3 = 6. So, 6 balloons remain. 2nd round: From the remaining 6 balloons, 3rd round: From the remaining 3 balloons, 1 more balloon is taken by each friend. 1 more balloon is taken by each friend. Now, each friend has 2 balloons. Now, each of them has 3 balloons. 6 – 3 = 3. So, 3 balloons remain. 3 – 3 = 0. So, 0 balloons remain. Each friend gets 3 balloons. We can write it as 9 divided by 3 equals 3. 9 divided by 3 equals 3 is written as ↓ ↓ ↓ Total Number of Number of number of objects in each groups objects group Quotient Dividend Divisor Division 28 NR_BGM_9789386663207 MAPLE G03 INTEGRATED TEXTBOOK TERM 2_Text.pdf 63 1/7/2019 2:26:07 PM
In a division, the number that is divided is called the dividend. The number that divides is called the divisor. The answer in division is called the quotient. The number (part of the dividend) that remains is called the remainder. The symbol for ‘is divided by’ is ÷. 9 ÷ 3 = 3 is called a division fact. In this, 9 is the dividend, 3 is the divisor and 3 is the quotient. Note: Representing the dividend, divisor and quotient using the symbols ÷ and = is called a division fact. We use multiplication tables to find the quotient in a division. We find the factor which when multiplied by the divisor gives the dividend. Let us understand this through a few examples. Example 1: 18 pens are to be shared equally by 3 children. How many pens does each of them get? Solution: Total number of pens = 18 Number of children = 3 Number of pens each child gets = 18 ÷ 3 = 6 (since 6 × 3 = 18) Therefore, each child gets 6 pens. Example 2: 10 flowers are put in some vases. If each vase has 2 flowers, how many vases are used? Solution: Number of flowers = 10 Number of flowers in each vase = 2 Number of vases used = 10 ÷ 2 = 5 (since 5 × 2 = 10) Therefore, 5 vases are used to put 10 flowers. We get two division facts from a multiplication fact. The divisor and the quotient are the factors of the dividend. 29 1/7/2019 2:26:07 PM NR_BGM_9789386663207 MAPLE G03 INTEGRATED TEXTBOOK TERM 2_Text.pdf 64
Observe the following table: Dividend ÷ Divisor = Quotient Multiplicand × Multiplier = Product 6 × 3 = 18 18 ÷ 6 = 3 ↓↓ ↓ ↓↓ ↓ Divisor Quotient Dividend Product Factor Factor (Multiplicand) (Multiplier) From the multiplication fact 6 × 3 = 18, we can write two division facts: a) 18 ÷ 3 = 6 and b) 18 ÷ 6 = 3 Multiplication and division are reverse operations. Let us now understand this through an activity. We can show a multiplication fact on the number line. For example, 5 × 3 = 15 means 5 times 3 is 15. To show 5 times 3 on the number line, we take steps of 3 for 5 times. We go forward from 0 to 15. Similarly, we can show the division fact 15 ÷ 3 = 5 on the number line. To show 15 divided by 3 on the number line, we take steps of 3 for 5 times. We go backward from 15 to 0 as shown. Division 30 NR_BGM_9789386663207 MAPLE G03 INTEGRATED TEXTBOOK TERM 2_Text.pdf 65 1/7/2019 2:26:07 PM
Concept 8.2: Divide 2-digit and 3-digit Numbers by 1-digit Numbers Think Farida has 732 stickers. She wants to distribute them equally among her three friends. How will she distribute? Recall In the previous section, we have learnt that division is related to multiplication. For every division fact, we can write two multiplication facts. For example, the two multiplication facts of 35 ÷ 7 = 5 are: a) 7 × 5 = 35 and b) 5 × 7 = 35. Let us answer these to recall the concept of division. a) The number which divides a given number is called _________________. b) T he answer we get when we divide a number by another is called ______________________. c) T he division facts for the multiplication fact 2 × 4 = 8 are ________________ and __________________. Division 32 NR_BGM_9789386663207 MAPLE G03 INTEGRATED TEXTBOOK TERM 2_Text.pdf 67 1/7/2019 2:26:07 PM
& Remembering and Understanding We can make equal shares or groups and divide with the help of vertical arrangement. A number divided by the same number is always 1. Let us see some examples. D ividing a 2-digit number by a 1-digit number (1-digit quotient) Example 7: Solve: 45 ÷ 5 Solution: Follow these steps to divide a 2-digit number by a 1-digit number. Steps Solved Solve these Step 1: Write the dividend and 5)45 Dividend = _____ Divisor = ______ )divisor as shown: Divisor Dividend Quotient = ____ Remainder = _____ Step 2: Find the multiplication fact 45 = 5 × 9 8) 56 which has the dividend and divisor. - Step 3: Write the other factor as the 9 quotient. Write the product of the factors below the dividend. 5)45 − 45 Step 4: Subtract the product 9 4) 36 Dividend = _____ from the dividend and write the Divisor = ______ difference below the product. 5)45 - Quotient = ____ This difference is called the Remainder = _____ remainder. − 45 00 45 = Dividend 5 = Divisor 9 = Quotient 0 = Remainder Note: If the remainder is zero, the divisor is said to divide the dividend exactly. Checking for correctness of division: The multiplication fact of the division is used to check its correctness. Step 1: Compare the remainder and divisor. The remainder must always be less than the divisor. 33 1/7/2019 2:26:07 PM NR_BGM_9789386663207 MAPLE G03 INTEGRATED TEXTBOOK TERM 2_Text.pdf 68
Step 2: Check if (Quotient × Divisor) + Remainder = Dividend Let us now check if our division in example 7 is correct or not. Step 1: Remainder < Divisor 0 < 5 (True) Step 2: Quotient × Divisor 9×5 Step 3: (Quotient × Divisor) + Remainder = Dividend 45 + 0 = 45 = Dividend Note: The division is incorrect if: a) Remainder > or = divisor b) (Quotient × Divisor) + Remainder ≠ Dividend 2-digit quotient In the examples we have seen so far, the quotients are 1-digit numbers. In some divisions, the quotients may be 2-digit numbers. Let us see some examples. Example 8: Solve: 57 ÷ 3 Solution: Follow these steps to divide a 2-digit number by a 1-digit number. Steps Solved Solve these Step 1: Check if the tens digit of the dividend is greater than the divisor. 5>3 5) 60 Step 2: Divide the tens and write the quotient. 1 − Write the product of quotient and divisor, below the tens digit of the dividend. 3)57 − Step 3: Subtract and write the difference −3 Step 4: Check if difference < divisor is true. 1 Dividend = _____ Divisor = ______ 3)57 Quotient = ____ Remainder = ___ −3 2 2 < 3 (True) Division 34 NR_BGM_9789386663207 MAPLE G03 INTEGRATED TEXTBOOK TERM 2_Text.pdf 69 1/7/2019 2:26:07 PM
Steps Solved Solve these Step 5: Bring down the ones digit of the 1 3) 42 dividend and write it beside the remainder. 3)57 − − − 3↓ 27 Step 6: Find the largest number in the 3 × 8 = 24 1 multiplication table of the divisor that can be subtracted from the 2-digit number in )3 × 9 = 27 3 57 the previous step. 3 × 10 = 30 24 < 27 < 30. − 3↓ So, 27 is the 27 required number. Step 7: Write the factor of required number, 19 Dividend = _____ other than the divisor, as the quotient. Write Divisor = ______ the product of the divisor and the quotient 3)57 Quotient = ____ below the 2-digit number. Subtract and Remainder = ___ write the difference. − 3↓ 27 Step 8: Check if remainder < divisor is true. Stop the division. − 27 00 0 < 3 (True) (If this is false, the division is incorrect.) QReumotaieinndte=Trr1=a90in My Brain Step 9: Write the quotient and the remainder. Step 10: Check if (Divisor × Quotient) + 3 × 19 + 0 = 57 Remainder = Dividend is true. 57 + 0 = 57 57 = 57 (True) (If this is false, the division is incorrect.) Divide 3-digit numbers by 1-digit numbers (2-digit quotient) Dividing a 3-digit number by a 1-digit number is similar to dividing a 2-digit number by a 1-digit number. Let us understand this through a few examples. Example 9: Solve: a) 265 ÷ 5 Solution: Follow these steps to divide a 3-digit number by a 1-digit number. 35 1/7/2019 2:26:08 PM NR_BGM_9789386663207 MAPLE G03 INTEGRATED TEXTBOOK TERM 2_Text.pdf 70
Steps Solved Solve these Step 1: Check if the hundreds digit of 4) 244 the dividend is greater than the divisor. 5)265 − If it is not, consider the tens digit too. 2 is not greater than 5. So, consider 26. Step 2: Find the largest number that 5 − can be subtracted from the 2-digit number of the dividend. Write the 5)265 Dividend = _____ quotient. Divisor = ______ − 25 Quotient = ____ Remainder = ___ Write the product of the quotient and 5 × 4 = 20 the divisor below the dividend. 5 × 5 = 25 9) 378 5 × 6 = 30 Step 3: Subtract and write the − difference. 25 < 26 − 5 5)265 − 25 1 Step 4: Check if difference < divisor 1 < 5 (True) is true. (If it is false, the division is incorrect.) Step 5: Bring down the ones digit 5 of the dividend. Write it beside the remainder. 5)265 Step 6: Find the largest number in the − 25↓ multiplication table of the divisor that 15 can be subtracted from the 2-digit number in the previous step. 5 5)265 − 25↓ 15 5 × 2 = 10 5 × 3 = 15 5 × 4 = 20 15 is the required number. Division 36 NR_BGM_9789386663207 MAPLE G03 INTEGRATED TEXTBOOK TERM 2_Text.pdf 71 1/7/2019 2:26:08 PM
Steps Solved Solve these Step 7: Write the factor of required 53 number, other than the divisor, as Dividend = _____ quotient. Write the product of divisor 5)265 Divisor = ______ and quotient below the 2-digit Quotient = ____ number. Then, subtract them. − 25↓ Remainder = ___ 15 Step 8: Check if remainder < divisor is true. Stop the division. (If this is false, − 15 the division is incorrect.) 00 0 < 5 (True) Step 9: Write the quotient and Quotient = 53 remainder. Remainder = 0 Step 10: Check if (Divisor × Quotient) + 5 × 53 + 0 = 265 Remainder = Dividend is true. (If this is 265 + 0 = 265 false, the division is incorrect.) 265 = 265 (True) 3-digit quotient Example 10: Solve: 784 by 7 Solution: Follow these steps to divide a 3-digit number by a 1-digit number. Steps Solved Solve these Step 1: Check if the hundreds digit of the dividend is greater than or equal to the 7)784 8) 984 divisor. Step 2: Divide the hundreds and write the 7=7 − quotient in the hundreds place. 1 − Write the product of the quotient and the divisor under the hundreds place of the 7)784 − dividend. −7 37 1/7/2019 2:26:08 PM NR_BGM_9789386663207 MAPLE G03 INTEGRATED TEXTBOOK TERM 2_Text.pdf 72
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