MAGNOLIA-STUDENT-TEXTBOOK-MATHEMATICS-G02-Combine

MATHEMATICS TEXTBOOK 2 Name: ___________________________________ Section: ________________ Roll No.: _________ School: __________________________________

Part 1 3 Numbers 3.1 Count by Hundreds .................................................................................... 18 3.3 Compare 3-digit Numbers ........................................................................ 31 0 74 Addition +4.1 Add 2-digit and 3-digit Numbers.............................................................. 38 3 416 -x5 Subtraction 9 55.1 Subtract 2-digit and 3-digit Numbers....................................................... 44 82

Chapter Numbers 3 Let Us Learn About • reading and writing numerals and number names up to 999. • p lace values, face values and expanded forms of numbers. • ordinal and cardinal numbers. • comparing two numbers. • forming the greatest and the smallest 3-digit numbers. Concept 3.1: Count by Hundreds Think David went to a toy store. He saw that ` 990 was `990 written on a toy. He could not read the number. Can you read it? Recall We know that 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 are 1-digit numbers. Numbers from 10 to 99 are 2-digit numbers. 10 is the smallest 2-digit number. 99 is the largest 2-digit number. We can count 2-digit numbers by ones and tens. 18

Look at the following picture. Start from 1 and connect all the dots in order. You will find a friend smiling back at you. & Remembering and Understanding Suppose shows 1. Ten such boxes show a 10. So, = 10 ones Numbers 19

= 1 ten Similarly, 10 such strips show 10 tens or 1 hundred. = 10 tens = 1 hundred = 1 hundred = 100 = 2 hundreds = 200 = 3 hundreds = 300 = 4 hundreds = 400 20

In the same way, we get 5 hundreds = 500, 6 hundreds = 600, 7 hundreds = 700, 8 hundreds = 800 and 9 hundreds = 900. The smallest 3-digit number is 100. The largest 3-digit number is 999. Let us understand this concept using a spike abacus. We have learnt how to show the number 99 on an abacus. To show the number 100, we remove all the green beads from the tens place. We also remove all the blue beads from the ones place. We then put 1 pink bead in the third spike (hundreds place). 1 = 1 unit in the ones spike TO H TO 1 = 1 unit in the tens spike 99 100 1 = 1 unit in the hundreds spike Thus, to show 999, we put 9 pink beads in the hundreds spike, 9 green beads in the tens spike and 9 blue beads in the ones spike. H TO 999 In the same way, we can show the numbers 298 and 459 on the abacus. H TO H TO H TO 124 298 459 Numbers 21

We can write the number names of these numbers as: 124 = One hundred and twenty-four 298 = Two hundred and ninety-eight 459 = Four hundred and fifty-nine Place value and face value Place Value: Every digit in a number has a place in the place value chart. Each digit gets its value from the place it occupies. This value is called its place value. Face Value: The value of a digit that remains the same at any place in a number is called its face value. Let us understand the place values of the digits in 3-digit numbers. Consider the 3-digit number 110. Its number name is one hundred and ten. 110 has 1 hundred, 1 ten and 0 ones. It is written in the place value chart as shown. Places Hundreds (H) Tens (T) Ones (O) Values 1 10 Example 1: Find the place values and the face values of the digits in 842. Solution: 842 2 ones 4 tens 8 hundreds Place Value Face Value 22 40 4 800 8 22

Expanded form of a 3-digit number Consider the number 425. We write 425 in the place value chart as shown. H TO Place values 425 5 ones = 5 2 tens = 20 4 hundreds = 400 We can write the place values of the digits of a given number with a ‘+’ sign between them. This gives the expanded form of the number. So, the expanded form of 425 is 400 + 20 + 5. The number name of 425 is four hundred and twenty-five. 425 is the standard form of the number. Consider the following examples to understand the concept better. Example 2: Write the standard forms of the following numbers. a) 9 hundreds + 4 tens + 6 ones b) 4 hundreds + 2 tens + 3 ones c) 3 hundreds + 0 tens + 8 ones Solution: To write the standard forms, write the numbers in the place value chart, as shown: HTO a) 9 4 6 b) 4 2 3 c) 3 0 8 So, the standard forms of the given numbers are: a) 946 b) 423 c) 308 Numbers 23

Example 3: Count and write the following numbers in their expanded forms. Then, write their number names. a) b) c) Solution: To write the expanded forms, write the numbers in the place value chart as shown below. Number Place Value Expanded Forms Number Names Chart H TO a) 523 523 523 = Five hundred and 500 + 20 + 3 twenty-three b) 432 432 432 = Four hundred and 400 + 30 + 2 thirty-two c) 634 634 634 = Six hundred and thirty-four 600 + 30 + 4 24

Concept 3.3: Compare 3-digit Numbers Think David has 504 colour pencils and his brother has 582 colour pencils. He wants to find out who has more colour pencils. How do you think David can find that out? Recall We have already learnt to compare numbers using the signs <, = or >. Let us recall the same. Count the number of objects in each image. Compare them using the proper sign <, > or = in the given boxes. a) Numbers 31

b) c) & Remembering and Understanding A 2-digit number is always smaller than a 3-digit number. Comparing two 3-digit numbers is similar to comparing two 2-digit numbers. We can compare two 3-digit numbers as shown in this example. Example 11: Compare: a) 723 and 456 b) 436 and 412 c) 623 and 628 Solution: Follow these steps to compare 3-digit numbers. 32

723 and 456 436 and 412 623 and 628 Step 1: Count the Step 1: Count the Step 1: Count the number number of digits number of digits of digits 723 456 436 412 623 628 Both have 3 digits. Both have 3 digits. Both have 3 digits. Step 2: Compare the Step 2: Compare the Step 2: Compare the hundreds hundreds hundreds 723 456 436 412 623 628 As 7 > 4, As 4 = 4, As 6 = 6, 723 > 456. compare the tens. compare the tens. Step 3: Compare the tens Step 3: Compare the tens 436 412 623 628 As 3 > 1, As 2 = 2, 436 > 412. compare the ones. Step 4: Compare the ones 623 628 As 3 < 8, 623 < 628. Numbers 33

Chapter Addition 4 Let Us Learn About • a dding 2-digit and 3-digit numbers. • properties of addition. Concept 4.1: Add 2-digit and 3-digit Numbers Think David had 306 stamps in one bag and 462 stamps in another bag. Meena had 12 stamps in one bag and 18 stamps in the other. David wants to find the total number of stamps with each of them. How do you think David can find that? 38

Recall We know how to add 2-digit numbers without regrouping. Let us recall the same. Write and add the number of objects in the boxes. a) b) c) d) Addition 39

& Remembering and Understanding Let us learn to add 2-digit numbers with regrouping and 3-digit numbers without regrouping. Add 2-digit numbers with regrouping Adding 2-digit numbers is similar to adding 1-digit numbers. While adding two numbers, always begin from the ones place. In some cases, we need to regroup the 2-digit sum. We carry forward its tens digit to the next place. Consider an example. Example 1: Add: 27 + 55 Solution: Arrange the numbers vertically. Steps Solved Solve these Step 1: Add the ones, 7 + 5 = 12. TO T O We can write only the ones digit of 1 44 the sum in the ones place. 2 7 +38 +5 5 So, we regroup 12 as 10 + 2. 2 Write 2 in the ones place. Carry forward 1 to the tens place. Step 2: Add the tens, 2 + 5 = 7. T O TO Add the carry forward 1 from the 1 ones place to this sum. 2 7 36 7+1=8 +5 5 +49 Write this sum in the tens place. 2 So, 27 + 55 = 82. 8 40

Add 3-digit numbers without regrouping Let us understand how to add 3-digit numbers through an example. Example 2: Add 343 and 125. Solution: Arrange the numbers vertically. Step 1: Step 2: Step 3: Add the ones Add the tens Add the hundreds H T O H T O HT O 34 3 34 3 34 3 +1 2 5 +1 2 5 +1 2 5 8 68 46 8 Solve these H TO H TO H TO H TO 634 144 122 108 +1 5 2 +3 3 4 +4 0 1 +2 0 1 Properties of addition Addition of numbers have some properties. Let us learn a few of them. 1) Zero property: When we add 0 to a number, the sum is the number itself. For example, 89 + 0 = 89; 12 + 0 = 12 and so on. 2) After numbers property: When we add 1 to a number, we get the number just after it. For example, 35 + 1 = 36; 77 + 1 = 78 and so on. 3) Commutative property: Changing the order in which we add two numbers does not change their sum. For example, 2 + 3 = 5 and 3 + 2 = 5; 15 + 14 = 29 and 14 + 15 = 29 and so on. Addition 41

Chapter Subtraction 5 Let Us Learn About • s ubtracting 2-digit and 3-digit numbers. • p roperties of subtraction. • mental Maths techniques for subtraction. Concept 5.1: Subtract 2-digit and 3-digit Numbers Think David got 83 candies from his parents for his birthday. He gives 27 candies to his friend Neha. How can David find the number of candies left with him without counting? Recall In class 1, we have learnt to subtract using a number line and also by counting. We have also learnt subtraction using the place value chart. Let us solve the following to recall the concept of subtraction. 44

Count, write and subtract the numbers in the boxes. a) b) c) d) Subtraction 45

& Remembering and Understanding Subtraction of 2-digit numbers with regrouping Place values of digits in 2-digit numbers are tens and ones. While subtracting, always start from the ones place. Sometimes, subtracting 2-digit numbers needs regrouping. Let us see some examples. Example 1: Subtract 48 from 56. Solution: To subtract, follow these steps: Steps Solved Solve these TO TO Step 1: Write the numbers according 56 44 to their places. Subtract the digits in the ones place. But, we cannot –4 8 –3 8 subtract 8 from 6. So, we have to regroup the tens. TO TO 4 16 98 5 tens = 4 tens + 1 ten. 56 –3 9 –4 8 We know that 1 ten = 10 ones. 8 Step 2: Add 1 ten to the ones place. So, it becomes 16 ones. Also, subtract 1 ten from the tens place (that is, 5 – 1 = 4). Now, subtract 8 from 16. That is, 16 – 8 = 8. Write the difference in the ones place. (Note: You cannot subtract from zero. You must borrow from the next place instead. For example, for subtracting 27 from 40, you cannot subtract 7 from 0. Hence, you borrow 1 from 4 (the tens place of 40) to give 10 for 0 and 3 for 4.) Step 3: Subtract the digits in the tens TO TO place. That is, 4 – 4 = 0. Write the 4 16 difference in the tens place. 56 86 –4 8 –2 7 So, 56 – 48 = 8. 08 46

Subtract 3-digit Numbers without regrouping Let us understand how to subtract 3-digit numbers through an example. Example 2: Subtract 141 from 943. Solution: To subtract the given numbers, follow these steps: Steps Solved Solve these Step 1: Arrange the numbers HTO HTO according to their place values. 943 784 –1 4 1 –3 3 2 HTO HTO 496 Step 2: Subtract the digits in the 943 –2 6 2 ones place. Write the difference in – 1 4 1 the ones place. That is, 3 – 1 = 2. 2 HTO HTO 636 Step 3: Subtract the digits in the 943 –1 3 0 tens place. Write the difference in –1 4 1 the tens place. That is, 4 – 4 = 0. 02 Step 4: Subtract the digits in HTO HTO the hundreds place. Write the 943 846 difference in the hundreds place. –4 2 0 That is, 9 − 1= 8. –1 4 1 So, 943 – 141 = 802. 802 Properties of subtraction 1) Zero property: When we subtract 0 from a number, the difference is the number itself. For example, 12 – 0 = 12 Subtraction 47

2) B  efore numbers property: When we subtract 1 from a number, we get the number that is just before it. For example, 35 – 1 = 34 3) Subtracting a number from itself: When we subtract a number from itself, the difference is 0. For example, 35 – 35 = 0 48

Contents 2Class Part 2 8 Multiplication 8.1 Concept of Repeated Addition ................................................................ 18 394501 +7-x8.2 Skip Counting .............................................................................................. 22 82

Chapter Multiplication 8 Let Us Learn About • repeated addition. • skip counting. • multiplication tables from 2 to 6. Concept 8.1: Concept of Repeated Addition Think David has five pet cats. He wants to know the number of legs they have altogether. How can David find that? Recall We already know how to add some objects by counting. Let us recall the same through the following exercise. 18

Count, add and write the number of objects. a) Number of honey bees = _____________ b) Number of trees = ___________ c) Number of birds = ___________ d) Number of windows = ___________ Multiplication 19

& Remembering and Understanding Repeated addition is adding the same number repeatedly (again and again). We put the objects into equal groups to find their total. Let us see a few examples. E xample 1: Use repeated addition to find the total number of houses. Solution: Number of groups = 4 The number of objects in each group = 2 Total number of objects = 2 + 2 + 2 + 2 = 8 So, there are 8 houses in all. We read it as 4 groups of 2 is 8. Example 2: Count and add: Solution: Number of groups = 3 Number of equal number of objects in each group = 4 Total number of objects = 4 + 4 + 4 = 12 We read it as 3 groups of 4 is 12. 20

Concept 8.2: Skip Counting Think While playing hopscotch, David knows to jump by skipping some of the boxes. Similarly, he can count numbers by skipping some of them. How could he do that? Recall [] Recall the concept of repeated addition through these examples. Write the values of the following. a) 5 groups of 2 22

b) 3 groups of 9 [ ] c) 2 groups of 8 [] d) 6 groups of 1 [] & Remembering and Understanding Skip Counting is counting by a number that is not 1. It helps you • to count many things quickly. • to learn multiplication tables. Count by 2s In counting by 2s, we begin with the given number and count every alternate number. Example 6: Help the frog to find its way to the snail using skip counting by 2. Write the numbers on which it jumps. One is done for you. a) Multiplication 23

b) c) Count by 3s In counting by 3s, we count every third number from the given number. Example 7: Begin with the given number and count by 3s. Write the numbers in the boxes given. One is done for you. a) b) c) We now know the concepts of repeated addition and skip counting. Let us now learn to construct the multiplication tables of numbers from 2 to 6. 24

Observe the following figure. It is a group of 2 stars. So, we see that 1 group of 2 is 2. We write it as ‘2 × 1 = 2’ which means ‘2 times 1 is 2’. The symbol ‘×’ is used for multiplication. It is read as ‘times’. We read it as ‘2 ones are 2’. There are 2 groups with 2 stars in each. We write it as 2 + 2 = 4 and read it as 2 groups of 2 is 4. We can also write it as ‘2 × 2 = 4’ which means ‘2 times 2 is 4’. We read it as ‘2 twos are 4’. These are 3 groups with 2 stars in each. We write it as 2 + 2 + 2 = 6 and read it as 3 groups of 2 is 6. This can be written as ‘2 × 3 = 6’ which means ‘2 times 3 is 6’. We read it as ‘2 threes are 6’. In this way, we can form the multiplication table of 2. Forming the multiplication table of 2 2×1=2 1 + 1 2 times 1 is 2. 2×2=4 2 + 2 2 times 2 is 4. Multiplication 25

2×3=6 3 + 3 2 times 3 is 6. 2×4=8 4 + 4 2 times 4 is 8. 2 × 5 = 10 5 + 5 2 times 5 is 10. 2 × 6 = 12 6 + 6 2 times 6 is 12. 2 × 7 = 14 7 + 7 2 times 7 is 14. 2 × 8 = 16 8 + 8 2 times 8 is 16. 2 × 9 = 18 9 + 9 2 times 9 is 18. 2 × 10 = 20 10 + 10 2 times 10 is 20. 26

The following are the multiplication tables of 3, 4, 5 and 6. Read them aloud. 3 4 5 6 3×1=3 4×1=4 5×1=5 6×1=6 3×2=6 4×2=8 5 × 2 = 10 6 × 2 = 12 3×3=9 4 × 3 = 12 5 × 3 = 15 6 × 3 = 18 3 × 4 = 12 4 × 4 = 16 5 × 4 = 20 6 × 4 = 24 3 × 5 = 15 4 × 5 = 20 5 × 5 = 25 6 × 5 = 30 3 × 6 = 18 4 × 6 = 24 5 × 6 = 30 6 × 6 = 36 3 × 7 = 21 4 × 7 = 28 5 × 7 = 35 6 × 7 = 42 3 × 8 = 24 4 × 8 = 32 5 × 8 = 40 6 × 8 = 48 3 × 9 = 27 4 × 9 = 36 5 × 9 = 45 6 × 9 = 54 3 × 10 = 30 4 × 10 = 40 5 × 10 = 50 6 × 10 = 60 Multiplication 27