1. Copyright © Ed2Net Learning, Inc.1 Multiplying of Proper Fraction & Whole Number Grade 4

2. Copyright © Ed2Net Learning, Inc.2 Let’s warm up : Add: 1) 4 + 1 5 2 2) 3 + 5 4 8 Subtract: 3) 4 - 1 5 2 4) 3 - 5 4 8

3. Copyright © Ed2Net Learning, Inc.3 Let’s review what we did in the last session We learnt the following terms: Adding unlike fractions is more complicated than adding like fractions. To add two fractions with unlike denominator do the following steps: Step1: Find the LCD ( Least Common Denominator) for each fraction. Step2: Express each fraction as an equivalent fraction whose denominator is the LCD for the two fractions. Step3: Add the fractions. Step4: Write the answer in simplest form.

4. Copyright © Ed2Net Learning, Inc.4 Review Find : 2 + 1 9 6 Prime factorization of 6 = 2 × 3 Prime factorization of 9 = 3 × 3 LCD = 2 × 3 × 3 = 18 Here the denominator are 6 and 9. STEP 1: Here, before you can add the fractions with different denominators, you must first find equivalent fractions with the same denominator, like this: Find the LCD ( Least Common Denominator) for each fraction.

5. Copyright © Ed2Net Learning, Inc.5 Review Let’s rewrite the fractions as equivalent fractions with the denominator 18. STEP 2: Here, And, 2 = 2 x 2 = 4 9 9 x 2 18 1 = 1 x 3 = 3 6 6 x 3 18 STEP 3: Add the fractions. STEP 4: Write the answer in simplest form. The answer is 7 18 Already in simplest form. 2 + 1 = 4 + 3 = 7 9 6 18 18 18

6. Copyright © Ed2Net Learning, Inc.6 Review Subtracting unlike fractions involves same process like adding unlike fractions. To subtract two fractions with unlike denominator do the following steps: Step1: Find the LCD ( Least Common Denominator) for each fraction. Step2: Express each fraction as an equivalent fraction whose denominator is the LCD for the two fractions. Step3: Subtract the fractions. Step4: Write the answer in simplest form.

7. Copyright © Ed2Net Learning, Inc.7 Review Find : 4 - 1 9 6 Prime factorization of 6 = 2 × 3 Prime factorization of 9 = 3 × 3 LCD = 2 × 3 × 3 = 18 Here the denominator are 6 and 9. STEP 1: Here, before you can subtract the fractions with different denominators, you must first find equivalent fractions with the same denominator, like this: Find the LCD ( Least Common Denominator) for each fraction.

8. Copyright © Ed2Net Learning, Inc.8 Review Let’s rewrite the fractions as equivalent fractions with the denominator 18. STEP 2: Here, And, 4 = 4 x 2 = 8 9 9 x 2 18 1 = 1 x 3 = 3 6 6 x 3 18 STEP 3: Subtract the fractions. STEP 4: Write the answer in simplest form. The answer is 5 18 Already in simplest form. 4 - 1 = 8 - 3 = 5 9 6 18 18 18

9. Copyright © Ed2Net Learning, Inc.9 Today we will see Multiplication of proper fraction & whole number When we do the process of multiplication, We are to repeatedly add the multiplicand as many times as there are 1's in the multiplier. When multiplying a fraction you do not need a common denominator. Here, we multiply the two numerators (the top numbers) to make the new numerator, and multiply the two denominators (the bottom numbers) to make the new denominator.

10. Copyright © Ed2Net Learning, Inc.10 # Simplify the final result. Change the improper fraction to a mixed fraction and simplify it if possible. # The whole number must be turned into a fraction, with the whole number as the numerator, and the number 1 as the denominator. # Multiply out the numerators. # Multiply out the denominators. This does not change the denominator. MULTIPLYING FRACTION BY WHOLE NUMBERS To multiply a fraction by a whole number follow the given steps:

11. Copyright © Ed2Net Learning, Inc.11 Find: 3 x 3 4 We draw a model: x 3 That is, ++ Now we count the number of blue boxes. The number of blue boxes = 9. Hence the solution is, 9494

12. Copyright © Ed2Net Learning, Inc.12 01212 2222 3232 4242 5252 6262 7272 8282 9292 10 2 Find: 3 x 3 2 3232 3232 3232 We can multiply by the means of Skip Counting also. By Skip Counting we mean that we can find the multiples of any number by hopping equal steps on the number line.  Here the numbers are taking 3 jumps each of 3 steps. 2 The product is 9. 2

13. Copyright © Ed2Net Learning, Inc.13 So, we can write 3 as Find: 3 x 3 4 STEP 1: 3131 The whole number must be turned into a fraction, with the whole number as the numerator, and the number 1 as the denominator. Multiply out the numerators. STEP 2: 3 x 3 = 9

14. Copyright © Ed2Net Learning, Inc.14 STEP 3: Multiply out the denominators. 4 x 1 = 4 This does not changes the denominator. STEP 4: Simplify the final result. Change the improper fraction to a mixed fraction and simplify it if possible. The result is 9. 4 After simplification, the final result is 2 1.41.4

15. Copyright © Ed2Net Learning, Inc.15 What is 4 times of 2 ? 5 Solution: 2 x 4 = 2 x 4 5 5 1 Write 4 as 4141 Here, we are given to multiply, 4 times. 2525 Hence, = 2 x 4 = 8 5 1 5 Multiply the numerators. Multiply the denominators. Change the result to a mixed fraction. = 3 5 1

16. Copyright © Ed2Net Learning, Inc.16 BREAK

17. Copyright © Ed2Net Learning, Inc.17

18. Copyright © Ed2Net Learning, Inc.18 Assignments Multiply: 1) 1 x 7 4 2) 2 x 5 3 3) 2 x 6 5 4) 5 x 2 7

19. Copyright © Ed2Net Learning, Inc.19 5) What is 8 times of 2 ? 9 6) What is 7 times of 3 ? 5

20. Copyright © Ed2Net Learning, Inc.20 Multiply: 7) 9 x 7 13 8) 5 x 5 4 9) 7 x 3 8 10) 5 x 6 11

21. Copyright © Ed2Net Learning, Inc.21 Very Good! Let's Review # Simplify the final result. Change the improper fraction to a mixed fraction and simplify it if possible. # The whole number must be turned into a fraction, with the whole number as the numerator, and the number 1 as the denominator. # Multiply out the numerators. # Multiply out the denominators. This does not change the denominator. MULTIPLYING FRACTION BY WHOLE NUMBERS To multiply a fraction by a whole number follow the given steps:

22. Copyright © Ed2Net Learning, Inc.22 Find: 3 x 3 4 We draw a model: x 3 That is, ++ Now we count the number of blue boxes. The number of blue boxes = 9. Hence the solution is, 9494 Review

23. Copyright © Ed2Net Learning, Inc.23 Review 01212 2222 3232 4242 5252 6262 7272 8282 9292 10 2 Find: 3 x 3 2 3232 3232 3232 We can multiply by the means of Skip Counting also. By Skip Counting we mean that we can find the multiples of any number by hopping equal steps on the number line.  Here the numbers are taking 3 jumps each of 3 steps. 2 The product is 9. 2

24. Copyright © Ed2Net Learning, Inc.24 Review So, we can write 3 as Find: 3 x 3 4 STEP 1: 3131 The whole number must be turned into a fraction, with the whole number as the numerator, and the number 1 as the denominator. Multiply out the numerators. STEP 2: 3 x 3 = 9

25. Copyright © Ed2Net Learning, Inc.25 Review STEP 3: Multiply out the denominators. 4 x 1 = 4 This does not changes the denominator. STEP 4: Simplify the final result. Change the improper fraction to a mixed fraction and simplify it if possible. The result is 9. 4 After simplification, the final result is 2 1.41.4

26. Copyright © Ed2Net Learning, Inc.26 Great Job! Remember to do the practice sheets!!