Multiplying a fraction by a whole number and by a fraction
الأسبوع 20 · ضرب كسر في عدد صحيح وفي كسر · 3 دروس
2
Will the product grow or shrink?
Discover Mathematics P5: Term 2, Unit 9, Lessons 1–4
GoalPredict whether a product is bigger or smaller than the number you multiply, by looking at the other factor.
New words
factor · a number that is multipliedscaling · making a number bigger or smaller by multiplyingcompare · to say if a number is greater than, less than or equal to another
Explanation
When you multiply a number by a factor greater than 1, the product is bigger than the number: 6 × 1 1/4 = 7 1/2 is more than 6. When you multiply by a factor less than 1, the product is smaller: 6 × 3/4 = 4 1/2 is less than 6. When you multiply by 1 (or a fraction equal to 1, like 5/5), the product stays the same. You can decide this without calculating. Look at the fraction: if its numerator is greater than its denominator, it is greater than 1; if its numerator is less, it is less than 1. Use this to check your answers.
Factor
Compared with 1
Product compared with 6
3/4
less than 1
smaller
5/5
equal to 1
same
1 1/4
greater than 1
bigger
Worked examples
Work out 6 × 3/4. The factor 3/4 is less than 1, so the product is less than 6. 6 × 3/4 = 18/4 = 4 1/2.
Work out 6 × 1 1/4. The factor is greater than 1, so the product is more than 6. 6 × 1 = 6 and 6 × 1/4 = 6/4 = 1 1/2. Total 7 1/2.
Without calculating, is 9 × 7/8 bigger or smaller than 9? 7/8 is less than 1, so the product is smaller than 9.
Class activity
Bigger, smaller or the same? Write a number (say 12) on a card and a factor on other cards (3/4, 5/4, 1 1/2, 2/2, 1/3, 9/10). The child turns two cards, says if the product will be bigger, smaller or equal, then works it out to check. Count how many predictions were right.
Practice
1
Without calculating, say if 15 × 5/6 is bigger or smaller than 15. Then work it out.
Smaller, because 5/6 is less than 1. 15 × 5/6 = 75/6 = 12 1/2.
2
Is 10 × 1 1/2 bigger or smaller than 10? Work it out.
Bigger. 10 × 1 = 10 and 10 × 1/2 = 5, so 15.
3
What is 20 × 6/6? Why does the number not change?
20, because 6/6 = 1 and multiplying by 1 does not change a number.
4
Mina says multiplying always makes a number bigger. Show an example that proves him wrong.
8 × 1/2 = 4, which is smaller than 8.
5
Put <, > or = in each gap: 7 × 3/5 __ 7; 7 × 7/5 __ 7; 7 × 5/5 __ 7.
