Multiplication as scaling · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Multiplication as scaling

Mathematics · Fractions · ages 10-11
Name ______________________   Date ____________

  1. Without multiplying first, is 1/4 times 1/5 less than, equal to, or greater than 1/4?

    • Less than 1/4
    • Equal to 1/4
    • Greater than 1/4

  2. You multiply a number by 3/4. Will the answer be bigger or smaller than the number?

    • Bigger
    • Smaller
    • The same

  3. Multiplying a number by 5/5 keeps the number exactly the same.

    Circle one:   True   False

  4. You multiply a number by 7/2. Will the answer be bigger or smaller than the number?

    • Bigger
    • Smaller
    • The same

  5. Rectangle A is 2 by 3. Rectangle B is 4 by 6 and is a scaled copy of A. What scale factor turns A into B?

    • 1/2
    • 1
    • 2
    • 4

  6. Which pair of fractions has a product equal to 1?

    • 2/3 times 3/2
    • 2/3 times 3/4
    • 3/2 times 3/2
    • 1/3 times 1/2

  7. Which fraction, multiplied by a number, would make it grow larger?

    • 3/8
    • 9/9
    • 11/6

  8. Without calculating, is 2/5 × 15 bigger or smaller than 15?

    • Bigger
    • Smaller
    • Equal

  9. Which group of three fractions has a product of 1?

    • 3/4 times 6/9 times 2/1
    • 3/4 times 6/9 times 1/2
    • 3/4 times 6/9 times 4/3
    • 2/3 times 6/9 times 2/1

  10. A recipe amount gets scaled by 5/3. Without calculating, will the new amount be more or less than the original?

    • More
    • Less
    • Exactly the same
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Answer key

For grown-ups. Fold this page away before handing over the rest.

Multiplication as scaling W1-mt_VKW8lOcFaw-s1

  1. Less than 1/4 · 1/5 is less than 1, so it shrinks 1/4. The real answer, 1/20, is smaller than 1/4.
  2. Smaller · 3/4 is less than 1, so multiplying by it makes the number smaller.
  3. True · 5/5 equals 1, and multiplying by 1 never changes a number.
  4. Bigger · 7/2 is greater than 1 (it's 3 and a half), so multiplying by it makes the number bigger.
  5. 2 · Each side doubled, so the scale factor is 2. A factor greater than 1 makes the shape grow, just like multiplying by 2 makes a number grow.
  6. 2/3 times 3/2 · 2/3 times 3/2 gives 6/6, and 6/6 is exactly 1 whole. A fraction times its flip always makes 1.
  7. 11/6 · 11/6 is greater than 1, since 11 is more than 6, so it grows the number. 3/8 is less than 1 and 9/9 equals 1, so neither grows it.
  8. Smaller · 2/5 is less than 1, so the product must be smaller than 15.
  9. 3/4 times 6/9 times 2/1 · 3/4 times 6/9 is 1/2, and 1/2 times 2 brings it back to exactly 1.
  10. More · 5/3 is greater than 1, since 5 is more than 3, so scaling by it always makes the amount larger.
Worksheet · LightMySky