Fractions to Hundredths Mastery

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Part 1: The Rule and Guided Examples

To convert a fraction to an equivalent fraction with denominator 100, multiply the numerator and denominator by the same whole-number factor.

Worked example: 10/20 = ?/100. Since 20 × 5 = 100, multiply both parts by 5: 10 × 5 / 20 × 5 = 50/100.

Worked example: 30/50 = ?/100. Since 50 × 2 = 100, multiply both parts by 2: 30 × 2 / 50 × 2 = 60/100.

1. Guided example: 5/25 = ?/100. What factor changes 25 into 100? Then complete the equivalent fraction.

2. Complete each conversion. Show the multiplier you used.

a) 7/20 = ______/100

b) 18/25 = ______/100

c) 23/50 = ______/100

3. Explain why the numerator and denominator must be multiplied by the same factor. Use the idea of equivalent fractions.

Part 2: Independent Practice and Challenge

4. Convert 13/20 to hundredths. Show your working.

5. Convert 17/25 to hundredths. Show your working.

6. Convert 41/50 to hundredths. Show your working.

7. Find each missing number.

a) ____/20 = 65/100

b) 19/____ = 76/100

c) ____/50 = 88/100

8. Insert <, > or =. Explain one comparison using hundredths.

a) 37/50 ____ 72/100

b) 9/20 ____ 46/100

9. Order these fractions from least to greatest: 3/5, 57/100, 13/25.

10. Complete the links between fractions, decimals and percentages.

a) 17/20 = ______/100 = ______ = ______%

b) 21/25 = ______/100 = ______ = ______%

11. Error analysis: Mia says, “3/20 = 3/100 because the denominator was changed to 100.” Identify her error and give the correct equivalent fraction.

12. Challenge: Decide whether each fraction can be converted to a denominator of 100 using a whole-number multiplier. If it can, convert it. If it cannot, explain why.

a) 7/16

b) 9/25

c) 11/40

d) 13/50

Answer Key

1. 25 × 4 = 100, so multiply both parts by 4: 5/25 = 20/100.

2. a) 20 × 5 = 100; 7 × 5 = 35, so 7/20 = 35/100.
b) 25 × 4 = 100; 18 × 4 = 72, so 18/25 = 72/100.
c) 50 × 2 = 100; 23 × 2 = 46, so 23/50 = 46/100.

3. Both parts must be multiplied by the same factor so the fraction’s value remains unchanged. Multiplying only the denominator changes the value.

4. 20 × 5 = 100; 13 × 5 = 65. Therefore, 13/20 = 65/100.

5. 25 × 4 = 100; 17 × 4 = 68. Therefore, 17/25 = 68/100.

6. 50 × 2 = 100; 41 × 2 = 82. Therefore, 41/50 = 82/100.

7. a) 13/20 = 65/100. b) 19/25 = 76/100. c) 44/50 = 88/100.

8. a) 37/50 = 74/100, so 37/50 > 72/100. b) 9/20 = 45/100, so 9/20 < 46/100.

9. 13/25 = 52/100, 57/100 = 57/100, and 3/5 = 60/100. Order: 13/25, 57/100, 3/5.

10. a) 17/20 = 85/100 = 0.85 = 85%. b) 21/25 = 84/100 = 0.84 = 84%.

11. Mia changed only the denominator. The multiplier must be 5 for both parts: 3/20 = 15/100.

12. a) Cannot: 16 is not a factor of 100, so no whole-number multiplier changes 16 to 100. b) Can: 9/25 = 36/100. c) Cannot: 40 × 2.5 = 100, and 2.5 is not a whole number. d) Can: 13/50 = 26/100.