Mathematics · Grades 5–8
Find the mistake: fractions and percentages
Equivalent fractions require multiplying or dividing numerator and denominator by the same nonzero number.
Understand the idea
Preserve the value
Equivalent fractions require multiplying or dividing numerator and denominator by the same nonzero number.
Use the right whole
A percentage comparison changes when the reference whole changes.
Examples and reasoning
Correct 1/3 + 1/4 = 2/7 and explain.
Use a common denominator: 4/12 + 3/12 = 7/12. Adding denominators is not the addition rule.
Use a common denominator: 4/12 + 3/12 = 7/12. Adding denominators is not the addition rule.
A pupil writes 3/5 ÷ 2 = 6/5. Correct it.
3/5 ÷ 2 = 3/10; dividing by 2 multiplies by 1/2.
3/5 ÷ 2 = 3/10; dividing by 2 multiplies by 1/2.
Check your understanding
A pupil says 0.8 is smaller than 0.75 because 8 < 75. Explain.
Write 35% as a decimal.
A 60-unit quantity rises by 25%. Find the new quantity.
Why does a 20% decrease followed by a 20% increase not generally restore the original amount?
Answers and marking notes
Answers and marking notes
- Write 0.8 as 0.80. Eighty hundredths is greater than seventy-five hundredths.
Write 0.8 as 0.80. Eighty hundredths is greater than seventy-five hundredths.
- 0.35
35 ÷ 100 = 0.35
- 75
60 × 1.25 = 75
- The second percentage uses a smaller base. The factor is 0.8 × 1.2 = 0.96, not 1.
The second percentage uses a smaller base. The factor is 0.8 × 1.2 = 0.96, not 1.
Learning preview · teacher review required. Grade bands are approximate, not official curriculum alignment.