Correct 1/3 + 1/4 = 2/7 and explain.
Answer and explanation
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.
Subjects
Fractions
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Sample exercises
A pupil writes 3/5 ÷ 2 = 6/5. Correct it.
Answer and explanation
3/5 ÷ 2 = 3/10; dividing by 2 multiplies by 1/2.
3/5 ÷ 2 = 3/10; dividing by 2 multiplies by 1/2.
A pupil says 0.8 is smaller than 0.75 because 8 < 75. Explain.
Answer and explanation
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.
Write 35% as a decimal.
Answer and explanation
0.35
35 ÷ 100 = 0.35
A 60-unit quantity rises by 25%. Find the new quantity.
Answer and explanation
75
60 × 1.25 = 75
Why does a 20% decrease followed by a 20% increase not generally restore the original amount?
Answer and explanation
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.
Study notes
Fractions of a set
Split into equal groups using the denominator, then take the numerator groups.
Grades 3–6Complete one whole
Keep the common denominator while finding the missing numerator.
Grades 3–5Subtract mixed numbers
Convert to improper fractions; then subtract with a common denominator.
Grades 4–7Fractions · Formula sheet
Rules, conditions and small examples in one printable reference.
Grades 3–5Fractions · Formula sheet
Rules, conditions and small examples in one printable reference.
Grades 6–7Fractions: the essential rules
A focused reference to use alongside your practice.
Grades 4–8Find the mistake: fractions and percentages
Equivalent fractions require multiplying or dividing numerator and denominator by the same nonzero number.
Grades 5–8Find the mistake: fractions and percentages · revision card
Equivalent fractions require multiplying or dividing numerator and denominator by the same nonzero number.
Grades 5–8Fraction reasoning and common mistakes
Comparisons require the same whole. Equal-sized parts give the denominator meaning.
Grades 4–7Fraction reasoning and common mistakes · Revision card
Comparisons require the same whole. Equal-sized parts give the denominator meaning.
Grades 4–7Fraction, decimal and percent benchmarks
Compare common representations and check the whole before using a percentage.
Grades 4–8Fractions as equal shares and numbers
Use the same whole and equal-size parts when interpreting fractions.
Grades 3–6Fractions as equal shares and numbers · Revision sheet
Use the same whole and equal-size parts when interpreting fractions.
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