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P6 Fractions & Decimals Questions (with Worked Solutions)

P6 prelim questions on fractions and decimals — the four operations, conversions, and word problems. Every question is from a real Singapore P6 preliminary exam, marked instantly, with step-by-step solutions.

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Example Fractions & Decimals questions

A few real fractions & decimals questions from P6 prelim papers. The full set — with marking and progress tracking — is inside SG Maths Exam.

Nanyang 2025 · Paper 2 · Q8 · 3 marks
Mr Soh spent $\frac{1}{5}$ of his money on a pair of shoes and $\frac{3}{4}$ of his remaining money on a bag, a shirt and a hat. The bag cost 3 times as much as the hat. The shirt cost $\frac{1}{2}$ as much as the hat. The pair of shoes cost $\$48$ more than the shirt. How much money did Mr Soh have at first?
Worked solution
  1. Let total money $= 20$ units. Shoes $= \frac{1}{5} \times 20 = 4$ units. Remaining $= 16$ units. Spent on bag, shirt, hat $= \frac{3}{4} \times 16 = 12$ units. Let the hat $= 2$ parts
  2. bag $= 6$ parts
  3. shirt $= 1$ part
  4. total $= 9$ parts $= 12$ units. The shirt $= \frac{1}{9} \times 12 = \frac{4}{3}$ units. Shoes $-$ shirt $= 4 - \frac{4}{3} = \frac{8}{3}$ units $= \$48$, so $1$ unit $= \$18$. Total $= 20 \times \$18 = \$360$.
ACS Junior 2025 · Paper 1 Booklet A · Q15 · 2 marks
Mollie had a container full of flour. Nellie and Ollie each had $\frac{2}{7}$ of what Mollie had. Mollie gave away some flour to Nellie and Ollie so that all 3 of them have the same amount of flour in the end. What fraction of flour did Mollie give away?
Worked solution
  1. \text{Let Mollie's flour} = m
  2. \text{Nellie} = \tfrac{2}{7}m,\ \text{Ollie} = \tfrac{2}{7}m
  3. \text{Total} = m + \tfrac{2}{7}m + \tfrac{2}{7}m = \tfrac{11}{7}m
  4. \text{Each ends with} = \tfrac{1}{3} \times \tfrac{11}{7}m = \tfrac{11}{21}m
  5. \text{Mollie gave away} = m - \tfrac{11}{21}m = \tfrac{10}{21}m
  6. \text{Fraction} = \tfrac{10}{21}
Catholic High 2025 · Paper 1 Booklet A · Q12 · 2 marks
Alex and Ben had \$190 altogether at first. After Alex gave Ben \$30, Alex had \$40 more than Ben. How much did Ben have at first?
Worked solution
  1. \text{Let Ben have } \$b\text{
  2. Alex had } \$(190 - b)
  3. \text{After Alex gives Ben } \$30: \text{Alex} = 160 - b,\ \text{Ben} = b + 30
  4. \text{Alex has } \$40 \text{ more}: (160 - b) - (b + 30) = 40
  5. 130 - 2b = 40
  6. 2b = 90
  7. b = 45
Catholic High 2025 · Paper 1 Booklet A · Q15 · 2 marks
Joe baked some chocolate muffins and vanilla muffins. He sold an equal number of chocolate muffins and vanilla muffins. He had $\frac{3}{4}$ of the vanilla muffins and $\frac{3}{7}$ of the chocolate muffins left. What fraction of the muffins were sold?
Worked solution
  1. \text{Vanilla sold} = 1 - \frac{3}{4} = \frac{1}{4} \text{ of the vanilla muffins}
  2. \text{Chocolate sold} = 1 - \frac{3}{7} = \frac{4}{7} \text{ of the chocolate muffins}
  3. \text{Equal numbers sold}: \frac{1}{4}v = \frac{4}{7}c \Rightarrow 7v = 16c
  4. \text{Total baked} = v + c = v + \frac{7}{16}v = \frac{23}{16}v
  5. \text{Total sold} = 2 \times \frac{1}{4}v = \frac{1}{2}v
  6. \text{Fraction sold} = \frac{1}{2}v \div \frac{23}{16}v = \frac{8}{23}
Tao Nan 2025 · Paper 2 · Q1 · 2 marks
A baker had 300 eggs at first. In the morning, he used some eggs. In the afternoon, he used $\frac{1}{3}$ of the remaining eggs. After that, there were 60 eggs left. How many eggs did the baker use in the morning?
Worked solution
  1. $1 - \frac{1}{3} = \frac{2}{3}$
  2. $\frac{2}{3}$ of remaining = 60
  3. $\frac{1}{3}$ of remaining = 30
  4. remaining = 90
  5. eggs used in morning = $300 - 90 = 210$
Nan Hua 2025 · Paper 1 Booklet A · Q13 · 2 marks
Roy and Jaya finished eating a jar of cookies over 2 days. On the first day, Roy ate 3 more cookies than Jaya. On the second day, Roy ate 12 cookies and Jaya ate 8 cookies. Jaya ate $\frac{2}{5}$ of the total number of cookies. How many cookies did Roy eat?
Worked solution
  1. \text{Jaya ate } \tfrac{2}{5} \text{ of total, so Roy ate } \tfrac{3}{5}
  2. \text{Roy} - \text{Jaya} = \tfrac{1}{5} \text{ of total}
  3. \text{Day 1: Roy} = j + 3, \text{ Jaya} = j
  4. \text{Total Roy} = j + 15, \text{ Total Jaya} = j + 8
  5. \text{Roy} - \text{Jaya} = 7
  6. \tfrac{1}{5} \text{ of total} = 7
  7. \text{Total} = 35
  8. \text{Roy} = \tfrac{3}{5} \times 35 = 21

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