Improve Tuition · Non-Calculator Maths · Year 6–9
Lesson · Practice · Steps

Fraction Problems

Multi-step questions — choose the right method, then read the answer in context.

12 questions · 3 sections · four interactive worked examples · no time pressure

What's really happening

These problems don't test a new skill — they test whether you can pick the right tool (multiply, add, compare) and then read the answer in context. The arithmetic itself is the simplifying, multiplying and dividing from the Fractions and Multiplying & Dividing Fractions pages.

Two habits that win marks: when an answer counts whole items (packs, buses, tins), a fraction means you must round up. And when a question says “the rest”, that fraction is 1 minus the others.

Type 1 · Multiply, then round to whole items

Each muffin needs 3/20 of a pack of butter. How many packs to bake 24 muffins? Tap through:

Multiply & round up24 muffins × 3/20 of a pack

Type 2 · A fraction of a fraction, then add

A rectangle is split into a left half and a right half. 2/5 of the left half is painted and 3/4 of the right half is painted. What fraction of the whole rectangle is painted?

Fraction of a fraction, then addFraction of the rectangle painted

Type 3 · Which is closer to 1?

Compare the distance each fraction is from 1. Which is closer to 1: 5/6 or 8/7?

Distance from 1Closer to 1: 5/6 or 8/7?

Type 4 · What fraction is left?

Of Sam's pens, 3/14 are red and 1/6 are blue; the rest are black. What fraction are black?

“The rest” = 1 minus the othersFraction of pens that are black
Read it in contextThe arithmetic answer isn't always the final answer. 3⅗ packs of butter means buying 4; “how many are left” needs 1 minus the rest; and “closer to 1” compares distances, so the bigger fraction can still be the closer one.
Learning Objective 1 · Year 6–7
Section A · Multiply & interpret
Multiply a fraction in a real context, then read the answer — rounding to whole items where needed.
Success criteria — I can:
Learning Objective 2 · Year 7–8
Section B · What fraction is left?
Combine fractions and find the remaining fraction using “1 minus the rest”.
Success criteria — I can:
Learning Objective 3 · Year 8–9
Section C · Fractions of fractions & comparing
Take a fraction of a fraction, and compare fractions by their distance from a value.
Success criteria — I can:
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