Fraction Remainders Practice
Fraction remainder questions test whether you can combine several fractional parts, work out what is left, and convert each part into a real amount. The same steps appear in budgets, journeys, surveys, recipes, and other word problems.
The Rules Every Fraction Remainder Question Uses
These questions usually give several named fractions and ask for either one part, a combined part, a difference, or the leftover remainder.
🧮 Rule 1: Put fractions over a common denominator
Before you add or subtract fractions, rewrite them with matching denominators.
Example: 12 + 14 + 112 = 612 + 312 + 112 = 1012.
🧩 Rule 2: The remainder is 1 minus the used fraction
If the listed parts do not make the whole, subtract their total from 1 to find the leftover part.
Example: 1 - 56 = 16 left.
🔢 Rule 3: Convert a fraction into an amount
To find a fraction of a total, divide by the denominator and multiply by the numerator.
Example: 512 of 108 km = 108 ÷ 12 × 5 = 45 km.
🎯 Rule 4: Match the answer type to the question
Some parts ask for a fraction, while others ask for kilometres, tickets, grams, dollars, or students.
Example: "What fraction is left?" gives 16, but "How many km are left?" gives 16 of the total.
How to Solve Fraction Remainder Word Problems
Three useful moves: find one part, find the leftover part, and avoid mixing up a fraction answer with an amount answer.
1. Find One Fraction of the Total
Question: A farm is 48 hectares in total. 112 of the land is wheat fields, 16 is orchards, and 13 is woodland. How many hectares of wheat fields are there?
Worked Method
What it is testing: Converting a single fraction of a total into an amount.
Step 1: Wheat fields are 112 of the farm.
Step 2: Find 112 of 48 hectares: 48 ÷ 12 = 4 hectares.
Tip: If the numerator is 1, you only need one division.
2. Find the Remainder After Several Parts
Question: A paint mix is 14 red paint, 12 white paint, and 112 blue paint. The rest is yellow paint. What fraction of the paint mix is yellow paint?
Worked Method
Step 1: Add the listed parts using denominator 12.
14 + 12 + 112 = 312 + 612 + 112 = 1012 = 56.
Step 2: Subtract from the whole: 1 - 56 = 16.
Tip: Write the whole as 1, not as 100, unless the question is asking for a percentage.
3. Do Not Stop at the Fraction When an Amount Is Asked
Question: A journey is 110 motorway, 12 country roads, and 310 city driving. The rest is dirt roads. If the journey is 80 km, how many km are not motorway, country roads, or city driving?
Worked Method
Step 1: Add the listed fractions: 110 + 12 + 310 = 110 + 510 + 310 = 910.
Step 2: Find the remainder: 1 - 910 = 110.
Step 3: The question asks for kilometres, so find 110 of 80 km: 80 ÷ 10 = 8 km.
The trap: 110 is only the fraction left. The final answer needs the unit from the question.
Before You Buy
Want to check the level and layout first? Download the free 3-question sample. It uses the same question style, printable format, and answer-key approach as the full pack.
Download Free Sample PDFGet the Full Practice Pack
The full Fraction Remainders pack contains 90 word problems across 3 printable test sets. Students practise adding fractions, finding remainders, comparing fractional parts, and converting fractions into real amounts.
Checkout and downloads are securely handled on Etsy.com