Fraction Remainders Practice Test Worksheets
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.
For students who understand fractions, but get stuck finding what remains after a fraction of a quantity is taken away.
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What Do Fraction Remainder Questions Look Like?
Fraction remainder questions test whether you can combine several fractional parts, work out what is left, and convert each part into a real amount. Students are given a total quantity divided into fractions for different categories and must calculate either one specific share, a remaining fraction, or a physical leftover amount. Here is a worked example.
Farm Land Fraction Breakdown
Question: Maya owns a farm. The land breakdown is:
The rest of the farm land is used for grazing land.
If the farm is 200 hectares in total
a) How many hectares of wheat fields are there?
b) What fraction of the farm land is grazing land?
c) How many hectares are orchards and woodland combined?
Worked Method
Part a) Wheat fields:
Wheat is 18 of the 200-hectare farm.
200 ÷ 8 = 25 hectares.
Part b) Fraction of grazing land:
Used fraction = 540 + 840 + 1240 = 2540 = 58.
Grazing fraction = 1 − 58 = 38.
Part c) Combined orchards and woodland:
Combined fraction = 15 + 310 = 210 + 310 = 510 = 12.
200 ÷ 2 = 100 hectares.
Tip: Check whether each part asks for a fraction or an area in hectares.
Rules to Help You Solve Fraction Remainder Questions
To solve fraction remainder word problems like the farm example above, write parts over a common denominator and keep track of whether the question asks for a fraction or an amount.
🧮 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
When the listed fractions describe separate, non-overlapping parts of the same whole, add them and subtract their total from 1. If a fraction is instead “of the remainder”, it refers to a different amount and cannot be added directly to fractions of the original whole.
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: If 16 of a 108 km journey remains, the fraction left is 16. The distance left is 108 ÷ 6 = 18 km.
Two More Worked Examples
Here are two more examples showing how to find a remaining fraction and how to convert a leftover fraction into a real-world amount.
Paint Mix Recipe Breakdown
Question: Leila is mixing paint for an art project. The paint mix recipe is:
The rest of the paint mix is yellow paint.
If the total paint mix is 240 ml
a) What fraction of the paint mix is yellow paint?
b) How many ml of red paint are there?
c) How many ml of red paint and blue paint are there combined?
Worked Method
Part a) Fraction of yellow paint:
Used fraction = 840 + 1540 + 440 = 2740.
Yellow fraction = 1 − 2740 = 1340.
Part b) Red paint:
Red paint is 15 of 240 ml.
240 ÷ 5 = 48 ml.
Part c) Combined red and blue paint:
Combined fraction = 15 + 110 = 210 + 110 = 310.
240 ÷ 10 × 3 = 72 ml.
Tip: Use a common denominator before adding fractions with different denominators.
Road Trip Journey Breakdown and Distance Comparisons
Question: Rowan is planning a road trip. The journey breakdown is:
The rest of the journey is on dirt roads.
If the total journey is 240 km
a) How many kilometres of the journey are on dirt roads?
b) How many km are spent on city driving?
c) How many more km of country roads are there than motorway?
Worked Method
Part a) Distance on dirt roads:
Used fraction = 424 + 924 + 324 = 1624 = 23.
Remaining fraction = 1 − 23 = 13.
240 ÷ 3 = 80 km.
Part b) Distance spent on city driving:
City driving is 18 of 240 km.
240 ÷ 8 = 30 km.
Part c) Country roads compared with motorway:
Difference = 38 − 16 = 924 − 424 = 524.
240 ÷ 24 × 5 = 50 km more on country roads.
Tip: Do not stop at 13 for part a. The question asks for kilometres, so multiply the remaining fraction by the total distance.
