Fractions of Amounts and Remainders
Fractions of Amounts and Remainders covers finding a fraction of a quantity, and worded problems where sharing or grouping an amount leaves a leftover, or remainder, that does not fit into a further whole share. It combines the fraction-of-an-amount method with division-with-remainder reasoning, both of which appear together in real-life worded 11+ questions such as sharing sweets, packing boxes, or portioning ingredients.
Before you start
Make sure you're comfortable with these topics first:
Method
- To find a fraction of an amount, divide the amount by the denominator first, then multiply by the numerator.
- If a division does not divide exactly, the remainder is whatever is left over after taking out as many whole 'shares' as possible.
- Decide what the question wants done with a remainder: some questions want it stated as a leftover amount, others want it rounded, and others want it discarded because you cannot have part of a person or a part of a box.
- For 'how many whole X can be made', divide and ignore any remainder in the final count, but still check whether the question also asks what the remainder is.
- For a two-step version, such as finding a fraction of an amount and then finding what remains, calculate the fraction first, then subtract it from the whole amount.
- Always express a remainder in the same units as the original amount, converting units first if necessary.
- Check your answer by adding the fraction found and the remainder together; this should return you to the original total.
Worked example
A charity collects 140 tins of food. 2/7 of the tins are donated to a local shelter. The remaining tins are packed into boxes of 15 tins each. (a) How many tins are donated to the shelter? (b) How many full boxes can be packed from the remaining tins, and how many tins are left over after packing?
- Find one-seventh of 140 by dividing by 7: 140 / 7 = 20.
- Find two-sevenths by multiplying by 2: 20 x 2 = 40 tins donated to the shelter.
- Find the tins remaining: 140 - 40 = 100.
- Divide the remaining tins into boxes of 15: find the largest multiple of 15 not exceeding 100, which is 15 x 6 = 90.
- So 6 full boxes can be packed, using 90 tins.
- Find the leftover tins: 100 - 90 = 10 tins are left over after packing.
Practice questions
Try each question, then tap to reveal the answer.
Q1Find 3/8 of 96.Show answer
Answer: 96 / 8 = 12, so 12 x 3 = 36.
Q245 pencils are shared equally among 7 students, each getting as many whole pencils as possible. How many pencils does each student get, and how many are left over?Show answer
Answer: 7 x 6 = 42, so each student gets 6 pencils, with 45 - 42 = 3 left over.
Q3Find 5/9 of 72.Show answer
Answer: 72 / 9 = 8, so 8 x 5 = 40.
Q4A rope of 100cm is cut into pieces of 12cm each. How many full pieces can be cut, and how much rope is left over?Show answer
Answer: 12 x 8 = 96, so 8 full pieces can be cut, with 100 - 96 = 4cm left over.
Q5Find 2/3 of 57.Show answer
Answer: 57 / 3 = 19, so 19 x 2 = 38.
Q668 sweets are shared equally among 9 children, each getting as many whole sweets as possible. How many sweets are left over?Show answer
Answer: 9 x 7 = 63, so 68 - 63 = 5 sweets are left over.
Q7Find 4/11 of 121.Show answer
Answer: 121 / 11 = 11, so 11 x 4 = 44.
Q8A baker has 92 eggs and wants to pack them into boxes of 6. How many full boxes can she pack, and how many eggs are left over?Show answer
Answer: 6 x 15 = 90, so 15 full boxes can be packed, with 92 - 90 = 2 eggs left over.
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
A school orders 156 footballs. 5/12 of the footballs are given to the primary section, and the rest are shared equally among 8 secondary classes, with any leftover footballs kept in the store cupboard. (a) How many footballs go to the primary section? (b) How many footballs does each secondary class receive, and how many are left over?
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 4 available
A carton contains 205 apples. 3/5 of the apples are sold at the market. The rest are packed into bags of 8 apples each. (a) How many apples are sold at the market? (b) How many full bags can be packed from the rest, and how many apples are left over?
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 4 available
Free printable worksheet
Want more practice on paper? Download the fractions of amounts and remainders worksheet pack - 7 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 39 of 11+ Maths Workbook 1, the whole course as one free printable PDF.
Next topics
Not quite what you needed?
Tell us what is missing on fractions of amounts and remainders, or which topic to write up next. Every request is read, and we reply to every one.
Build a full practice pack.
This topic is one of hundreds in the library - pick the ones a student needs and generate a printable PDF in minutes.