Fractions and Problem Solving
Fractions and Problem Solving applies halving, quartering and thirding to money, objects and measures inside two-step word problems, rather than practising fractions in isolation.
Before you start
Make sure you're comfortable with these topics first:
Method
- Start concrete: before any word problem, let the child physically split a real quantity, counters, a strip of paper or a jug of water, into the number of equal parts the problem describes.
- Move to pictorial: draw a bar model of the whole amount, split into equal sections, and shade the number of sections the question asks about.
- Only then write the abstract number sentence, e.g. 'half of 14' becomes 14 / 2 = 7.
- Teach the child to spot fraction language hidden inside a problem: 'shared equally between two' means halves, 'between four' means quarters, 'one in every three' means thirds.
- For two-step problems, solve the fraction part FIRST, then use that answer in the next step, for example find half of an amount, then add or subtract from it.
- Always check a fraction answer makes sense: a half of an amount must be exactly half the size of the whole, so it can be checked by doubling the answer to see if it returns the original number.
- Watch for the classic misconception that a bigger denominator means a bigger piece: children think a third must be more than a half because 3 is a bigger number than 2, when the opposite is true, the whole has been cut into more, smaller pieces.
Worked example
A ribbon is 24 cm long. Halle cuts off one quarter of the ribbon to use for a bookmark, then gives half of what is LEFT to her brother. How many cm of ribbon does Halle have left for herself?
- Find one quarter of the ribbon: a quarter of 24 cm is 24 / 4 = 6 cm, which Halle cuts off for the bookmark.
- Find how much ribbon is left after the bookmark piece: 24 cm - 6 cm = 18 cm.
- Find half of what is left, to give to her brother: half of 18 cm is 18 / 2 = 9 cm.
- Subtract her brother's share from the 18 cm that was left: 18 cm - 9 cm = 9 cm.
- Halle has 9 cm of ribbon left for herself.
Practice questions
Type your answer and press Check to be marked straight away, or reveal the answer and mark yourself.
Q1A pizza is shared equally between Nathaniel and 3 friends, so 4 people share it in total. What fraction of the pizza does each person get?Show answer
Answer: One quarter (1/4)
Q2Isobel has 18 conkers and gives half of them to her cousin. How many conkers does she give away?Show answer
Answer: 9 conkers (half of 18 is 18 / 2 = 9)
Q3A jug holds 32 ml of juice. One quarter of the juice is poured into a cup. How much juice is in the cup?Show answer
Answer: 8 ml (a quarter of 32 is 32 / 4 = 8)
Q4Amelie has one third of a chocolate bar. Jayden has one quarter of an identical chocolate bar. Who has the bigger piece?Show answer
Answer: Amelie (one third is bigger than one quarter, because the bar is cut into fewer, larger pieces)
Q5A farmer has 30 eggs and sells one third of them at the market. How many eggs does the farmer sell?Show answer
Answer: 10 eggs (a third of 30 is 30 / 3 = 10)
Q6A packet of stickers is split into 3 equal sets. What fraction is 2 of the sets?Show answer
Answer: Two thirds (2/3)
Q7Zainab has 28 marbles. She gives away one quarter of them to her cousin, then gives one third of what remains to her neighbour. How many marbles does Zainab have left?Show answer
Answer: 14 marbles (a quarter of 28 is 7, leaving 21 marbles; a third of 21 is 7, which goes to her neighbour, leaving 21 - 7 = 14)
Exam-style questions
Written in the style of a KS1 Maths exam paper, with a full mark scheme.
A bookshop has 36 comics. One third of them are sold on Monday. How many comics are sold on Monday, and how many are left in the shop? Show your working.
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 3 available
One pizza is cut into 3 equal slices for one table. An identical pizza is cut into 4 equal slices for another table. Marnie says the second table's slices must be bigger, because 4 is a bigger number than 3. Is Marnie correct? Explain your answer.
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 2 available
A box has 40 crayons. Half of the crayons are given to one classroom, and the rest are shared equally between 2 other classrooms. How many crayons does each of the 2 other classrooms get? Show your working.
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 3 available
Free printable worksheet
Want more practice on paper? Download the fractions and problem solving worksheet pack - 9 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.
Next topics
Not quite what you needed?
Tell us what is missing on fractions and problem solving, 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.