Fractions: mixed numbers and more
Mixed numbers, equivalent fractions, comparing, adding and subtracting, and a fraction of an amount. Read one step, play with it, then tap “I understand this”.
Mixed numbers and improper fractions
An improper fraction has a numerator bigger than its denominator, like 74. It is more than one whole. As a mixed number we write it as 134: one whole and three quarters.
Fill the wholes
Change the numerator and denominator. See how many wholes fill up.
Improper → mixed: divide the numerator by the denominator; the remainder is the new numerator. Mixed → improper: whole × denominator + numerator.
Every whole is made of as many pieces as the denominator: 1 whole is 4 quarters. So 2 wholes are 2 × 4 = 8 quarters. Add the 3 quarters you already have: 11 quarters.
Equivalent fractions
Multiply the numerator and the denominator by the same number and the fraction stays the same size: 23 = 46 = 69.
Cut the pieces smaller
Change the fraction and the number you multiply by.
It works the other way too: divide top and bottom by the same number to simplify: 68 = 34.
Cut every piece into 3. Now there are 3 times as many pieces (denominator × 3) and also 3 times as many coloured pieces (numerator × 3). The amount of pizza has not changed, only the size of the pieces.
Compare fractions
To compare 23 and 56, make the denominators the same: 23 = 46. Now it is easy: 56 > 46.
Bigger, smaller or equal?
Choose the right sign.
Correct: 0You can only fairly compare pieces of the same size. Is 2 thirds or 5 sixths more? Cut the thirds into sixths, then you compare sixths with sixths.
Adding and subtracting mixed numbers
With the same denominator you only add or subtract the numerators. Turn mixed numbers into improper fractions first.
125 + 45 = 75 + 45 = 115 = 215
The fraction machine
Choose plus or minus and change the numbers.
Never add the denominators: 25 + 15 = 35, not 310.
A half and a quarter are not the same size pieces, just like R1 and 50c are not the same coins. You can’t say “1 + 1 = 2 somethings”. First change them into the same kind of piece: 12 = 24, then 24 + 14 = 34.
A fraction of an amount
Divide the amount by the denominator to get one part, then multiply by the numerator.
Share the strip
Change the fraction and how many in each group.
Word problem: a class has 35 learners and 35 are girls. 35 ÷ 5 = 7, and 7 × 3 = 21 girls.
Check yourself
- Improper fraction to mixed number: divide the numerator by the denominator.
- Mixed number to improper fraction: whole × denominator + numerator.
- Multiply or divide top and bottom by the same number: the fraction stays the same size.
- Compare and add only with the same denominator. Never add the denominators.
Write these points in your maths book. Read them again the night before the test.
Quick questions
Tap an answer. If you get one wrong, read why and go back to that step. You get new questions every time.
You ticked all 5 steps! Now you are ready for the quiz.- Practice sheet for this classQuestions + memo · 2 A4 pagesPractice sheet
- Numbers16 pages · PDFPaperMemo
Ready for more? The Grade 5 fractions quiz gives you new questions every time.
- One step a day is enough. Ten calm minutes work better than an hour the night before the test.
- Use a pizza or a chocolate bar: “If we cut 2 pizzas into 4 each and you eat 5 slices, how much pizza did you eat?” (114)
- Ask your child to tell you the rule in their own words. If they can explain it, they understand it.
- The ticks (“I understand this”) are saved on this device only. We never ask for names or emails.
Follows CAPS for Grade 5 Maths. Always check your teacher’s notes and textbook too.