Math · Unit 5

Fractions and Decimals

Parts of a whole, equivalent fractions, decimals and percents

Fractions are where mathematics stops being about counting things and starts being about relationships, and it is the point where a lot of people quietly decide they are bad at maths.

The unit covers parts of a whole, equivalent fractions, adding them, and then decimals and percentages - which are the same idea in two more notations. Seeing all three as one concept is the thing that makes it click.

This unit breaks down into 21 short steps and 120 questions, starting at difficulty 2 and building to 3. Below you can see exactly what it covers, how the path is structured, and worked examples with explanations.

Steps: 21
Questions: 120
Difficulty: 2-3

What this unit covers

Percentages
Decimals
Equivalent Fractions
Parts of a Whole
Adding Fractions

Where this fits

Needs Times Tables and Sharing. Feeds Ratio, Proportion and Percent directly.

Where people slip

A bigger denominator means smaller pieces. A third is larger than a fifth, which contradicts every intuition built up from whole numbers.

How the unit is structured

Fractions and Decimals runs as 21 short steps that unlock in order. 15 are practice rounds and 6 are challenge rounds that pull together everything before them. Questions start at difficulty 2 and climb to 3 as you progress.

Step 1 · easierStep 21 · harder

Challenge rounds

Example questions

30 real questions from this unit, with the answer and the reason behind it, grouped by what they practise. There are 120 in the unit altogether.

Adding Fractions

Build the sentenceLevel 2
1. Build a true sentence about adding fractions.
Answer: To add fractions keep the same denominator
When denominators match, you keep the denominator and add the numerators.
Fact or fibLevel 2
2. 1/3 + 1/3 = 2/3.
Answer: True
Same denominators, so add the tops: 1 + 1 = 2, giving 2/3.
Fill the blankLevel 2
3. 4/7 + 2/7 = ____.
- 6/7correct
- 6/14
- 2/7
- 8/7
Add the tops over 7: 4 + 2 = 6, so 6/7.
Guess the numberLevel 2
4. What is 3/10 + 4/10 written as a decimal? Move the slider.
Answer: 0.7
3/10 + 4/10 = 7/10, which is 0.7.
Choose all that applyLevel 3
5. Select the two sums that equal exactly 1.
- 1/2 + 1/2correct
- 3/4 + 1/4correct
- 1/3 + 1/3
- 2/5 + 1/5
1/2 + 1/2 and 3/4 + 1/4 each make one whole.
Match the pairsLevel 3
6. Match each sum to its total.
Answer: 1/6 + 2/6 = 3/6; 1/8 + 3/8 = 4/8; 2/9 + 4/9 = 6/9
Add the tops over the same denominator for each.

Decimals

Build the sentenceLevel 2
7. Build a true sentence about decimals.
Answer: A decimal point separates ones from tenths
The decimal point sits between the ones place and the tenths place.
Choose all that applyLevel 2
8. Select all decimals that are equal to one half.
- 0.5correct
- 0.50correct
- 0.05
- 0.15
0.5 and 0.50 both mean one half.
Fact or fibLevel 2
9. 0.1 is the same as one tenth.
Answer: True
0.1 means one tenth, or 1/10.
Fill the blankLevel 2
10. The decimal for 1/4 is ____.
- 0.25correct
- 0.5
- 0.14
- 0.4
One quarter equals 0.25.
Match the pairsLevel 2
11. Match each fraction to its decimal.
Answer: 1/2 = 0.5; 1/4 = 0.25; 3/4 = 0.75
Each fraction has an equal decimal value.
Multiple choiceLevel 2
12. What is 0.75 written as a fraction in simplest form?
- 3/4correct
- 7/5
- 3/5
- 75/10
0.75 is seventy-five hundredths, which simplifies to 3/4.

Equivalent Fractions

Choose all that applyLevel 2
13. Select all fractions that are equal to 1/2.
- 2/4correct
- 3/6correct
- 2/3
- 1/3
2/4 and 3/6 both simplify to 1/2.
Fact or fibLevel 2
14. 4/8 is equal to 1/2.
Answer: True
4/8 simplifies to 1/2.
Match the pairsLevel 2
15. Match each fraction to its simplest form.
Answer: 2/4 = 1/2; 3/9 = 1/3; 6/8 = 3/4
Each fraction reduces to the simpler one beside it.
Build the sentenceLevel 3
16. Build a true sentence about equivalent fractions.
Answer: Equivalent fractions have the same value
Equivalent fractions are worth the same even if they look different.
Fill the blankLevel 3
17. 3/5 = ____/10.
- 6correct
- 5
- 8
- 15
Multiply the top and bottom by 2 to get 6/10.
Guess the numberLevel 3
18. What is the missing number? 3/4 = ?/12. Move the slider.
Answer: 9
3/4 equals 9/12, so the missing number is 9.

Parts of a Whole

Build the sentenceLevel 2
19. Build a true sentence about fractions.
Answer: The top number is the numerator
The numerator sits on top of the fraction.
Multiple choiceLevel 2
20. A chocolate bar has 8 equal pieces. What fraction is 1 piece?
- 1/8correct
- 1/6
- 8/1
- 1/4
One piece out of eight equal pieces is 1/8.
Picture questionLevel 2
21. 🍫 A chocolate bar like this has 4 equal squares. You eat 1 square. What fraction is left?
- 3/4correct
- 1/4
- 1/2
- 4/4
If 1 of 4 squares is gone, 3 of 4 remain, which is 3/4.
Fact or fibLevel 3
22. The fraction 8/8 equals 1.
Answer: True
When the top and bottom match, the fraction equals one whole.
Fill the blankLevel 3
23. A fraction like 7/4, where the top is bigger than the bottom, is called ____.
- impropercorrect
- proper
- equivalent
- mixed
When the numerator is bigger, the fraction is improper.
Odd one outLevel 3
24. Which is the odd one out because it is a proper fraction?
- 3/4correct
- 5/4
- 7/3
- 9/8
3/4 is less than 1, while the others are improper fractions.

Percentages

Build the sentenceLevel 2
25. Build a true sentence about what percent means.
Answer: Percent means out of one hundred
Per cent literally means for each hundred.
Fact or fibLevel 2
26. 50% is the same as one half.
Answer: True
50 out of 100 is exactly one half.
Fill the blankLevel 2
27. One half written as a percent is ____.
- 50%correct
- 25%
- 15%
- 5%
One half is 50%.
Choose all that applyLevel 3
28. Select the two values that equal 3/4.
- 75%correct
- 0.75correct
- 0.34
- 34%
Three quarters is both 75% and 0.75.
Guess the numberLevel 3
29. What is 30% of 60? Move the slider.
Answer: 18
30% of 60 is 18.
Match the pairsLevel 3
30. Match each percent to its decimal.
Answer: 5% = 0.05; 60% = 0.6; 150% = 1.5
Divide each percent by 100 to get its decimal.

Where these questions come from. Each unit starts as a plan of the concepts it should cover and the difficulty it should span. Questions are written against that plan with AI assistance, then checked by a validator that rejects anything without a single defensible answer, an explanation, or plausible wrong options. How we write questions sets out the whole process, and corrections are fixed in the bank and reach the site and the app the same day.

How you practise

This unit mixes 14 different question formats, so you are recalling and applying rather than recognising the same layout every time.

Build the sentence
Choose all that apply
Fact or fib
Fill the blank
Guess the number
Match the pairs
Multiple choice
Odd one out
Picture question
Put in order
Sort into groups
Spell it
True or false
Type the answer

Practise Fractions and Decimals

120 questions across 21 steps. Start with step one and crawl at your own pace.

Play this unit

Read about Fractions and Decimals

Explainers from our blog on what this unit covers. Each one ends with real questions from the bank.

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