Fractions & Decimals — All Four Operations
Match Fractions to Decimals
Draw a line to match each fraction to its decimal equivalent.
Adding Fractions — Same Denominator
Circle the correct answer.
1/5 + 2/5
2/7 + 3/7
3/8 + 1/8
5/9 + 2/9
Adding Fractions — Different Denominators
Circle the correct answer.
1/2 + 1/4
2/3 + 1/6
3/4 + 1/8
1/3 + 1/2
Subtracting Fractions
Circle the correct answer.
3/4 − 1/4
5/6 − 1/3
1 − 3/8
7/10 − 2/5
Multiplying Fractions
Multiply across: (a/b) × (c/d) = (a×c)/(b×d). Circle the correct answer.
1/2 × 2/3
3/4 × 2/5
2/3 × 3/4
4/5 × 5/8
Adding & Subtracting Decimals
Circle the correct answer.
3.6 + 1.75
8.4 − 2.65
0.48 + 1.3
12.0 − 4.35
Multiplying Decimals
Circle the correct answer.
1.2 × 3
0.5 × 0.4
2.5 × 4
0.7 × 0.3
Match Fractions to Decimals — Extended
Draw a line to match each fraction to its decimal form.
Estimate: Greater or Less Than 1?
Sort each expression by whether its answer is greater than, equal to, or less than 1.
Real-World Fractions & Decimals
Solve each problem. Show your working.
A recipe needs 2/3 cup of flour. If you make 1.5 times the recipe, how much flour do you need?
Three friends share a pizza. Tom eats 1/4, Sara eats 3/8. What fraction is left?
A jacket costs $64.80. It is reduced by 0.25 (one quarter). What is the new price?
Dividing Fractions
Use 'keep, change, flip': a ÷ b/c = a × c/b. Circle the correct answer.
1/2 ÷ 1/4
3/4 ÷ 1/2
2/3 ÷ 4
5/6 ÷ 5/12
Mixed Numbers and Improper Fractions
Match each mixed number to its equivalent improper fraction.
Order on a Number Line
Sort these fractions and decimals from smallest to largest.
Decimal Multiplication — More Practice
Circle the correct product.
3.4 × 2.1
0.6 × 0.8
1.5 × 1.5
4.2 × 0.5
Fraction Division in Context
Write a number sentence and solve.
A length of rope is 5/6 of a metre. It is cut into pieces that are each 1/12 of a metre long. How many pieces are there?
You have 2¾ litres of juice to pour into glasses that hold ¼ litre each. How many glasses can you fill?
Multi-Step Fraction Problems
Show full working for each problem.
Find: (3/4 + 1/2) × 2/3. Show all steps.
Find: (5/6 − 1/3) ÷ (1/2). Show all steps.
Sort Fractions — Smallest to Largest
Sort each set of fractions from smallest to largest.
BODMAS with Fractions
Apply order of operations. Circle the correct answer.
1/2 + 3/4 × 4
(1/2 + 1/4) ÷ 3
2 × (3/4 − 1/4)
Fraction Story Problems
Solve. Show your working.
Maya has 3/5 of a litre of paint. She uses 2/3 of what she has. How much does she use?
A water tank is ¾ full. It holds 360 L when full. How much water is in it? If 80 L is removed, what fraction full is it now?
Comparing and Ordering Mixed Numbers
Write these in order from smallest to largest and explain your method.
Order: 2⅓, 2¾, 2½, 2⅛. Explain how you decided.
Insert < or > between each pair: 3¼ ○ 3.3, 1⅔ ○ 1.6, 4.5 ○ 4½
Fractions in Measurement
Solve these measurement problems using fraction and decimal operations.
A shelf is 2.4 m long. You want to cut it into pieces each ⅔ m long. How many pieces can you cut? Any leftover?
A ribbon 3.5 m long is cut into pieces each 0.7 m long. How many pieces?
Fractions, Decimals and Percentages
Match each equivalent set.
Investigating Recurring Decimals
Use long division to convert fractions to decimals.
Convert 1/3, 2/3, 1/6 to decimals using division. What do you notice about these decimals?
Which fractions with denominator 12 produce recurring decimals? List them all.
Fraction Equations
Solve for the unknown fraction.
x + 1/4 = 3/4. Find x.
2/3 × y = 4/9. Find y.
z ÷ 3/4 = 8. Find z.
Scale Drawing
Use fraction and decimal operations to solve this scale problem.
A map has scale 1:50 000. On the map, a road measures 4.5 cm. What is the actual length of the road in kilometres?
A room is 6.4 m × 4.8 m. On a plan with scale 1:80, what are the dimensions of the room on paper (in cm)?
Fraction and Decimal Problem Solving — Shopping
Use fractions and decimals to solve each problem.
A shirt costs $48.00. There is a 1/4 off sale. What is the sale price?
Apples cost $2.80 per kg. You buy 2½ kg. What is the total cost?
A 1.25 kg block of cheese costs $7.50. What is the cost per 100 g?
Order of Operations with Fractions
Sort each expression — evaluate first, then sort results from smallest to largest.
Project: Fraction Art Grid
Create a colouring grid that demonstrates fraction equivalence.
Draw a 10×10 grid (100 squares). Shade 35 squares one colour and 25 squares another. Write the fraction, decimal and percentage shaded in each colour, and the unshaded fraction.
Can 35/100 be simplified? What is the simplest form?
Fraction Inequalities
Solve each inequality. Find all positive integers n that satisfy the condition.
Find all positive integers n such that 1/3 < n/10 < 2/3.
Find the fraction with denominator 12 that is closest to 0.6 but not equal to it.
Repeated Operations — Fractions
Explore what happens when you repeatedly multiply or divide a fraction.
Start with 1. Multiply by 1/2 repeatedly: 1, 1/2, 1/4, 1/8, … Write the first 8 terms. What is happening to the value?
Start with 1. Repeatedly divide by 2/3: 1, 3/2, 9/4, … Write the first 5 terms. What is happening?
Writing Fractions as Infinite Sums
Investigate the connection between repeating decimals and infinite sums.
0.333… = 3/10 + 3/100 + 3/1000 + … Write the first 4 terms and show why this sum equals 1/3.
Use the pattern to explain why 0.999… = 1.
Create a Recipe — Fractions in Context
Design a recipe problem and solve it.
Write your own recipe that serves 4. Then scale it to serve 7 people. Show all fraction calculations.
If all your ingredients are priced by kg, estimate the total cost of the scaled recipe.
Reflection: Fractions vs Decimals
Summarise your understanding.
When would you prefer to work with a fraction rather than a decimal? Give two examples.
What is the most challenging operation (add, subtract, multiply, divide) with fractions? Why?
Design a 'fraction fact card' — 5 key rules or facts a student should know about fraction operations.
Fractions and Decimals at Home
Apply fraction and decimal skills in everyday situations.
- 1Find three recipes and scale each to different numbers of servings using fraction arithmetic.
- 2At the supermarket or in a catalogue, calculate unit prices ($ per 100 g or per litre) using decimal division.
- 3Measure household items in both fractions (of a metre) and decimals. List five items with both forms.
- 4Play 'fraction snap': write fractions and decimals on cards and match equivalent pairs.
- 5Investigate: what happens when you calculate 1 ÷ 3, 1 ÷ 7, 1 ÷ 11 on a calculator? What patterns do you see?
Extending — Fraction and Decimal Proof
Use algebraic or logical reasoning to explain each result.
Prove algebraically that any fraction a/b ÷ c/d = ad/bc. Write your proof step by step.
A student claims: 'Dividing by a fraction always makes the result larger than the original.' Is this always, sometimes, or never true? Justify with examples.
Extending — Egyptian Fractions Investigation
Every positive fraction can be written as a sum of distinct unit fractions (fractions with numerator 1).
Write 7/12 as a sum of two distinct unit fractions. Show your working.
Write 5/6 as a sum of three distinct unit fractions in two different ways.
Research: why did the ancient Egyptians use unit fractions? Write 2–3 sentences.