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Operations with fractions Quiz

Grade 3 • 3B • 10 Questions (35 Marks)

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Score: 0 / 10
Operations with fractions — Notes & Worked Examples Show / Hide

Explanation:

Before adding, subtracting, multiplying, or dividing mixed numbers, always convert any mixed numbers into improper (top-heavy) fractions first. To add or subtract fractions, find a common denominator, convert both numerators, and then add or subtract the numerators only.

To multiply fractions, multiply the numerators together and multiply the denominators together. To divide by a fraction, use Keep, Change, Flip: keep the first fraction, change ÷ to ×, and flip the second fraction upside down. Simplify your final answer and convert back to a mixed number if required.

Example 1: Work out 234 − 125

Solution:

Improper fractions: 114 − 75
Common denominator of 4 and 5 is 20:
= 5520 − 2820 = 2720
Answer: 1720

Example 2: Work out 145 ÷ 310

Solution:

Improper fraction: 145 = 95
Keep, Change, Flip: 95 × 103
Multiply across: 9 × 105 × 3 = 9015
Answer: 6
Question 1 AQA Jun 2018 1F Q7
[2 marks]
A rectangular carpet measures 8 m by 6 m
Part of the carpet is covered by a square rug of length 2 m
8 m6 m2 mNot drawnaccurately
Show that 112 of the carpet is covered by the rug.
Worked Solution & Answer
Area of carpet = 8 × 6 = 48 m2 M1
Area of rug = 2 × 2 = 4 m2
Fraction of carpet covered = 448 = 112 C1
Question Paper (PDF) • Mark Scheme (PDF)
Question 2 IGCSE Nov 2020 2F Q15
[2 marks]
Show that 25 ÷ 1120 = 811
Worked Solution & Answer
(2/5) ÷ (11/20) = (2/5) × (20/11) = 40/55 = 8/11 M1 C1
Answer: 25 × 2011 = 4055 = 811
Question Paper (PDF) • Mark Scheme (PDF)
Question 3
[2 marks]
Work out 67 × 512
Give your answer as a fraction in its simplest form.
Worked Solution & Answer
(6 × 5) / (7 × 12) = 30 / 84 = 5 / 14 M1 A1
Answer: 514
Question Paper (PDF) • Mark Scheme (PDF)
Question 4
[3 marks]
Work out 35 ÷ 16
Give your answer as a mixed number.
Worked Solution & Answer
3/5 × 6/1 = 18/5 = 3 3/5 M2 A1
Answer: 335
Question Paper (PDF) • Mark Scheme (PDF)
Question 5 Specimen Set 2 1H Q6
[4 marks]
Work out
(a) Work out 2 1/4 × 3 1/3 (3) (b) Place 3, 4, 5 and 6 in the boxes for greatest total. (1)
(a) Work out 214 × 313
Give your answer as a mixed number in its simplest form. [3 marks]
(b) Write the numbers 3, 4, 5 and 6 in the boxes to give the greatest possible total.
You may write each number only once. [1 mark]
1+2
Worked Solution & Answer
(a)
9/4 × 10/3 = 90/12 = 15/2 = 7 1/2 M2 A1
Answer (a): 712
(b)
Largest whole numbers are 5 and 6
put smaller denominator 3 under larger numerator 2: 5 1/4 + 6 2/3 = 11 11/12 B1
1+25463
Answer (b): 514 + 623
Question Paper (PDF) • Mark Scheme (PDF)
Question 6 OCR Jun 2025 3F Q12
[4 marks]
The diagram shows a large rectangle made from 10 smaller rectangles of equal area.
The large rectangle is divided into two unequal parts, A and B.
AB
(a) Tick (✓) all the correct statements.
@@TABULAR0@@ [2 marks]
(b) The area of Part A is 18k.
Write an expression, in terms of k, for the area of Part B.
Give your answer in its simplest form. [2 marks]
Worked Solution & Answer
(a)
(The area of a rectangle is length × width)
Part A has 3 small rectangles and Part B has 7 small rectangles out of 10 M1
So A : B = 3 : 7 and A is 3/10 of the large rectangle. A1
Answer (a): Tick 2nd row (A : B = 3 : 7) and 3rd row (A is 3/10 of the large rectangle)
(b)
(The area of a rectangle is length × width)
1 small rectangle = 18k ÷ 3 = 6k M1
Area of Part B (7 small rectangles) = 7 × 6k = 42k. A1
Answer (b): 42k
Question Paper (PDF) • Mark Scheme (PDF)
Question 7
[4 marks]
Work out
(a) Work out 5/12 + 1/6. (2) (b) Work out 3/10 × 5/8 in its simplest form. (2)
(a) Work out 512 + 16 [2 marks]
(b) Work out 310 × 58
Give your answer as a fraction in its simplest form. [2 marks]
Worked Solution & Answer
(a)
5/12 + 2/12 = 7/12 M1 A1
Answer (a): 712
(b)
15/80 = 3/16 M1 A1
Answer (b): 316
Question Paper (PDF) • Mark Scheme (PDF)
Question 8
[4 marks]
(a) Work out 2/3 – 1/5 (2) (b) Work out 2/3 × 3/4 in its simplest form (2)
(a) Work out 23 - 15 [2 marks]
(b) Work out 23 × 34
Give your answer as a fraction in its simplest form. [2 marks]
Worked Solution & Answer
(a)
10/15 – 3/15 = 7/15 M1 A1
Answer (a): 715
(b)
6/12 = 1/2 M1 A1
Answer (b): 12
Question Paper (PDF) • Mark Scheme (PDF)
Question 9 IGCSE Nov 2023 1F Q5
[4 marks]
Here is a shape made of squares.
(a) Shade 23 of the shape. [1 mark]
(b) Write 310 as a percentage. [1 mark]
%
(c) Write 48150 as a fraction in its simplest form. [1 mark]
(d) Write 467 as a mixed number. [1 mark]
Worked Solution & Answer
(a)
(2/3) × 12 = 8 squares B1
Answer (a): 8 squares shaded
(b)
3/10 = 30/100 = 30% B1
Answer (b): 30 %
(c)
Divide top and bottom by 6: 48/150 = 8/25 B1
Answer (c): 825
(d)
46 ÷ 7 = 6 remainder 4 → 6 4/7 B1
Answer (d): 647
Question Paper (PDF) • Mark Scheme (PDF)
Question 10 IGCSE Jan 2019 2FR Q3
[6 marks]
(a) Shade 3/7 (1) (b) 23/3 as mixed number (1) (c) 2/5 of 60 cm (2) (d) Is 1/6 halfway between 1/4 and 1/8? (2)
(a) Shade 37 of the rectangle. [1 mark]
(b) Write 233 as a mixed number. [1 mark]
(c) Find 25 of 60 cm. [2 marks]
cm
(d) Is Claude correct?
You must give a reason for your answer. [2 marks]
Worked Solution & Answer
(a)
9 squares shaded
Answer (a): 9 squares shaded
(b)
723
Answer (b): 723
(c)
To change an improper fraction to a mixed number, divide the top by the bottom and write the remainder over the denominator. M1
e.g. 114 = 234
Answer: 24 A1
Answer (c): 24 cm
(d)
1/4 = 4/16, 1/8 = 2/16, halfway = 3/16 ≠ 1/6 M1 C1
Answer (d): No — halfway is 316, not 16
Question Paper (PDF) • Mark Scheme (PDF)
Score: 0 / 10 (0 / 35 marks)
Operations with fractions Worksheets Next: Estimation →

Grade 3 Quizzes

24 Topics
3A - Error intervals3B - Operations with fractions
3C - Estimation3D - Writing and simplifying ratio
3E - Ratio3F - Proportion recipes
3G - Percentages3H - Percentage change
3J - Exchange rates3K - Conversions and units
3L - Scale drawings3M - Best buy questions
3N - Substitution3P - Solving linear equations
3Q - Straight line graphs3R - Area and circumference
3S - Rotations3T - Reflections
3U - Enlargements3V - Translations
3W - Mixed transformations3X - Area of compound shapes
3Y - Frequency trees3Z - Two way tables