Number Foundations practice questions

Question 1

Write $\dfrac{3}{4}$ as a percentage.

Accepted Answer

$\dfrac{3}{4} 	imes 100\% = 75\%$.

Answer

$0.75\%$

Answer

$34\%$

Answer

$75\%$

Answer

$43\%$

Question 2

Write $0.2$ as a fraction in its simplest form.

Accepted Answer

$0.2 = \dfrac{2}{10} = \dfrac{1}{5}$.

Answer

$\dfrac{2}{100}$

Answer

$\dfrac{1}{5}$

Answer

$\dfrac{1}{20}$

Answer

$\dfrac{2}{5}$

Question 3

Find $15\%$ of $80$.

Accepted Answer

$0.15 	imes 80 = 12$.

Answer

$12$

Answer

$15$

Answer

$1.2$

Answer

$20$

Question 4

Which of these is the largest: $\dfrac{3}{5}$, $\ 0.55$, $\ 58\%$?

Accepted Answer

$\dfrac{3}{5} = 0.6$ and $58\% = 0.58$.

Since $0.6 > 0.58 > 0.55$, the largest is $\dfrac{3}{5}$.

Answer

$0.55$

Answer

$58\%$

Answer

$\dfrac{3}{5}$

Answer

They are all equal

Question 5

What is the highest common factor (HCF) of $24$ and $36$?

Accepted Answer

$24 = 2^3 \cdot 3$ and $36 = 2^2 \cdot 3^2$.

Shared primes at their lowest powers: $2^2$ and $3$.

$	ext{HCF} = 4 \cdot 3 = 12$.

Answer

$6$

Answer

$4$

Answer

$12$

Answer

$72$

Question 6

What is the lowest common multiple (LCM) of $6$ and $8$?

Accepted Answer

$6 = 2 \cdot 3$ and $8 = 2^3$.

Highest powers: $2^3$ and $3$.

$	ext{LCM} = 8 \cdot 3 = 24$.

Answer

$2$

Answer

$24$

Answer

$48$

Answer

$14$

Question 7

Which of these numbers is prime?

Accepted Answer

$51 = 3 \cdot 17$, $57 = 3 \cdot 19$, $63 = 7 \cdot 9$.

$59$ has no factor up to $\sqrt{59} < 8$, so $59$ is prime.

Answer

$51$

Answer

$57$

Answer

$59$

Answer

$63$

Question 8

Which is the prime factorisation of $60$?

Accepted Answer

$60 = 2 \cdot 30 = 2 \cdot 2 \cdot 15 = 2^2 \cdot 3 \cdot 5$.

Answer

$2 \cdot 3 \cdot 5$

Answer

$2^2 \cdot 3 \cdot 5$

Answer

$2^2 \cdot 15$

Answer

$2^3 \cdot 3 \cdot 5$

Question 9

Work out $2 + 3 	imes 4$.

Accepted Answer

$3 	imes 4 = 12$, then $2 + 12 = 14$.

Answer

$20$

Answer

$14$

Answer

$9$

Answer

$10$

Question 10

Work out $(5 + 1)^2 \div 4$.

Accepted Answer

$(5 + 1)^2 = 6^2 = 36$, then $36 \div 4 = 9$.

Answer

$9$

Answer

$1.5$

Answer

$6.25$

Answer

$3$

Number Foundations

Problems & worked solutions

Problem 1 — Fractions, Decimals & Percentages

Problem 2 — Fractions, Decimals & Percentages

Problem 3 — Fractions, Decimals & Percentages

Problem 4 — Fractions, Decimals & Percentages

Problem 5 — Integers, Primes, HCF & LCM

Problem 6 — Integers, Primes, HCF & LCM

Problem 7 — Integers, Primes, HCF & LCM

Problem 8 — Integers, Primes, HCF & LCM

Problem 9 — Order of Operations & Calculation

Problem 10 — Order of Operations & Calculation

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