Simplifying fractions | Maths | Quizalize & Oak National Academy

Starter quiz

What word should go in the blank spaces to complete the following statement? Terminating __________ have a finite number of __________ places.

'decimal' ✓
Write $0.825$ as a simplified fraction.

$7\over8$

$825\over1000$

$33\over40$ ✓

$31\over40$

$15\over16$
The fraction which is halfway between 0.2 and 0.9 is $\square \over 20$ . What number should be written in the square? ______

'11' ✓
Which of the following are equivalent to $5.555$ ?

$1111\over200$ ✓

$5555\over200$

$5 \frac{55}{200}$

$5 \frac{111}{200}$ ✓
Match each decimal to a fraction with the denominator in exponential form.

$0.00067$

⇔

$\frac{67}{10^5}$ ✓

$6.7$

⇔

$\frac{67}{10^1}$ ✓

$0.067$

⇔

$\frac{67}{10^3}$ ✓

$0.67$

⇔

$\frac{67}{10^2}$ ✓
Sofia writes $12.34 = \frac {1234}{10^ \square}$ . What number should she write in the box to make her statement true? ______

'2' ✓

Complete the statement. A ______ is a term which exactly divides another term.

'factor' ✓
Select all the fractions that simplify to $2 \over 3$ .

$8\over 12$ ✓

$9\over 12$

$15\over 18$

$12\over 18$ ✓

$9\over 15$
Which of the following factors of 24 and 90 is the best choice to efficiently simplify $24\over90$ ?

3

6 ✓

12

15
Write 180 as a product of prime factors.

$2^2 \times 3^2 \times 5$ ✓

$2 \times 3^2 \times 5$

$2 \times 3^2 \times 5^2$

$2 \times 3 \times 5$

$2^2 \times 3^2 \times 5^2$
Which of these fractions is equivalent to $360 \over 700$

$\frac{2^2 \times 3^2 \times 5}{2^2 \times 5^2 \times7}$

$\frac{2^3 \times 3^2 \times 5}{2^2 \times 5 \times7}$

$\frac{2^3 \times 3^2 \times 5^2}{2^2 \times 5^2 \times7^2}$

$\frac{2^3 \times 3^2 \times 5}{2^2 \times 5^2 \times7}$ ✓

$\frac{2^3 \times 3 \times 5}{2^2 \times 5 \times7}$
Match each fraction to its simplified equivalent fraction. Use the fact that $120 = 2^3 \times 3 \times 5$ ; $84 = 2^2 \times 3 \times 7$ and $210 = 2 \times 3 \times 5 \times 7$

$84\over210$

⇔

$2\over5$ ✓

$84\over120$

⇔

$7\over10$ ✓

$120\over210$

⇔

$4\over7$ ✓

$120\over84$

⇔

$1 \frac{3}{7}$ ✓

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When a fraction is multiplied by 1 it remains the same but may look different.
Simplifying fractions can be shown to be the inverse of multiplying to find equivalent fractions.
A fraction can be written more simply but remain equivalent by dividing the numerator and denominator by a common factor
A fraction can be written in simplest form by dividing the numerator.

Pupils may think they just 'get rid' of integers which appear in both numerator and denominator.

Reinforce that you are multiplying by 1, which doesn't change the value and therefore can be omitted from further calculations.

Factor - A factor is a term which exactly divides another term.
Highest common factor - The highest common factor is the common factor which can be divided by all other possible common factors.
Product of primes - Expressing a number as a product of primes means writing it uniquely as a product of its factors that are prime numbers.