Convert the first fraction so that it is an improper fraction

$1 \frac{7}{12} = \frac{12 \times 1 + 7}{12} = \frac{19}{12}$

The lowest common multiple of $12$ and $20$ can be found by listing the first few multiples

Multiples of $12 : 12, 24, 36, 48, 60 . . .$

Multiples of $20 : 20, 40, 60 . . .$

The lowest common multiple of $12$ and $20$ is $60$

Find the equivalent fraction to $\frac{19}{12}$ with the denominator of $60$ , by multiplying the numerator and denominator by 5

$\frac{19 \times 5}{12 \times 5} = \frac{95}{60}$

Find the equivalent fraction to $\frac{13}{20}$ with the denominator of $60$ , by multiplying the numerator and denominator by 3

$\frac{13 \times 3}{20 \times 3} = \frac{39}{60}$

[1]

Now that both fractions have a common denominator, add the two fractions together

$\frac{95}{60} + \frac{39}{60}$

[1]

$= \frac{95 + 39}{60}$

$= \frac{134}{60}$

Convert the fraction back to a mixed number

$\frac{134}{60} = \frac{120}{60} + \frac{14}{60}$

$= 2 \frac{14}{60}$

Simplify the fraction fully by dividing the numerator and denominator by 2

$2 \frac{7}{30}$ [1]

Operations with Fractions (CIE IGCSE Maths: Core)

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