Addition & Subtraction with Fractions (SQA National 5 Maths): Revision Note

You should be familiar with converting between equivalent fractions from your National 4 Maths course.

(a) Evaluate $3\frac{1}{3}+\frac{3}{5}$.

(b) Evaluate $5\frac{1}{4}-\frac{5}{8}$.

Answer:

Part (a)

Change $3\frac{1}{3}$ into an improper fraction

• Multiply the denominator by the whole part and add to the numerator

• Write this value over the denominator

$3\frac{1}{3}=\frac{3\times 3+1}{3}=\frac{10}{3}$

So

$3\frac{1}{3}+\frac{3}{5}=\frac{10}{3}+\frac{3}{5}$

Find the lowest common denominator of 3 and 5

• 15 is the smallest number that can be divided by both 3 and 5

The lowest common denominator is 15

Write both fractions as equivalent fractions with a common denominator of 15

• Multiply the numerator and denominator of the first fraction by 5

• Multiply the numerator and denominator of the second fraction by 3

$\frac{10\times 5}{3\times 5}+\frac{3\times 3}{5\times 3}=\frac{50}{15}+\frac{9}{15}$ 

Add the numerators and write over a single denominator

$\frac{50+9}{15}=\frac{59}{15}$ 

The question does not specify a form for the answer, so you can give it as either that improper fraction, or as a mixed number

$\frac{59}{15}\left(\mathrm{or}3\frac{14}{15}\right)$

Part (b)

Change $5\frac{1}{4}$ into an improper fraction

• Multiply the denominator by the whole part and add to the numerator

• Write this value over the denominator

$5\frac{1}{4}=\frac{5\times 4+1}{4}=\frac{21}{4}$ 

So

$5\frac{1}{4}-\frac{5}{8}=\frac{21}{4}-\frac{5}{8}$

Find the lowest common denominator of 4 and 8

• 8 is the smallest number that by divided by both 4 and 8

The lowest common denominator is 8

Write both fractions as equivalent fractions over 8

• Multiply the numerator and denominator of the first fraction by 2

$\frac{21\times 2}{4\times 2}-\frac{5}{8}=\frac{42}{8}-\frac{5}{8}$

Subtract the numerators and write over a single denominator

$\frac{42-5}{8}=\frac{37}{8}$

The question does not specify a form for the answer, so you can give it as either that improper fraction, or as a mixed number

$\frac{37}{8}\left(\mathrm{or}4\frac{5}{8}\right)$