1.4 Fractions | IGCSE Mathematics 0580

1. Addition and Subtraction

Find the lowest common multiple (LCM) of the denominators.
Write each fraction as an equivalent fraction with the LCM as its denominator.
Add or subtract the numerators and keep the denominator: $\frac{a}{b} \pm \frac{c}{d} = \frac{a d \pm b c}{b d}$ .
Simplify the answer by dividing by the highest common factor, and write improper answers as mixed numbers.

1.Calculate

\frac{3}{4} + \frac{2}{5}

Common denominator: LCM of 4 and 5 is 20

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2.Calculate

\frac{7}{9} - \frac{2}{3}

Common denominator: LCM of 9 and 3 is 9

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3.Calculate

\frac{11}{12} - \frac{1}{4}

Common denominator 12, then simplify by dividing by 4

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4.Calculate

\frac{7}{8} - \frac{3}{10}

Common denominator: LCM of 8 and 10 is 40

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Multiply straight across: $\frac{a}{b} \times \frac{c}{d} = \frac{a c}{b d}$ . No common denominator is needed.
Cancel first: divide any numerator and any denominator by a common factor before multiplying.
To divide, keep the first fraction, change ÷ to ×, and flip the second: $\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$ .
Simplify the final answer if possible.

1.Calculate

\frac{2}{3} \times \frac{3}{4}

Cancel first: 3 with 3, and 2 with 4

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2.Calculate

\frac{2}{5} \times \frac{15}{8}

Cancel first: 5 with 15, and 2 with 8

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3.Calculate

\frac{3}{4} \div \frac{2}{5}

Keep, change ÷ to ×, flip the second fraction

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4.Calculate

\frac{5}{8} \div \frac{1}{4}

Flip the second fraction and multiply, cancelling 4 with 8

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To improper: $a \frac{b}{c} = \frac{a c + b}{c}$ , e.g. $3 \frac{2}{5} = \frac{17}{5}$ .
To mixed: divide the numerator by the denominator; the quotient is the whole number and the remainder is the new numerator, e.g. $\frac{11}{4} = 2 \frac{3}{4}$ .
Convert mixed numbers to improper fractions before any operation; this is essential for multiplying and dividing.
Convert back to a mixed number after simplifying the result.

1.Calculate

2 \frac{1}{2} + 1 \frac{2}{3}

Change to improper fractions, then use the common denominator 6

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2.Calculate

3 \frac{3}{4} - 1 \frac{1}{2}

Change to improper fractions, then use the common denominator 4

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3.Calculate

1 \frac{5}{6} \times 2 \frac{2}{3}

Change to improper fractions, then cancel 6 with 8

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4.Calculate

2 \frac{1}{4} \div 1 \frac{1}{2}

Change to improper fractions, flip the second and multiply

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The same rules apply: treat letters like numbers.
Add and subtract using the LCM of the denominators, including the letters: the LCM of $3 x$ and $5 x$ is $15 x$ .
Multiply after cancelling common factors; divide by flipping the second fraction and multiplying.
Cancel letters just like numbers, $\frac{x}{x} = 1$ , so the final answer has no common factors.

Common denominator: LCM of 2 and 3 is 6

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1.Calculate

\frac{x}{3} + \frac{2 x}{9}

Common denominator: LCM of 3 and 9 is 9

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2.Calculate

\frac{3 x}{4} - \frac{x}{8}

Common denominator: LCM of 4 and 8 is 8

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3.Calculate

\frac{3 x}{4 y} + \frac{5}{2 y}

Common denominator: LCM of 4y and 2y is 4y

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4.Calculate

\frac{4 x}{15} \div \frac{2 x}{9}

Flip and multiply, then cancel x, 4 with 2, and 9 with 15

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