Fractions

A fraction is made up of:

$$ \dfrac{numerator}{denominator} $$

To write a fraction as a decimal, divide the top number by the bottom number:

$$ \dfrac{1}{2} = 1\div2 = 0.5 $$

To divide a fraction, turn it upside down and multiply:

$$ \dfrac{1}{2} \div \dfrac{3}{4} = \dfrac{1}{2} \times \dfrac{4}{3} = \dfrac{4}{6} = \dfrac{2}{3} $$

When adding and subtracting fractions, the denominators must be the same

$$ \dfrac{1}{2} + \dfrac{3}{4} = \dfrac{2}{4} + \dfrac{3}{4} = \dfrac{5}{4} = 1\dfrac{1}{4} $$

To convert a fraction to a decimal, divide the numerator by the denominator

To convert a decimal to a fraction, place the decimal number over the place value

$$ 0.65 = \dfrac{65}{100} = \dfrac{13}{20} $$

Significant Figures and Decimal Points

The first significant figure is the first non-zero digit in a number

$$ 1361 \,\textrm{to}\, \,\textrm{2 s.f.}\, = 1400 $$

For decimal places count after the decimal point from left to right

$$ 7.1361 \,\textrm{to}\, \,\textrm{2 d.p.}\, = 7.14 $$

Percentages

$x$ as a percentage of $y$

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