Year 8 Fractions, decimals and percentages: revision mind map

1Equivalent fractions

Multiply or divide the top and bottom by the same number.

$\tfrac23 = \tfrac{8}{12}$   $\tfrac{18}{24} = \tfrac34$

2Operations with fractions

Add or subtract: common denominator first. Divide: flip the second fraction and multiply.

$\tfrac23 + \tfrac14 = \tfrac{8}{12} + \tfrac{3}{12} = \tfrac{11}{12}$

$1\tfrac12 \times \tfrac23 = \tfrac32 \times \tfrac23 = 1$   $\tfrac34 \div \tfrac12 = \tfrac32$

3Negative fractions

The same sign rules as integers.

$-\tfrac12 + \tfrac13 = -\tfrac36 + \tfrac26 = -\tfrac16$

$-\tfrac23 \times \left(-\tfrac34\right) = \tfrac12$

4Understanding decimals

Compare place by place, starting from the left.

0.305 is 3 tenths and 5 thousandths

0.5 is bigger than 0.45: 5 tenths beats 4 tenths

Watch out: more digits doesn't mean bigger.

5Operations with decimals

Line up the decimal points to add or subtract. To multiply, count the decimal places. To divide, make the divisor whole.

$2.75 + 1.4 = 4.15$

$0.3 \times 0.2 = 0.06$ (two decimal places)

$4.8 \div 0.6 = 48 \div 6 = 8$

6Recurring decimals and rounding

Divide the top by the bottom. It either stops (terminating) or repeats (recurring).

$\tfrac38 = 0.375$   $\tfrac13 = 0.\dot{3}$   $\tfrac{2}{11} = 0.\dot{1}\dot{8}$

2.467 to 1 decimal place is 2.5

7Converting

Fraction to decimal: divide. Decimal to percentage: multiply by 100.

$\tfrac35 = 0.6 = 60\%$

$\tfrac18 = 0.125 = 12.5\%$

$7\% = 0.07 = \tfrac{7}{100}$

8Finding percentages

Percentage of an amount: multiply. Express as a percentage: divide and multiply by 100.

25% of 80 is 20

18 out of 40: $\tfrac{18}{40} \times 100\% = 45\%$

9Increasing and decreasing

Use a multiplier: 100% plus the increase, or 100% minus the decrease.

Up 15%: $60 \times 1.15 = 69$

Down 20%: $45 \times 0.8 = 36$

10Percentage change, profit and loss

% change $= \dfrac{\text{change}}{\text{original}} \times 100\%$

Bought for $50, sold for $65: profit $15, $\tfrac{15}{50} = 30\%$

11The unitary method

Find what 1% is worth, then multiply to get what you need.

15% of an amount is $60

1% is $60 \div 15 = \$4$, so 100% is $\$400$

Check: 15% of $400 is $60 ✓