Year 7 Fractions and percentages: revision mind map

1Introduction to fractions

The bottom says how many equal parts. The top says how many you have.

$\tfrac34$: 3 of 4 equal parts

Improper: $\tfrac54$ is more than a whole

2Equivalent fractions

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

$\tfrac34 = \tfrac68$

Simplify: $\tfrac{12}{18} = \tfrac23$

3Mixed and improper

Multiply the whole by the bottom, then add the top.

$2\tfrac13 = \tfrac73$

$\tfrac{11}{4} = 2\tfrac34$

4Ordering fractions

Rewrite with a common denominator, then compare the tops.

$\tfrac23$ and $\tfrac34$: $\tfrac{8}{12} < \tfrac{9}{12}$, so $\tfrac23 < \tfrac34$

5Adding fractions

Common denominator first, then add the tops only.

$\tfrac14 + \tfrac24 = \tfrac34$

$\tfrac12 + \tfrac13 = \tfrac36 + \tfrac26 = \tfrac56$

$1\tfrac12 + 2\tfrac13 = 3\tfrac56$

Watch out: don't add the bottoms: $\tfrac12 + \tfrac13 \ne \tfrac25$

6Subtracting fractions

Common denominator first, then subtract the tops.

$\tfrac34 - \tfrac13 = \tfrac{9}{12} - \tfrac{4}{12} = \tfrac{5}{12}$

$2\tfrac12 - \tfrac34 = \tfrac{10}{4} - \tfrac34 = 1\tfrac34$

7Multiplying fractions

Top times top, bottom times bottom. No common denominator needed.

$\tfrac23 \times \tfrac35 = \tfrac{6}{15} = \tfrac25$

$\tfrac12$ of 12 is 6

8Dividing fractions

Flip the second fraction, then multiply.

$\tfrac34 \div \tfrac18 = \tfrac34 \times 8 = 6$

$\tfrac23 \div 4 = \tfrac23 \times \tfrac14 = \tfrac16$

9Fractions and percentages

Per cent means out of 100.

$\tfrac14 = 25\%$   $\tfrac35 = 60\%$

$35\% = \tfrac{35}{100} = \tfrac{7}{20}$

10Percentage of a number

Find 10% first, or multiply by the percentage as a fraction.

10% of 60 is 6, so 20% of 60 is 12

15% of 80: $\tfrac{15}{100} \times 80 = 12$

11Introduction to ratios

A ratio compares amounts. Order matters.

3 red and 5 blue: red to blue is 3 : 5

Simplify: $6 : 8 = 3 : 4$

12Problems with ratios

Add the parts, find one part, then multiply.

$40 in the ratio 3 : 5: 8 parts, 1 part = $5

So $15 and $25