Below are the intermediate topics available for the category "Ratio proportion rate" at ** Free Maths Games**.

These free maths topics offer a complete set of basic Ratio proportion rate topics for intermediate pupils aged 11 to 14. The Ratio proportion rate category is divided into sub-categories such as "Place value: measures", "Ratio", "Compound units", etc. Each sub-category has multiple sub-sub-categories, and within them are the topics with between 6 and 10 question and answer pairs for the lessons, plus additional question answer pairs for the games and tests.

For each question/answer pair in a topic you get the question as picture, equation or text, the spoken question read by a robot, and an answer as both number or text and as audio. For most topics there are also 3 wrong answers prepared for each question.

mm → cm

Convert mm into cm

Convert lengths given in millimetres (mm) to centimetres (cm) by dividing the value by 10

g → mg

Convert grams to milligrams

Convert masses given in grams (g) to milligrams (mg) by multiplying the value by 1000

1 kg → 1000 g

Convert kilograms to grams

Convert masses given in kilograms (kg) to grams (g) by multiplying the value by 1000

cm → m

Convert cm to m

Convert lengths given in centimetres (cm) into metres (m) by dividing the value by 100

1 t → 1000 kg

Convert tonnes to kilograms

Convert masses given in tonnes (t) into kilograms (kg) by multiplying by 1000

m → km

Convert m to km

Convert distances given in metres (m) into kilometres (km) by dividing the value by 1000

km → m

Convert km to m

Convert distances given in kilometres (km) into metres (m) by multiplying by 1000

m → cm

Convert m to cm

Convert lengths given in metres (m) into centimetres (cm) by multiplying by 100

cm → mm

Convert cm to mm

Convert lengths given in centimetres (cm) into millimetres (mm) by multiplying by 10

cm³ → L

ml → L

ml → L

Convert cm³ or ml to litres (L)

Convert volumes given in cubic centimetres (cm³) or millilitres (ml) to litres (L) by multiplying by 1000

1 L :

1000 ml

1000 ml

Convert L to ml

Convert volumes given in litres (L) into millilitres (ml) by multiplying by 1000

1 L :

1000 cm³

1000 cm³

Convert L to cm³

Convert litres (L) to cubic centimetres (cm³) by multiplying by 1000

15:17

Express quantities as ratios

Express each of the sets of quantities as a part to part ratio, simplified if possible

6:10 → 3:5

Ratio in its simplest form

Use division to express each ratio in its simplest form

1:2 → 3:6

Equivalent ratios

Identify the ratios that are equivalent e.g. 1:2 and 3:6

30 @ 2:1

is 20:10

is 20:10

Share a quantity into parts

Add up the parts and divide the quantity by the total number of parts to get the different shares

d=10m, t=2s

s = 5m/s

s = 5m/s

Calculate speed

Use the speed formula speed s = distance d / time t to calculate speeds to 1 d.p.

Fastest speed, slowest speed

Using speed time graphs identify the highest speed or the lowest speed attained

s=10m/s, t=2s

d = 20m

d = 20m

Calculate distance, time

Re-arrange the speed formula to calculate distance or time to 1 d.p.

mile → km

Convert miles to kilometres

Use the approximation 1 mile ≈ 1.6 km to convert imperial miles to metric kilometres (km)

inches → cm

Convert inches to cm

Use the approximation 1 inch ≈ 2.54 cm to convert imperial inches (") to metric centimetres (cm) to 2 d.p.

mile → km

Convert km to miles

Use the approximation 1.6 kilometres ≈ 1 mile to convert distances in kilometres to imperial miles to 1 d.p.

cm → inches

Convert cm to inches

Use the approximation 1 inch ≈ 2.5 cm to convert centimetres to imperial inches

cm → feet

Convert cm to feet

Use the approximation 1 foot ≈ 30 cm to convert lengths in centimetres (cm) to imperial feet (') to 1 d.p.

3 of 15

is 20%

is 20%

Express as a percentage

Express quantities as percentages by creating a fraction and multiplying by 100

cm³ → L

ml → L

ml → L

Convert cm³ or ml to litres (L)

Convert volumes given in cubic centimetres (cm³) or millilitres (ml) to litres (L) by multiplying by 1000

1 L :

1000 ml

1000 ml

Convert L to ml

Convert volumes given in litres (L) into millilitres (ml) by multiplying by 1000

1 L :

1000 cm³

1000 cm³

Convert L to cm³

Convert litres (L) to cubic centimetres (cm³) by multiplying by 1000

1 m³ :

1000000 cm³

1000000 cm³

Convert m³ to cm³

Convert cubic metres (m³) to cubic centimetres (cm³) by multiplying by 1,000,000

1 cm³ :

1000 mm³

1000 mm³

Convert cm³ to mm³

Convert cubic centimetres (cm³) to cubic millimetres (mm³) by multiplying by 1000

15:17

Express quantities as ratios

Express each of the sets of quantities as a part to part ratio, simplified if possible

½ = 1:2

Express fractions as ratios

Express each of the given fractions as a part to whole ratio

25% = 1:4

Express percentages as ratios

Express each of the given percentages as a part to whole ratio

0.25 = 1:4

Express decimals as ratios

Express each of the given decimals as a part to whole ratio

6:10 → 3:5

Ratio in its simplest form

Use division to express each ratio in its simplest form

1:2 → 3:6

Equivalent ratios

Identify the ratios that are equivalent e.g. 1:2 and 3:6

30 @ 2:1

is 20:10

is 20:10

Share a quantity into parts

Add up the parts and divide the quantity by the total number of parts to get the different shares

d=10m, t=2s

s = 5m/s

s = 5m/s

Calculate speed

Use the speed formula speed s = distance d / time t to calculate speeds to 1 d.p.

Fastest speed, slowest speed

Using speed time graphs identify the highest speed or the lowest speed attained

D = M / V

Density

In each instance calculate the density using the density formula d = mass / volume to 1 d.p.

unit price

Unit price: best value

Identify the better value for money option by doing unit price calculations

s=10m/s, t=2s

d = 20m

d = 20m

Calculate distance, time

Re-arrange the speed formula to calculate distance or time to 1 d.p.

mile → km

Convert miles to kilometres

Use the approximation 1 mile ≈ 1.6 km to convert imperial miles to metric kilometres (km)

inches → cm

Convert inches to cm

Use the approximation 1 inch ≈ 2.54 cm to convert imperial inches (") to metric centimetres (cm) to 2 d.p.

mile → km

Convert km to miles

Use the approximation 1.6 kilometres ≈ 1 mile to convert distances in kilometres to imperial miles to 1 d.p.

cm → inches

Convert cm to inches

Use the approximation 1 inch ≈ 2.5 cm to convert centimetres to imperial inches

cm → feet

Convert cm to feet

Use the approximation 1 foot ≈ 30 cm to convert lengths in centimetres (cm) to imperial feet (') to 1 d.p.

Jack +10%

Increase by a percentage

Derive the actual increase from the percentage increase and add it to the original quantity or amount

Jack -10%

Decrease by a percentage

Derive the actual decrease from the percentage decrease and subtract it from the original quantity

3 of 15

is 20%

is 20%

Express as a percentage

Express quantities as percentages by creating a fraction and multiplying by 100

Jack +10%

Calculate percentage increase

Get the percentage increase by expressing the increase as a fraction of the original and multiplying by 100

Jack -10%

Calculate percentage decrease

Get the percentage decrease by expressing the decrease as a fraction of the original and multiplying that amount by 100

45 + 12%

is 50.4

is 50.4

Increase by % with calculator

Derive the actual increase from the percentage increase and add it to the original quantity or amount (to 1 d.p.)

24 - 6%

is 22.56

is 22.56

Decrease by % with calculator

Calculate the new quantity or amount by using a decimal multiplier; answers to 2 d.p.

54 of 72

is 75%

is 75%

Express quantities as % with calculator

Express quantities of wholes as percentages by converting to a fraction and multiplying by 100 to (1 d.p.)

1 m³ :

1000000 cm³

1000000 cm³

Convert m³ to cm³

Convert cubic metres (m³) to cubic centimetres (cm³) by multiplying by 1,000,000

1 cm³ :

1000 mm³

1000 mm³

Convert cm³ to mm³

Convert cubic centimetres (cm³) to cubic millimetres (mm³) by multiplying by 1000

Directly or inversely proportional

Identify which of the graphs and equations are directly proportional, inversely proportional or neither

Direct proportion problems

Solve problems involving direct proportion where two quantities increase at the same rate

Inverse proportion problems

Solve problems involving inverse proportion where one quantity increases as the other decreases (to 2 d.p.)

½ = 1:2

Express fractions as ratios

Express each of the given fractions as a part to whole ratio

25% = 1:4

Express percentages as ratios

Express each of the given percentages as a part to whole ratio

0.25 = 1:4

Express decimals as ratios

Express each of the given decimals as a part to whole ratio

1:2 → 3:6

Equivalent ratios

Identify the ratios that are equivalent e.g. 1:2 and 3:6

1:4 → 1/5

Express ratios as fractions

Express part to part ratios as fraction proportions of the whole

1:4 = 25%

Express ratios as percentages

Express each part to whole ratio as a part to whole percentage

Jack and Jill

3:4

3:4

Specific parts and quantity

Pair up specific quantities with specific parts

1 : 30,000

Actual distance

Work out the real distance between two points represented on maps and scale diagrams (to 2 d.p.)

22.74 km

1:40,000

1:40,000

Distance on a map or diagram

Use a scale and an actual distance to work out the distance between 2 points on a map or scale diagram to 2 d.p.

In addition to the Ratio proportion rate topics shown above, the intermediate section of Free Maths Games has 4 other top level categories of topics to choose from. Each top level category offers a full breadth of topics to cover the intermediate curriculum. Use these topics to reinforce key maths concepts in a fun and engaging way that will keep your pupils enthused and energised with the maths they are learning. The top level categories available are:

Intermediate math home | Intermediate topics | Intermediate lessons | Intermediate games | Intermediate tests

Preschool maths | Beginner maths | Intermediate maths

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