# Ratio proportion rate topics for Secondary

Below are the Secondary topics available for the category "Ratio proportion rate" at Free Math Games.

These free math topics offer a complete set of basic Ratio proportion rate topics for Secondary pupils (Grade 7 to Grade 9, ages 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.

### Ratio proportion rate ➔ Place value: measures

#### Ratio proportion rate ➔ Place value: measures ➔ Distance

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

#### Ratio proportion rate ➔ Place value: measures ➔ Mass

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

#### Ratio proportion rate ➔ Place value: measures ➔ Distance

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

#### Ratio proportion rate ➔ Place value: measures ➔ Mass

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

#### Ratio proportion rate ➔ Place value: measures ➔ Distance

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

#### Ratio proportion rate ➔ Place value: measures ➔ Volume

cm³ → L

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

### Ratio proportion rate ➔ Ratio

#### Ratio proportion rate ➔ Ratio ➔ Ratio notation

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

#### Ratio proportion rate ➔ Ratio ➔ Ratio problems

30 @ 2:1
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

### Ratio proportion rate ➔ Compound units

#### Ratio proportion rate ➔ Compound units ➔ Problem solving

d=10m, t=2s
s = 5m/s
Calculate speed
Use the speed formula speed s = distance d / time t to calculate speeds to 1 d.p.
Speed from a graph
Using speed time graphs find the speed at the given time
Fastest speed, slowest speed
Using speed time graphs identify the highest speed or the lowest speed attained
s=10m/s, t=2s
d = 20m
Calculate distance, time
Re-arrange the speed formula to calculate distance or time to 1 d.p.

### Ratio proportion rate ➔ Imperial to metric

#### Ratio proportion rate ➔ Imperial to metric ➔ Length

mile → km
Convert miles to kilometres
Use the approximation 1 mile ≈ 1.6 km to convert imperial miles to kilometres
inches → cm
Convert inches to cm
Use the approximation 1 inch ≈ 2.54 cm to convert imperial inches to centimetres to 2 d.p.

### Ratio proportion rate ➔ Metric to imperial

mile → km
Convert km to miles
Use the approximation 1.6 kilometres ≈ 1 mile to convert 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 centimetres to imperial feet to 1 d.p.

### Ratio proportion rate ➔ Percentages

#### Ratio proportion rate ➔ Percentages ➔ Non calculator

3 of 15
is 20%
Express as a percentage
Express quantities as percentages by creating a fraction and multiplying by 100

### Ratio proportion rate ➔ Place value: measures

#### Ratio proportion rate ➔ Place value: measures ➔ Volume

cm³ → L

ml → L
Convert cm³ or ml to litres (L)
Convert volumes given in cubic centimetres (cm³) or millilitres (ml) to litres (L)
1 L :
1000 ml
Convert litres to millilitres
Convert volumes given in litres (L) into millilitres (ml) by multiplying by 1000
1 L :
1000 cm³
Convert litres to cm³
Convert litres (L) to cubic centimetres (cm³) by multiplying by 1000
1 m³ :
1000000 cm³
Convert m³ to cm³
Convert cubic metres (m³) to cubic centimetres (cm³) by multiplying by 1,000,000
1 cm³ :
1000 mm³
Convert cm³ to mm³
Convert cubic centimetres (cm³) to cubic millimetres (mm³) by multiplying by 1000

### Ratio proportion rate ➔ Ratio

#### Ratio proportion rate ➔ Ratio ➔ Ratio notation

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

#### Ratio proportion rate ➔ Ratio ➔ Ratio problems

30 @ 2:1
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

### Ratio proportion rate ➔ Compound units

#### Ratio proportion rate ➔ Compound units ➔ Problem solving

d=10m, t=2s
s = 5m/s
Calculate speed
Use the speed formula speed s = distance d / time t to calculate speeds to 1 d.p.
Speed from a graph
Using speed time graphs find the speed at the given time
Fastest speed, slowest speed
Using speed time graphs identify the highest speed or the lowest speed attained
D = M / V
Calculate 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
Calculate distance, time
Re-arrange the speed formula to calculate distance or time to 1 d.p.

### Ratio proportion rate ➔ Imperial to metric

#### Ratio proportion rate ➔ Imperial to metric ➔ Length

mile → km
Convert miles to kilometres
Use the approximation 1 mile ≈ 1.6 km to convert imperial miles to kilometres
inches → cm
Convert inches to cm
Use the approximation 1 inch ≈ 2.54 cm to convert imperial inches to centimetres to 2 d.p.

### Ratio proportion rate ➔ Metric to imperial

mile → km
Convert km to miles
Use the approximation 1.6 kilometres ≈ 1 mile to convert 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 centimetres to imperial feet to 1 d.p.

### Ratio proportion rate ➔ Percentages

#### Ratio proportion rate ➔ Percentages ➔ Non calculator

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%
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

#### Ratio proportion rate ➔ Percentages ➔ Calculator

45 + 12%
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
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%
Express quantities as % with calculator
Express quantities of wholes as percentages by converting to a fraction and multiplying by 100 to (1 d.p.)

### Ratio proportion rate ➔ Place value: measures

#### Ratio proportion rate ➔ Place value: measures ➔ Volume

1 m³ :
1000000 cm³
Convert m³ to cm³
Convert cubic metres (m³) to cubic centimetres (cm³) by multiplying by 1,000,000
1 cm³ :
1000 mm³
Convert cm³ to mm³
Convert cubic centimetres (cm³) to cubic millimetres (mm³) by multiplying by 1000

### Ratio proportion rate ➔ Proportions

#### Ratio proportion rate ➔ Proportions ➔ Proportions

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.)

### Ratio proportion rate ➔ Ratio

#### Ratio proportion rate ➔ Ratio ➔ Ratio notation

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

#### Ratio proportion rate ➔ Ratio ➔ Ratio into other forms

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

#### Ratio proportion rate ➔ Ratio ➔ Ratio problems

Jack and Jill
3:4
Specific parts and quantity
Pair up specific quantities with specific parts

### Ratio proportion rate ➔ Scale

#### Ratio proportion rate ➔ Scale ➔ Scale diagrams

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
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 secondary section of Free Math 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 secondary curriculum. Use these topics to reinforce key math concepts in a fun and engaging way that will keep your pupils enthused and energised with the math they are learning. The top level categories available are:

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