AQA · GCSE · Mathematics
Course version: 8300 · Version from Sept 2015
Divide a given quantity into two parts in a given part : part or part :…
Full specification wording
Ratio, proportion and rates of change: divide a given quantity into two parts in a given part : part or part : whole ratio express the division of a quantity into two parts as a ratio apply ratio to real contexts and problems (such as those involving conversion, comparison, scaling, mixing, concentrations)
To divide a quantity in a part : part ratio, add the parts to find the total number of shares, divide the quantity by that total to find one share, then multiply by each part.
Checked against the AQA 8300 specification (opens in a new tab) on .
- Point 6 of 21
- 3 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
To divide a quantity in a part : part ratio, add the parts to find the total number of shares, divide the quantity by that total to find one share, then multiply by each part. For example, £60 in the ratio 2 : 3 has 5 shares, so one share is £12 and the parts are £24 and £36. For a part : whole ratio such as 2 : 5, the whole is 5 shares and the two parts are 2 shares and 3 shares. To express a division as a ratio, compare the two part amounts in simplest form. Ratio applies to real contexts: convert units before comparing, scale recipes or maps by multiplying all parts, mix ingredients or solutions in the given ratio, and calculate concentrations as a ratio of solute to solution or solvent.
What earns the marks
- Add the parts of a part : part ratio to find the total number of shares.
- Divide the quantity by the total number of shares to find the value of one share.
- Multiply the value of one share by each part to find the two required amounts.
- For a part : whole ratio, subtract the given part from the whole to find the other part before sharing.
- Express a division of a quantity into two parts as a ratio by comparing the two amounts and simplifying.
- Apply ratio to real contexts such as unit conversion, comparison, scaling, mixing and concentrations.
Common mistakes and how to put them right
Dividing the quantity by the number of parts instead of the total number of shares.
Put it right: Add 2 + 3 = 5 shares, so one share is £12, giving £24 and £36.
Treating a part : whole ratio as a part : part ratio: for example, reading 2 : 5 as two parts to five parts.
Put it right: The whole is 5 shares, so the parts are 2 shares and 3 shares.
Forgetting to convert units before applying a ratio in a real context.
Put it right: Convert to the same unit, giving 200 : 1000, then simplify to 1 : 5.
Exam tips
- Write down the total number of shares before dividing the quantity.
- Check that the two amounts add back to the original quantity.
- In real contexts, identify the units and convert them before setting up the ratio.
Try the lesson
The start of the Ratio, proportion and rates of change: divide a given quantity into two parts in a given part : part or part : whole ratio express the division of a quantity into two parts as a ratio apply ratio to real contexts and problems (such as those involving conversion, comparison, scaling, mixing, concentrations) lesson, made from checked teaching notes for this specification point.
Have a go first
A length of wood 80 cm long is cut into two pieces in the ratio 3 : 5. How long is the shorter piece?
Listen
To divide a quantity in a part : part ratio, add the parts to find the total number of shares, divide the quantity by that total to find one share, then multiply by each part. For example, £60 in the ratio 2 : 3 has 5 shares, so one share is £12 and the parts are £24 and £36. For a part : whole ratio such as 2 : 5, the whole is 5 shares and the two parts are 2 shares and 3 shares. To express a division as a ratio, compare the two part amounts in simplest form. Ratio applies to real contexts: convert units before comparing, scale recipes or maps by multiplying all parts, mix ingredients or solutions in the given ratio, and calculate concentrations as a ratio of solute to solution or solvent. A strong answer earns marks for these points. Add the parts of a part : part ratio to find the total number of shares. Divide the quantity by the total number of shares to find the value of one share. Multiply the value of one share by each part to find the two required amounts. For a part : whole ratio, subtract the given part from the whole to find the other part before sharing. A common slip: Dividing the quantity by the number of parts instead of the total number of shares: for example, sharing £60 in the ratio 2 : 3 by dividing by 2 and by 3. Instead, add 2 + 3 = 5 shares, so one share is £12, giving £24 and £36. Exam tip: Write down the total number of shares before dividing the quantity.
Watch it explained
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Read the described scene instead
This lesson looks at ratio: how to divide a quantity into parts, how to read part-to-part and part-to-whole ratios, and how ratio applies in real contexts. Ratio compares amounts, and the order matters. For a part-to-part ratio, add the parts to find the total number of shares. In the ratio two to three, there are five shares. For a part-to-whole ratio such as two to five, the whole is five shares, so the two parts are two shares and three shares. To divide a quantity in a part-to-part ratio, first add the parts to find total shares. Next divide the quantity by total shares to find one share. Then multiply one share by each part. Write down total shares before dividing, and check the two amounts add back to the original quantity. Pause to think how you would share sixty pounds in the ratio two to three, then follow the steps. First add the parts: two plus three equals five shares. Then divide sixty pounds by five: one share is twelve pounds. Multiply twelve pounds by two and by three. The two amounts are twenty-four pounds and thirty-six pounds. Check: twenty-four plus thirty-six equals sixty pounds. A common mistake is dividing the quantity by the number of parts instead of the total number of shares. For sixty pounds in the ratio two to three, add two and three to get five shares, so one share is twelve pounds. Another mistake is treating a part-to-whole ratio as part-to-part. In two to five, the whole is five shares, so the parts are two shares and three shares. Also convert units before comparing: two hundred millilitres to one litre is two hundred to one thousand, which simplifies to one to five. Remember four ideas. Add the parts of a part-to-part ratio to get total shares, then divide and multiply. For a part-to-whole ratio, subtract the given part from the whole to find the other part. To express a division as a ratio, compare the two amounts and simplify. In real problems, convert units first, then scale, mix, compare or calculate concentrations using the ratio.
Key words
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Dividing in a ratio
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Expressing division as a ratio
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Real-life ratio problems
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See every definition
- Dividing in a ratio
- Adding the parts of a part : part ratio to find the total number of shares, dividing the quantity by that total to find one share, then multiplying by each part.
- Expressing division as a ratio
- Comparing the two part amounts in simplest form.
- Real-life ratio problems
- Applying ratio to real contexts such as those involving conversion, comparison, scaling, mixing and concentrations.
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