  # Divide into a Ratio (when given One Part or Difference)

In this worksheet, students will divide amounts into ratios when one part of the ratio or the difference between the amounts has been provided, by finding the value of one part and applying this knowledge to solve a problem. Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR,

Curriculum topic:   Ratio, Proportion and Rates of Change

Curriculum subtopic:   Ratio, Proportion and Rates of Change Calculations with Ratio

Difficulty level:   #### Worksheet Overview

This activity focuses on the two elements of ratio that frequently catch students out - finding a missing amount when provided with one part of the ratio to use or the difference between the two amounts

As with all ratio questions, the key to success is finding what one part is worth.

Let's look at these concepts in action in a pair of examples.

One Part of the Ratio Given

e.g. Orange squash is made from concentrate and water in the ratio 2:5.

If we use 300 ml of concentrate, how much water do we need to use?

Step 1: Identify how many parts the amount you have is worth.

We are told that we use 300 ml of concentrate.

In the ratio, we are told that this is worth 2 parts of the total amount.

Step 2: Find out what one part is worth.

We know that 2 parts represents 300 ml in total.

So 1 part must represent 150 ml.

Step 3: Use the information gathered to work out the answer.

We are asked '...how much water do we need to use?'

We are also told that the water element represents 5 parts in the ratio.

5 × 150 ml = 750 ml

So we will need to use 750 ml of water with 300 ml of concentrate to create orange squash in the ratio requested.

The Difference is Given

e.g. Two people split some money in the ratio 2:7.

If one gets £250 more than the other, how much money do they split in total?

Step 1: Identify how many parts the amount you have is worth.

We are told that £250 is the difference between the 7 parts and the 2 parts.

This means that it must be worth 5 parts.

Step 2: Find out what one part is worth.

We know that 5 parts represents £250.

So 1 part must represent £50.

Step 3: Use the information gathered to work out the answer.

We are asked '...how much money do they split in total?'

This means we need to find the value of all the parts, so 9 parts in total (as 2 + 7 = 9).

9 × 50 = £450

So the two people in the question originally split £450 in the ratio 2:7.

In this activity, we will divide amounts into ratios, when one part of the ratio to use or the difference between the amounts has been provided, using the method shown above.

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