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.