# Functional Skills: Proportion

## Functional Skills: Proportion Revision

**Proportion**

Two quantities are **proportional** if, as one changes, the other changes in a certain way.

We will explain **direct proportion** and **inverse proportion**.

Make sure you are happy with the following topics before continuing.

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**Proportional Quantities**

**Example:** Antonia has a recipe for a fruit drink shown below. She wants to make a big batch of this drink. Assuming the ingredients remain in proportion, calculate how much of the drink she makes if she uses 1100 ml of lemonade.

The ingredients remaining “**in proportion**” means that even after increasing their amounts, their ratio stays the same.

We need to determine by what **scale factor **the amount of lemonade has increased:

\textcolor{purple}{1100} \div 200 = \textcolor{limegreen}{5.5}

So, we can now calculate the amount of orange juice and cranberry juice used:

orange juice: 150 \times \textcolor{limegreen}{5.5} = 825 ml

cranberry juice: 80 \times \textcolor{limegreen}{5.5} = 440 ml

Therefore, the total amount the big batch of drink is:

1100 + 825 + 440 = \textcolor{black}{2365} ml

**Note:** This is an example of **direct proportion**.

**Direct Proportion**

Two quantities are **directly proportional **if as one **increases**, the other one **increases** at the **same rate**, e.g. as one is doubled, the other is doubled.

**Example:** Toni uses \textcolor{red}{150\text{ g}} of chocolate to make \textcolor{blue}{6} cookies. How much chocolate would Toni need to make \textcolor{purple}{20} cookies?

**Step 1: **Divide the amount of chocolate by 6 to find the amount needed for 1 cookie.

\textcolor{blue}{150} \div \textcolor{red}{6} = 25 g of chocolate

**Step 2: **Multiply the amount of chocolate needed for 1 cookie by the \textcolor{purple}{20} cookies needed.

\textcolor{purple}{20} \times 25 = 500 g of chocolate

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**Inverse Proportion**

Two quantities are **inversely proportional **if as one **increases**, the other one **decreases** at the **same rate**, e.g. as one is doubled, the other is halved.

**Example:** It takes \textcolor{red}{8} workers \textcolor{blue}{25} months to build 10 houses. Assuming they all work at the same rate, how long would it take \textcolor{limegreen}{20} workers to build the same number of houses?

**Step 1: **Multiply the number of workers by the number of months, to find the time it would take 1 worker to build 10 houses:

\textcolor{red}{8} \times \textcolor{blue}{25} = 200 months

**Step 2:** Divide the time it takes 1 worker to build 10 houses by \textcolor{limegreen}{20} workers, to get the answer:

200 \div \textcolor{limegreen}{20} = \textcolor{black}{10} months

**Notes:**

When answering proportion questions, you need to assume that everything it done at the same rate, e.g. workers working at the same rate or someone running at the same rate.

## Functional Skills: Proportion Example Questions

**Question 1:** Chantel is making tomato soup, using the ingredients in the recipe below:

4 tablespoons of butter

\dfrac{1}{2} of an onion

1 tin of tomatoes

400 ml of stock

This recipe makes 2 servings.

Work out how much of each ingredient Chantel would need to make 5 servings of tomato soup.

**[2 marks]**

Calculate the amount of each ingredient needed for 1 serving, by dividing the quantity of each ingredient by 2:

4 \div 2 = 2 tablespoons of butter

\dfrac{1}{2} \div 2 = \dfrac{1}{4} of an onion

1 \div 2 = \dfrac{1}{2} of a tin of tomatoes

400 \div 2 = 200 ml of stock

Then, multiply each quantity by 5, to find out how much of each ingredient is needed for 5 servings:

2 \times 5 = 10 tablespoons of butter

\dfrac{1}{4} \times 5 = \dfrac{5}{4} = 1 \dfrac{1}{4} onions

\dfrac{1}{2} \times 5 = \dfrac{5}{2} tins of tomatoes

200 \times 5 = 1000 ml of stock

**Question 2:** Aryna walks 4 km in 52 minutes. How long would it take her to walk 6 km?

Assume that she walks at the same rate.

**[2 marks]**

Divide 52 minutes by 4 to find the time it takes to walk 1 km:

52 \div 4 = 13 minutes

Then, multiply by 6 to find how long it would take to walk 6 km:

13 \times 6 = 78 minutes

**Question 3:** It takes 60 minutes for 3 gardeners to cut the grass of a field. Assuming they all work at the same rate, how long would it 5 gardeners to cut the same grass?

**[2 marks]**

Multiply 60 by 3 to find how long it would take 1 gardener to cut the grass:

60 \times 3 = 180 minutes

Then, divide by 5 to calculate how long it would take 5 people to cut the grass:

180 \div 5 = 36 minutes

## Functional Skills: Proportion Worksheet and Example Questions

### Proportion L1

FS Level 1NewOfficial PFS### Proportion L2

FS Level 2NewOfficial PFS[responsive-flipbook id=”pfs_pocket_revision_guide_-_sample”]

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