Functional Skills: Proportion

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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.

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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.

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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

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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

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

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

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

Additional Resources

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Exam Tips Cheat Sheet

FS Level 2
PFS

Formula Booklet

FS Level 2

Functional Skills: Proportion Worksheet and Example Questions

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Proportion L1

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Proportion L2

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