Simple Proportion
Two quantities are in direct proportion when they increase or decrease in the same ratio.
For example, you could increase something by doubling it, or decrease it by halving.
Example
\(10\) pencils cost \(拢2.20\), what is the cost of \(30\) pencils?
Question
A car travels \(90\) km in two hours. How far will it travel in one hour?
Answer
In one hour the car will travel \(45\) km.
Unitary Method for Proportion
In the unitary method we divide to find the cost/weight/etc for one item and then multiply to find the cost/weight/etc for the number of items we want.
Example
\(8\) apples cost \(拢2.56\).
What would be the cost of \(6\) apples?
Find the cost of one apple by dividing the price by the number of apples.
Multiply the cost of one apple by the number of apples you want to buy.
\(1\) apple costs \({拢2.56}\div{8} = {拢0.32}\)
\(6\) apples cost \({拢0.32}\times{6} = {拢1.92}\)
Question
Kate can run \(5\) km in \(27\) \(\frac{1}{2}\) mins.
How long will it take her to run \(8\) km?
What assumption have you made?
Answer
Find the time it takes Kate to run \(1\) km by dividing the time by \(5\)
Multiply the time taken for \(1\) km by \(8\) to find the time it will take for Kate to run \(8\) km.
\(1\) km takes \({27.5}\div{5} = {5.5}\) mins.
\(8\) km will take \({5.5}\times{8} = {44}\) mins.
The assumption you have made is that Kate continues to run at the same speed.
Proportion in recipes
To change the number of people you can serve when using a recipe follow these steps:
- Read how many is the recipe for or how many it makes.
- Divide each of the quantities by this number to calculate how much you need for \(1\) person.
- Multiply the quantities for \(1\) person by the number of people you want to serve.
Example
Abigail is using this recipe to make pancakes for her family.
She wants to make \(15\) pancakes.
How much milk will she need?
This recipe makes \(6\) pancakes.
\(6\) pancakes need \(300\) ml of milk.
\(1\) pancake needs \(300\) ml \(\div{6} = {50}\) ml of milk.
\(15\) pancakes need \(50\) ml \(\times{15} = {750}\) ml of milk.
OR
\(6\) pancakes need \(300\) ml of milk.
\(3\) pancakes need \(300\) ml \(\div{2} = {150}\) ml of milk.
\(15\) pancakes need \(150\) ml \(\times{5} = {750}\) ml of milk.
Question
Archie is making pizza for his birthday party.
The recipe says he will need \(300\) g of flour to make pizza for \(4\) people.
How much flour will Archie need to make pizza for \(18\) people?
Answer
The recipe serves \(4\) people
\(4\) servings - \(300\) g flour
\(1\) serving - \(300\) g \(\div{4} = {75}\) g
\(18\) servings - \(75\) g \(\times{18} = {1350}\) g \(= {1.35}\) kg flour
Using proportion to get the best value
When products are available in different sizes it is useful to work out which size is the best value.
Always compare like with like.
Example
A \(750\) ml tin of paint costs \(拢6\).
A \(2\) L tin of paint costs \(拢14\).
Which tin is better value for money?
To compare the prices we must find the price for the same quantity of paint.
We can use the unitary method and compare by finding the cost of \(1\) ml but in this case we can compare the cost of \(250\) ml as it divides exactly into both \(750\) ml and \(2\) L or \(2000\) ml.
For the 750 ml tin
\({750}\div{3} = {250}\) ml
\(250\) ml costs \({拢6}\div{3} = {拢2}\)
For the 2l tin
\({2000}\div{8} = {250}\) ml
\(250\) ml costs \({拢14}\div{8} = {拢1.75}\)
It is clear that the \(2\) L tin is better value as it is cheaper per \(250\) ml
Question
A \(3\) kg bag of potatoes costs \(87p\)
A \(5\) kg bag of potatoes costs \(拢1.40\)
Which is better value?
Answer
For the \(3\) kg bag
\(1\) kg costs \({87p}\div{3} = {29p}\)
For the 5kg bag
\(1\) kg costs \({拢1.40}\div{5} = {28p}\)
The \(5\) kg bag is better value.
Test section
Question 1
Four candles cost \(拢6\).
How much would \(12\) candles cost?
Answer
袄(拢18袄)
Question 2
Raj and Harry work in the local shop.
They both get paid the same amount per hour.
Raj worked \(5\) hours and was paid \(拢40\).
How much was Harry paid for \(7\) hours?
Answer
袄(拢56袄)
Question 3
Violet is making shortbread for 20 people.
How much butter will she need?
Recipe
(makes 8)
\(300\)g plain flour
\(150\)g corn flour
\(150\)g sugar
\(300\)g butter
Answer
\(750\) g
Question 4
A \(1\)kg box of cereal costs \(拢3.20\), a \(500\)g box costs \(拢1.70\) and a \(200\)g box costs \(拢1.20\).
Which is the best value?
Answer
\(1\)kg for \(拢3.20\).
Question 5
A pack of \(9\) toilet rolls cost \(拢4.50\).
A \(6\) pack of toilet rolls costs \(拢3.20\) with \(2\) free rolls.
Which is best value?
Answer
\(6\) pack with \(2\) free.
More on Ratio and proportion
Find out more by working through a topic
- count3 of 3
- count1 of 3
