 What you need to know

Things to remember:

• Ratios are concerned with multiplying and dividing, so we have to multiply or divide to find equivalent ratios.
• 3:5 and 5:3 mean different things. The order of your ratio matters.

We have seen ratios before and how we can convert them into equivalent ratios by multiplying and dividing.

Find some equivalent ratios to 24:36

24 : 36

Divide by 2                 12 : 18

Divide by 4               3  :  4.5

Divide by 6                  4 : 6

Divide by 12                2 : 3

Multiply by 2               48 : 72

Multiply by 3                72 : 108

Multiply by 4                96 : 144

We need to be careful with what we divide by. For example, look at the ratio in bold. We don’t like to have decimal values in ratios, so we wouldn’t use this one.

We can use this to help us fine solve ratios that involve unknowns.

If 15 : 5 is an equivalent ratio to $x:1$, what is the value of $x$?

We will look at this in 4 steps.

Step 1: Write the two ratios with the one we know above the one we’re trying to find.

15 : 5

$x:1$

Step 2: Look at how we can change the first one into the second one.

Hint: Remember, we change ratios by multiplying or dividing.

Comparing the two ratios we can see that we are trying to turn the 15 into $x$ and 5 into 1. We know that to turn 5 into 1 we have to divide by 5.

$$5\div5=1$$

Step 3: Divide the other part(s) of the ratio by the number found in Step 2.

$$15\div5:5\div5$$

$$3:1$$

Step 4: Compare with the other ratio to find the missing value of $x$

$$3:1$$

$$x:1$$

Comparing them, we can see that the missing value must be $x=3$.

Ratios don’t have to have 2 numbers, they could have 3 or more!

If 14 : 35 : 21 is an equivalent ratio to $x:5:y$, what are the values of $x$ and $y$?

Step 1: Write the two ratios with the one we know above the one we’re trying to find.

14 : 35 : 21

$x:5:y$

Step 2: Look at how we can change the first one into the second one.

Hint: Remember, we change ratios by multiplying or dividing.

Comparing the two ratios we can see that we are trying to turn the 14 into $x$, 35 into 5, and 21 into $y$. We know that to turn 35 into 5 we have to divide by 7.

$$35\div7=5$$

Step 3: Divide the other part(s) of the ratio by the number found in Step 2.

$$14\div7:35\div7:21\div7$$

$$2 : 5 : 3$$

Step 4: Compare with the other ratio to find the missing value of $x$

$$2 : 5 : 3$$

$$x : 5 : y$$

Comparing them, we can see that the missing values must be $x=2$ and $y=3$.

Example Questions

$$26:13$$

$$26\div13:13\div13$$

$$2:1$$

$$2:z$$

$$z=1$$

$$18:6:24$$

$$18\div6:6\div6:24\div6$$

$$3:1:4$$

$$n:1:m$$

$n=3$ and$m=4$