Basic Ratios

What Is a Ratio?

A ratio compares two amounts using division.

Think about a chef mixing spices. Two spoons of one spice with three spoons of another keeps the flavour balanced every single time.

Ground cinnamon · TheDeliciousLife · CC BY 2.0 · Wikimedia Commons

That comparison between the two amounts is a ratio.

Three Ways to Write It

One ratio, three outfits.

You can write 3 to 4, or 3 : 4, or the fraction 3/4. All three mean exactly the same comparison.

Read them out loud as you practise. Say "three to four" for each form.

The Spice Recipe

Here is a barbecue spice recipe.

It uses 4 spoons of dried lemon powder and 6 spoons of coriander.

Compare lemon powder to coriander: 4 spoons to 6 spoons.

Simplify to Simplest Form

A ratio is usually written as a fraction in simplest form.

Take 4/6. Divide the top and the bottom by 2. You get 2/3.

So the ratio of lemon powder to coriander is 2/3, or 2 : 3, or 2 to 3.

What 2 : 3 Really Means

The ratio 2 : 3 tells you a rule for mixing.

For every 2 units of dried lemon powder, there are 3 units of coriander.

Notice that every group keeps 2 spoons of lemon powder next to 3 spoons of coriander, so the pattern repeats without changing.

Two little, three more. That pattern repeats through the whole bowl.

Ratios That Match

Ratios that show the same relationship between the same two amounts are called equivalent ratios.

They have the same value.

4/6 and 2/3 are equivalent. The recipe can be bigger or smaller, but the balance stays exactly the same.

Your Practice Checklist

Every ratio question follows the same short path.

Find the two amounts. Write them as a fraction. Simplify. Then say the answer in all three forms.

Try it with your own numbers: 6 and 8, then 10 and 15.

A ratio compares two quantities using division.

• True
• False

Answer: True

This is true. A ratio shows how one amount compares with another amount using division.

A ratio may be written in _____ form as 3 to 4, in _____ form as 3 : 4, or in _____ form as 3/4.

Answer: A ratio may be written in word form as 3 to 4, in colon form as 3 : 4, or in fraction form as 3/4.

The word form uses “to,” the colon form uses “:”, and the fraction form uses a numerator over a denominator. These three forms show the same comparison.

A spice mix has 4 spoons of lemon powder and 6 spoons of coriander. What is the ratio of lemon powder to coriander in simplest form?

• 1 : 2
• 2 : 3
• 3 : 2
• 4 : 6

Answer: 2 : 3

Write the ratio as 4/6. Divide both numbers by 2 to get 2/3, so the simplest form is 2 : 3.