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Intro to Ratios
Overview
Understanding Ratios
A ratio expresses the relationship between two quantities.
Look at the shapes below. We can see that there are some hearts as well as some
stars, but what is the ratio of stars to hearts?
Step 1: Calculate the first quantity
First we need to calculate the number of stars because the question is asking the
ratio of “stars” to “hearts”.
There are 2 stars
Step 2: Calculate the second quantity
Next, we need to calculate the number of hearts.
There are 3 hearts
Step 3: Express the relationship between the first and second quantities
The relationship can be expressed as:
The ratio of stars to hearts is
We can also say:
For every 2 stars there are 3 hearts
or
2 to 3
Let’s look at a more challenging example.
What is the ratio of stars to hearts?
Step 1: First we calculate the number of stars, which is 3.
Step 2: Next we calculate the number of hearts, which is 6.
Step 3: Now, we express the relationship as
Step 4: We can simplify the ratio just as we simplify fractions.
The common factor is 3. So, the ratio of stars to hearts is
Step 5: You can check your answer by looking at the quantities
We can see that for every 1 star, there are 2 hearts ✓
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What is the ratio of apples to oranges?
Answer
4 to 3
There are 4 apples and 3 oranges. This ratio cannot be simplified.
What is the ratio of apples to oranges?
Answer
4 to 3
There are 4 apples and 3 oranges. This ratio cannot be simplified.
What is the ratio of fish to cats?
Answer
2 to 1
There are 6 fish and 3 cats. The ratio 6 : 3 can be simplified to 2 : 1
What is the ratio of fish to cats?
Answer
2 to 1
There are 6 fish and 3 cats. The ratio 6 : 3 can be simplified to 2 : 1
What is the ratio of cats to dogs?
Answer
7 : 2
There are 7 cats and 2 dogs. This ratio cannot be simplified.
What is the ratio of cats to dogs?
Answer
7 : 2
There are 7 cats and 2 dogs. This ratio cannot be simplified.
What is the ratio of carrots to ice cream cones?
Answer
5 : 2
There are 5 carrots and 2 ice cream cones. This ratio cannot be simplified.
What is the ratio of carrots to ice cream cones?
Answer
5 : 2
There are 5 carrots and 2 ice cream cones. This ratio cannot be simplified.
What is the ratio of donuts to candy?
Answer
1 : 1
There is one donut and 1 candy.
What is the ratio of donuts to candy?
Answer
1 : 1
There is one donut and 1 candy.
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