Ratios
What is a ratio?
3 apples to 5 oranges
3 apples: 5 oranges
3 apples/5 oranges
How can ratio tables be used to compare quantities?
Ratio tables organize equivalent ratios in a structured format, allowing for easy comparison of different quantities or parts in relation to a whole.
Are the Ratios Equivalent?
2/4 = 8/12
No!
Draw a double-number line to show 1 fish to 3 mice. Show how you find how many fish, if there are 15 mice. How many fish are there?
There are 5 fish.
When are ratios used in real life?
Ratios are used in cooking (like in recipes), in finance (such as financial ratios), in sports statistics (like batting averages), and in everyday tasks requiring proportionate comparisons.
Solve: If a recipe calls for 2 cups of flour and 3 cups of sugar, what is the ratio of flour to sugar?
The ratio of flour to sugar is 2:3.
Complete the ratio table: 3 boxes of crayons to 5 markers = ? to 20 markers
12 crayons
Are the Ratios Equivalent?
5/10 = 30/60
Draw a double number line to solve the missing value. There are 2 lizards to 7 crickets. How many crickets are there if there were 20 lizards?
Your number lines should have labels with the ratios of 2:7 and 20:70. There are 70 crickets.
How do you simplify a ratio?
To simplify a ratio, divide both parts by their greatest common divisor.
In a ratio of 2 cats to 1 dog, if there are 12 cats, how many dogs are there?
There are 6 dogs.
Using the ratio table, find the missing value: 4 apples to ? oranges = 12 apples to 18 oranges
6 oranges
Solve for x to make the Ratios Equivalent:
7/14 = x/42
x = 21
Draw a double number line to solve the missing value. There are 8 pictures to 30 words on a page. How many words are there if there were 32 pictures?
Your number lines should have labels with the ratios of 8:30 and 32:120. There are 120 words.
Compare and contrast ratios and fractions.
Both ratios and fractions express part-to-part or part-to-whole relationships, but ratios compare quantities using division, while fractions represent parts of a whole using division.
Given a ratio with 3 parts representing apples and 5 parts representing oranges, what is the ratio of apples to oranges?
The ratio of apples to oranges is 3:5.
Analyze the ratio table: 5 pencils to 10 pens = ? to 20 pens
10 pencils
Solve for x to make the Ratios Equivalent:
2/16 = x/80
x = 10
Draw a double number line to solve the missing value. There are 40 dogs to 66 cats at the shelter. After adoption days, people adopted half of all dogs and cats. What is the ratio now? How many total animals were left at the shelter?
Your number lines should have labels with the ratios of 40:66 and 20:33. The ratio is 20 dogs to 33 cats. The total amount of animals are 53 dogs and cats.
Explain how to find an equivalent ratio.
To find an equivalent ratio, multiply or divide both parts of the original ratio by the same number.
Explain how you solve this problem. If a:b is 2:7 and b:c is 14:3, what is a:b:c?
Using the ratio table, complete the table:
brownies: 9 12 ? 21
cookies: ? 44 55 ?
What is the simplified ratio of brownies:cookies?
brownies: 9 12 15 21
cookies: 33 44 55 77
3 brownies:11 cookies
Are the Ratios Equivalent?
8/32 = 32/128
YES!
Draw a double number line to solve the missing value. There are 250 students to 10 teachers. If there were only 50 students, how many teachers would there be?
Your number lines should have labels with the ratios of 250:10. There would be 2 teachers.