Ratios
What is a ratio?
How can tape diagrams help understand ratios?
Tape diagrams visually represent ratios using segments to show parts of a whole or parts-to-parts relationships, making ratios easier to conceptualize.
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!
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
How do you simplify a ratio?
To simplify a ratio, divide both parts by their greatest common divisor.
In a tape diagram, if the length of a segment represents 4 units, what does a segment twice as long represent?
A segment twice as long represents 8 units.
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
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 tape diagram 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
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.
How can tape diagrams help solve ratio problems involving more than two quantities?
Tape diagrams can segmentally represent multiple quantities, helping visualize and solve complex ratio problems involving more than two quantities.
Using the ratio table, determine the missing value: ? apples to 24 oranges = 6 apples to 8 oranges
18 apples
Are the Ratios Equivalent?
8/32 = 32/128
YES!