Solve Multi-Step Ratio Problems by Using Proportional Reasoning

A proportional relationship is

• when two proportions like each other.

• a relationship between equivalent ratios with a constant multiple.

• a ratio that can be multiplied.

• when you add a number to both sides of a ratio.

How can you change two quantities (numbers) so that they stay in the same proportional relationship?

• You can add the same number to each quantity.

• You can multiply both quantities by the same number.

• You can add different numbers to each quantity.

• You can multiply both quantities by different numbers.

A recipe calls for 15 oz of flour for every 8 oz of milk. Is the relationship between ounces of flour and ounces of milk proportional?

• Yes

• No

A recipe calls for 15 oz of flour for every 8 oz of milk. Which equation can we use to represent this proportional relationship?

Can you use proportional reasoning to solve the following problem?

If Hector is 8 years old and Mary is 3 years old, how old will Mary be when Hector is 16?

• Yes, because Hector's age and Mary's age have a proportional relationship.

• No, because there is no constant multiple, so there is no proportional relationship.

Can you use proportional reasoning to solve the following problem?

Marco needs to buy some cat food. At the nearest store, 3 bags of cat food cost $15.75. How much would Marco spend on 5 bags of cat food?

• Yes, because each bag of cat food costs the same, so there is a constant multiple.

• No, because there is no proportional relationship between the cost of bags of cat food.

Emily and Andy each go to a hardware store to buy wire. The table shows the relationship between the cost and the length of wire. Emily needs 24 feet of wire. How much will she spend on wire?

(Hint: the cost is per INCH and Emily needs FEET)

• $0.04

• $0.96

• $25.00

• $11.52

Emily and Andy each go to a hardware store to buy wire. The table shows the relationship between the cost and the length of the wire. Andy needs 13 yards of wire. How much will be spend on wire?

(Hint: the table shows INCHES. Andy needs YARDS.)

• $75.00

• $900.00

• $18.72

• $0.52

The weights of Michael's and Brittney's new puppies are shown in the table and graph. Whose dog gains weight more quickly?

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