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Direct Proportion

The term direct proportion means that two (or more) quantities increase or decrease in the same ratio. In our previous paint example we could use direct proportion to mix enough paint to decorate just one wall, or enough to paint one room, or enough to paint an entire apartment block; if the ratio remains the same, the mixture of paint will remain the same color.

Make sure your child can identify the difference between ratios and total quantities. For example, in the purple paint mixture, the ratio of blue to red of 4:3. This does not necessarily mean we every mixture would have 4 red and 3 blue cans. It does mean we would have 4 red for every 3 blue cans.

Direct Proportion Examples

In our first example we had 7 cans of paint in a ratio of blue to red of 4:3.
What would we need if we doubled the amount of paint in direct proportion?

We would double the amount of blue paint. 4 x 2 = 8
We would double the amount of red paint. 3 x 2 = 6

We would need 8 cans of blue and 6 cans of red paint.

Here are some more examples of the types of problems that can be solved using direct proportion.

You have found that a good ratio of pizzas to people is 1:3. You are having a party and there will be 12 people there. How many pizzas do you need for the party?

Ratio of pizza to people is 1:3
1 pizza feeds 3 people.
We have 12 people.
How many groups of 3 are in 12?
12 ÷ 3 = 4
We would need 4 pizzas to feed 12 people.

In the following examples we will ask ourselves, “how much for one?” Problems with ratio and proportion can often be solved using this strategy.

You are using a recipe for meatloaf that calls for 10 oz. of ground beef.
The recipe is for 5 servings but you want to make enough for 8.
How much ground beef should you use?
Ratio of people to beef is 5 people : 10oz.
First calculate how much beef is needed for 1 serving. 10 ÷ 5 = 2
1 serving needs 2 oz. For 8 servings multiply by 8. 2 x 8 = 16
You should use 16 oz. of ground beef.

Feeling hungry? Try this Changing Recipe QuantitiesWorksheet.

How much fertilizer?

A lawn fertilizer should be spread in a ratio of 20 lbs to every 1,000 square feet.
How much fertilizer should be used to treat a lawn that is 700 square feet?

Ratio of fertilizer to area is 20 lbs : 1,000 sq. ft.
First calculate how much fertilizer is needed for 1 square foot. 20 ÷ 1,000 = .02
1 sq. ft. requires .02 lbs. For 700 sq. ft. multiply by 700. .02 x 700 = 14
14 lbs. of fertilizer should be used for a 700 sq. ft. lawn.
Since we are dealing with bigger numbers
we could also solve this problem by asking “how much for 100 sq. ft.”
How much fertilizer is needed for 100 sq. ft. ? 20 ÷ 10 = 2
How many hundreds do we have?
We have 7 so we multiply by 7.
2 x 7 = 14
There is usually more than one way to solve ratio and proportion problems.

Try this Proportional Ratios worksheet

You will find other worksheets on ratio and proportion here.