7.2 Solving Proportion Problems by Reasoning with Multiplication and

Division

Chelsea Ogilvie & Ashley Regan

Method 1: Finding the Amount in One PartExample: At a perfume factory, the workers want to

mix rose oil and lily oil in a ratio of 4 to 3. How much rose oil will the workers need to mix with 24 liters of lily oil?

Since the perfume consists of 4 parts rose oil and 3 parts lily oil, then the 3 parts lily oil must equal 24.

Since all parts are the same size, each part must contain 8 liters. (24/3=8)

The rose oil consists of 4 parts, and since we just discovered each part is equivalent to 8 liters, we multiply the 4 parts by 8 liters, to get 32 liters of rose oil in the perfume. (4x8=32)

Method 2: Comparing Like and Unlike QuantitiesExample: Mr. Arias used 4 gallons of gas to drive 100

miles. Assuming that Mr. Arias continues to get the same gas mileage, how far will he be able to drive with 20 gallons of gas?

Comparing Like Quantities: Since 20 gallons of gas is 5 times as much as 4 gallons of gas, Mr. Arias will be able to drive 5 times as far, so he will be able to drive 5x100=500 miles.

Comparing Unlike Quantities: If we think of dividing the 100 miles equally among the 4 gallons of gas, we see that each gallon will take Mr. Arias 25 miles. So the number of miles that Mr. Arias can drive is always 25 times the number of gallons of gas he has. Since Mr. Arias has 20 gallons of gas, he can drive 20x25=500 miles.

Method 3: “Go Through 1”Example: If we want to use 4 cups of flour in a muffin

recipe in which the ratio of flour to milk is 7 to 2, how much milk should we use?

The ratio of flour to milk is 7:2, so we know that 7 cups of flour require 2 cups of milk. We want to use 4 cups of flour, but it seems hard to get from 7 cups to 4 cups, so let’s go through 1 cup first.

We first ask how much milk we would need for 1 cup of flour. If 7 cups of flour takes 2 cups of milk, then we can think of the 2 cups of milk as divided equally among the 7 cups of flour. Therefore each cup of flour takes 2/7 of a cup of milk.

Now, since we want to use 4 cups of flour, we multiply 4 by 2/7, which equals 8/7.