Activity 6.3: Percents

Purpose: Explore representations of percentages and solve percentage problems graphically and with proportions.

Materials: Paper, colored pens or pencils, a ruler and/or graph paper.

Part 1: Using a 10 by 10 grid as one whole represent the following:

Example: 65%

Your turn.

1. 1. 33%
   2. 0.3
   3. 1/3
   4. 120%
   5. 5/4

Part 2: Use a 100% bar to solve the following problems:

Example: Your store needs to mark up a new shipment of shoes by 40%. If the shoes cost $160, then what will the selling price be?

In the image notice there there are 10 sections making up the 100%, or the $160, in the purple part. This means that each section is worth 10% or $16. The green part adds on 4 more sections of the same size, 4x16 = 64. 160 + 64 = 224

$\frac{Sale\:Price}{Cost}=\frac{140}{100}=\frac{?}{160}$

If the markup is 40% and the shoes cost $160, then the shoes should sell for $224.

Example: There is an online sale for tech gear, 75% off. The sale price of new ear buds is $20. What was the original price?

In the image notice that there are 10 sections in the whole 100%. There are 2.5 sections in the purple part, or 5 groups of 5%. Split $20 into 5 pieces. This tells us that each 5% section is worth $4. There are 20 sections 5% in the whole 100%, or 20 groups of $4, for a total of $80.

$\frac{sale\:price}{original\:price}=\frac{25}{100}=\frac{20}{?}$

If the percent off is 75%, then we pay 25%, and the original price must have been $80.

Your turn.

For each of the problems below, draw a rectangular model like those shown above. Use the rectangular model and groups of 10% or 5% to find the missing value. Then set up a proportion to find the missing value.

1. 1. There is a sale at your favorite bicycle shop, 45% off. You need to know the sale price of a new shirt that was originally priced at $40.
   2. There is an online sale for tech gear, 40% off. The sale price of new ear buds is $108. What was the original price?
   3. Your store needs to mark up a new shipment of shoes by 40%. If the shoes cost $80, then what will the selling price be?
   4. Your store marked up a new shipment of jackets by 50%. If the jackets will sell for $120, then what was the original cost of the jackets?
   5. Your store marked up a new shipment of shoes by 40%. If the shoes will sell for $252, then what was the original cost of the shoes?