# Using Grid Models to Solve Percentage Problems

To compare a number to 100, you have to use percentages.

The percentage of a number means a ratio between that number and 100.

For instance, 47 percent is the same as:

\(\frac{47}{100}\) (or) 47 to 100 (or) 47:100

## Step-by-Step Guide to Using Grid Models to Solve Percentage Problems

- Understand the problem: Read the problem carefully and identify the information provided and the information that needs to be found.
- Draw a grid model: Draw a grid with labeled columns and rows to represent the given and unknown information.
- Identify the part and whole: Identify which quantity represents the part and which represents the whole.
- Write the equation: Write the equation using the information provided in the problem. For example, if the problem states that an item is 20% off, the equation is: (part/whole) = percent/100
- Fill in the grid: Use the information provided in the problem to fill in the grid.
- Solve the equation: Substitute the known values into the equation and solve for the unknown value.
- Check your work: Use the information in the grid to check that the solution makes sense.
- Write the final answer in a complete sentence.

**Using Grid Models to Solve Percentage Problems – Examples 1**

Problem: A shirt is on sale for 20% off. The original price of the shirt is $40. What is the sale price of the shirt?

- We are given that the shirt is on sale for 20% off and the original price is $40.
- Draw a grid model with labeled columns and rows. Original price, discount, and sale price columns, and whole, percent, and part rows.
- Identify the part and whole: The original price is the whole and the discount is the part.
- Write the equation: (part/whole) = percent/100
- Fill in the grid:

Original price $40 Discount 20% Sale price x

- Solve the equation: (part/whole) = percent/100 => (part/40) = 20/100 => (part) = 8
- Check your work: $40 – $8 = $32, which is the price of the shirt after a 20% discount.
- The sale price of the shirt is $32.

It’s worth noting that this is just one way to use grid models to solve percentage problems, and you can use different models depending on the information provided in the problem.

**Using Grid Models to Solve Percentage Problems – Examples **2

In Anne’s library, there are 80 books on the shelves. 20% of those books are short stories. Shade the grid to show the percentage of books that are short stories. And how many books are short stories?

**Solutions:****Step 1: **The grid is made of 100 equal squares. Since, 20% of the books are short stories, shade 20 of the 100 squares in the grid.**Step 2: **To know the number of short stories, you have to multiply the number of all books by the percentage of short stories.

\(80×20%=\frac{80}{1}×\frac{20}{100}=\frac{1600}{100}=16\)

16 books are short stories.

**Using Grid Models to Solve Percentage Problems – Examples **3

4 of the 25 students at the school got A in an exam. Shade the grid to show the fraction of the students that got an A in an exam. What percent of the students got A on an exam?

**Solutions:****Step 1:** Since 4 of the 25 students got A in an exam, write it as a fraction: \(\frac{4}{25}\)**Step 2:** To know the percentage of the students who got an A in an exam, divide 4 by 25. It is 16%.

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