practice and problem solving
use a 10-by-10 grid to model the percent.
5. 10%
6. 55%
7. 35%
write the percent as a fraction or mixed number in simplest form.
8. 45%
9. 90%
10. 15%
11. 7%
12. 34%
13. 79%
14. 77.5%
15. 188%
16. 8%
17. 224%
18. 0.25%
19. 0.4%

Question

Accepted Answer

Let's solve these problems one by one. We'll start with the "Write the percent as a fraction or mixed number in simplest form" section.

### Problem 8: 45%
# Explanation:
## Step 1: Recall the definition of percent
A percent is a ratio that compares a number to 100. So, 45% can be written as $\frac{45}{100}$.
## Step 2: Simplify the fraction
To simplify $\frac{45}{100}$, we find the greatest common divisor (GCD) of 45 and 100, which is 5. Then we divide both the numerator and the denominator by 5: $\frac{45 \div 5}{100 \div 5} = \frac{9}{20}$.
# Answer: $\frac{9}{20}$

### Problem 9: 90%
# Explanation:
## Step 1: Write the percent as a fraction
90% is $\frac{90}{100}$.
## Step 2: Simplify the fraction
The GCD of 90 and 100 is 10. Dividing both by 10: $\frac{90 \div 10}{100 \div 10} = \frac{9}{10}$.
# Answer: $\frac{9}{10}$

### Problem 10: 15%
# Explanation:
## Step 1: Write the percent as a fraction
15% is $\frac{15}{100}$.
## Step 2: Simplify the fraction
The GCD of 15 and 100 is 5. Dividing both by 5: $\frac{15 \div 5}{100 \div 5} = \frac{3}{20}$.
# Answer: $\frac{3}{20}$

### Problem 11: 7%
# Explanation:
## Step 1: Write the percent as a fraction
7% is $\frac{7}{100}$. Since 7 and 100 have no common divisors other than 1, this fraction is already in simplest form.
# Answer: $\frac{7}{100}$

### Problem 12: 34%
# Explanation:
## Step 1: Write the percent as a fraction
34% is $\frac{34}{100}$.
## Step 2: Simplify the fraction
The GCD of 34 and 100 is 2. Dividing both by 2: $\frac{34 \div 2}{100 \div 2} = \frac{17}{50}$.
# Answer: $\frac{17}{50}$

### Problem 13: 79%
# Explanation:
## Step 1: Write the percent as a fraction
79% is $\frac{79}{100}$. Since 79 is a prime number and does not divide 100, this fraction is in simplest form.
# Answer: $\frac{79}{100}$

### Problem 14: 77.5%
# Explanation:
## Step 1: Convert the decimal percent to a fraction
77.5% can be written as $\frac{77.5}{100}$. To eliminate the decimal, multiply both the numerator and the denominator by 10: $\frac{77.5 	imes 10}{100 	imes 10} = \frac{775}{1000}$.
## Step 2: Simplify the fraction
The GCD of 775 and 1000 is 25. Dividing both by 25: $\frac{775 \div 25}{1000 \div 25} = \frac{31}{40}$.
# Answer: $\frac{31}{40}$

### Problem 15: 188%
# Explanation:
## Step 1: Write the percent as a fraction
188% is $\frac{188}{100}$.
## Step 2: Simplify the fraction and convert to a mixed number (if needed)
The GCD of 188 and 100 is 4. Dividing both by 4: $\frac{188 \div 4}{100 \div 4} = \frac{47}{25}$. Converting $\frac{47}{25}$ to a mixed number: $47 \div 25 = 1$ with a remainder of 22, so it's $1\frac{22}{25}$.
# Answer: $1\frac{22}{25}$

### Problem 16: 8%
# Explanation:
## Step 1: Write the percent as a fraction
8% is $\frac{8}{100}$.
## Step 2: Simplify the fraction
The GCD of 8 and 100 is 4. Dividing both by 4: $\frac{8 \div 4}{100 \div 4} = \frac{2}{25}$.
# Answer: $\frac{2}{25}$

### Problem 17: 224%
# Explanation:
## Step 1: Write the percent as a fraction
224% is $\frac{224}{100}$.
## Step 2: Simplify the fraction and convert to a mixed number
The GCD of 224 and 100 is 4. Dividing both by 4: $\frac{224 \div 4}{100 \div 4} = \frac{56}{25}$. Converting $\frac{56}{25}$ to a mixed number: $56 \div 25 = 2$ with a remainder of 6, so it's $2\frac{6}{25}$.
# Answer: $2\frac{6}{25}$

### Problem 18: 0.25%
# Explanation:
## Step 1: Convert the decimal percent to a fraction
0.25% is $\frac{0.25}{100}$. Multiply both the numerator and the denominator by 100 to eliminate the decimal: $\frac{0.25 	imes 100}{100 	imes 100} = \frac{25}{10000}$.
## Step 2: Simplify the fraction
The GCD of 25 and 10000 is 25. Dividing both by 25: $\frac{25 \div 25}{10000 \div 25} = \frac{1}{400}$.
# Answer: $\frac{1}{400}$

### Problem 19: 0.4%
# Explanation:
## Step 1: Convert the decimal percent to a fraction
0.4% is $\frac{0.4}{100}$. Multiply both the numerator and the denominator by 10 to eliminate the decimal: $\frac{0.4 	imes 10}{100 	imes 10} = \frac{4}{1000}$.
## Step 2: Simplify the fraction
The GCD of 4 and 1000 is 4. Dividing both by 4: $\frac{4 \div 4}{1000 \div 4} = \frac{1}{250}$.
# Answer: $\frac{1}{250}$

For the "Use a 10 - by - 10 grid to model the percent" section:

### Problem 5: 10%
# Explanation:
## Step 1: Understand the 10 - by - 10 grid
A 10 - by - 10 grid has a total of $10	imes10 = 100$ squares. Each square represents 1% of the whole grid.
## Step 2: Shade the appropriate number of squares
To model 10%, we need to shade 10 out of the 100 squares. So we shade 10 squares in the 10 - by - 10 grid.
# Answer: Shade 10 squares in the 10 - by - 10 grid.

### Problem 6: 55%
# Explanation:
## Step 1: Recall the grid has 100 squares
Since each square is 1%, for 55% we need to shade 55 squares.
## Step 2: Shade 55 squares
Shade 55 out of the 100 squares in the 10 - by - 10 grid.
# Answer: Shade 55 squares in the 10 - by - 10 grid.

### Problem 7: 35%
# Explanation:
## Step 1: Grid has 100 squares (1% per square)
For 35%, we need to shade 35 squares.
## Step 2: Shade 35 squares
Shade 35 out of the 100 squares in the 10 - by - 10 grid.
# Answer: Shade 35 squares in the 10 - by - 10 grid.

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QUESTION IMAGE

Question

Explanation:

Problem 8: 45%

Step 1: Recall the definition of percent

Step 2: Simplify the fraction

Step 1: Write the percent as a fraction

Step 2: Simplify the fraction

Step 1: Write the percent as a fraction

Step 2: Simplify the fraction

Answer:

Problem 9: 90%