Marcy’s goal was to collect 100 cans of food for a local food bank. She collected 160 cans. Use the grid model to understand how to write this as a ratio, a fraction, and a percent.

Question

2 grid models, each with 100 squares. 160 squares are shaded.

As a ratio, this is expressed as
.
As a fraction, this is expressed as
.
As a percent, this is expressed as
.

Answer 1

To analyze Marcy's goal using the grid model, we can see that out of the 160 cans she collected, we can compare this to her goal of 100 cans.

1. Ratio: We can express this as a ratio of cans collected to the goal. Thus, the ratio of cans collected (160) to the goal (100) is: \[ 160:100 \] This can be simplified to: \[ 16:10 \quad \text{or} \quad 8:5 \quad (\text{dividing both sides by 20}) \]

2. Fraction: The fraction representing the cans collected out of the goal can be written as: \[ \frac{160}{100} \] This can be simplified to: \[ \frac{16}{10} \quad \text{or} \quad \frac{8}{5} \quad (\text{dividing both the numerator and the denominator by 20}) \] Alternatively, since she exceeded her goal, we can express the fraction of cans collected relative to the goal as: \[ \frac{160}{100} = 1.6 \quad \text{(this shows she collected 1.6 times her goal)} \]

3. Percent: To express this as a percent, we can calculate how much of her goal was achieved, which is: \[ \frac{160}{100} \times 100 = 160% \] This indicates that Marcy collected 160% of her goal.

To summarize:

• As a ratio: 8:5
• As a fraction: \(\frac{8}{5}\) or 1.6
• As a percent: 160%