Ch. 5.3 Homework 1 - Writing Proportions

Front

What is a proportion?

Back

A proportion is an equation that states that two ratios are equal.

Front

How do you set up a proportion?

Back

To set up a proportion, you can use the formula \( \frac{a}{b} = \frac{c}{d} \), where a and b are one ratio, and c and d are another.

Front

What is the cross-multiplication method?

Back

Cross-multiplication is a method used to solve proportions by multiplying the numerator of one ratio by the denominator of the other ratio.

Front

If \( \frac{3}{4} = \frac{x}{20} \), what is x?

Back

Using cross-multiplication: \( 3 \times 20 = 4 \times x \) leads to \( x = 15 \).

Front

What is the missing value in the proportion \( \frac{5}{x} = \frac{10}{20} \)?

Back

Cross-multiplying gives \( 5 \times 20 = 10 \times x \), so \( x = 10 \).

Front

How do you find a missing value in a proportional relationship?

Back

You can set up a proportion and solve for the missing value using cross-multiplication.

Front

What is the formula to find a percentage of a number?

Back

The formula is \( \text{Percentage} = \frac{\text{Part}}{\text{Whole}} \times 100 \).

Front

If a test is worth 36 points, how many points do you need to score to achieve 30%?

Back

Set up the proportion: \( \frac{p}{36} = \frac{30}{100} \). Solving gives \( p = 10.8 \).

Front

What is the relationship between ratios and proportions?

Back

Ratios compare two quantities, while proportions state that two ratios are equal.

Front

How can you use proportions to solve real-world problems?

Back

Proportions can be used to find missing values in scenarios like scaling recipes, calculating distances, or determining percentages.