Solving Proportions

Front

What is a proportion?

Back

A proportion is an equation that shows two equivalent ratios.

Front

How do you solve the proportion \( \frac{6}{y} = \frac{15}{30} \)?

Back

Multiply both sides by 30y to get 6 * 30 = 15y, which simplifies to 15y = 180.

Front

What is the first step to solve the proportion \( \frac{c}{10} = \frac{6}{15} \)?

Back

Cross-multiply to get 6 * 10 = 15c, which simplifies to 60 = 15c.

Front

How do you solve the proportion \( \frac{3}{4} = \frac{x}{64} \)?

Back

Cross-multiply to get 3 * 64 = 4x, which simplifies to 4x = 192.

Front

What is the correct proportion to find out how much George will pay for 25 donuts if he pays $3 for every 5 donuts?

Back

The proportion is \( \frac{3}{5} = \frac{x}{25} \).

Front

What does cross-multiplication involve when solving proportions?

Back

Cross-multiplication involves multiplying the numerator of one ratio by the denominator of the other ratio.

Front

What is the relationship between equivalent ratios and proportions?

Back

Proportions are formed by equivalent ratios, meaning they represent the same relationship between two quantities.

Front

How can you check if two ratios form a proportion?

Back

You can check by cross-multiplying and seeing if the products are equal.

Front

What is the formula for finding a missing value in a proportion?

Back

If \( \frac{a}{b} = \frac{c}{d} \), then \( ad = bc \).

Front

What is the significance of the constant of proportionality in a proportion?

Back

The constant of proportionality is the factor that relates the two quantities in a proportional relationship.