Solve Proportions 74B

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 format \( \frac{a}{b} = \frac{c}{d} \), where a, b, c, and d are numbers.

Front

What is cross-multiplication in proportions?

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 \( \frac{w}{8} = \frac{21}{12} \), what is the value of w?

Back

To find w, cross-multiply: \( w \cdot 12 = 21 \cdot 8 \) which gives \( w = \frac{21 \cdot 8}{12} = 14 \).

Front

What is the first step to solve the proportion \( \frac{8}{12} = \frac{21}{w} \)?

Back

The first step is to cross-multiply: \( 8 \cdot w = 12 \cdot 21 \).

Front

How do you find the number of women doctors if 4 out of every 9 doctors are women and there are 126 doctors?

Back

Set up the proportion \( \frac{4}{9} = \frac{x}{126} \) and solve for x.

Front

What is the solution to the equation \( 5x = 98 \)?

Back

To solve for x, divide both sides by 5: \( x = \frac{98}{5} = 19.6 \).

Front

If there are 24 brownies sold and the ratio of ice cream cones to brownies is 5:3, how many ice cream cones were sold?

Back

Set up the proportion \( \frac{5}{3} = \frac{x}{24} \) and solve for x, which gives \( x = 40 \).

Front

What does it mean if two ratios are equivalent?

Back

If two ratios are equivalent, it means they represent the same relationship between quantities.

Front

How can you check if two fractions are equivalent?

Back

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