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 to solve for an unknown?

Back

To set up a proportion, you can use the formula a/b = c/d, where a and b are one ratio, and c and d are another ratio. Cross-multiply to solve for the unknown.

Front

What is the cross-multiplication method in solving proportions?

Back

The cross-multiplication method involves multiplying the numerator of one ratio by the denominator of the other ratio and setting the two products equal to each other.

Front

If 3 pounds of hamburger costs $6, what is the cost per pound?

Back

The cost per pound is $2.

Front

How do you find the height of an object using similar triangles?

Back

To find the height of an object using similar triangles, set up a proportion comparing the height and shadow length of the known object to the height and shadow length of the unknown object.

Front

What is the formula to calculate the total time needed to produce a certain number of items based on a production rate?

Back

Total time = (Total items needed) / (Production rate per time period).

Front

How do you convert weeks into days when calculating production time?

Back

To convert weeks into days, multiply the number of weeks by 7 (since there are 7 days in a week).

Front

What is the relationship between the height of an object and the length of its shadow in similar triangles?

Back

In similar triangles, the ratio of the height of an object to the length of its shadow is constant and can be used to find unknown heights or shadow lengths.

Front

If a 6-foot person casts a 2-foot shadow, what is the ratio of height to shadow length?

Back

The ratio of height to shadow length is 6:2, which simplifies to 3:1.

Front

How do you solve for an unknown height using a known shadow length?

Back

Set up a proportion using the known height and shadow length, and the unknown height and its corresponding shadow length, then solve for the unknown.