3. Proportional Reasoning

Front

What is proportional reasoning?

Back

Proportional reasoning is the ability to compare ratios and understand the relationship between quantities. It involves recognizing that two ratios are equivalent.

Front

How do you convert inches to centimeters?

Back

To convert inches to centimeters, multiply the number of inches by 2.54.

Front

If the ratio of white cars to grey cars is 3:4, how do you find the total number of cars?

Back

To find the total number of cars, add the parts of the ratio (3 + 4 = 7) and then use the number of white cars to find the total: (120 white cars / 3 parts) * 7 parts = 280 total cars.

Front

What is the unit rate?

Back

The unit rate is a comparison of two different quantities when they are combined together. It is often expressed as a quantity per one unit, such as dollars per pound.

Front

How do you calculate the cost of one item when given the total cost for multiple items?

Back

To find the cost of one item, divide the total cost by the number of items. For example, if 3 shirts cost $37.50, then one shirt costs $37.50 / 3 = $12.50.

Front

What is a ratio?

Back

A ratio is a relationship between two numbers indicating how many times the first number contains the second. It can be expressed in different forms, such as fractions, decimals, or with a colon.

Front

How do you find the percentage of a part compared to a whole?

Back

To find the percentage, divide the part by the whole and then multiply by 100. For example, if 8 out of 50 candy bars are Milky Way, the percentage is (8 / 50) * 100 = 16%.

Front

What is the formula for finding the total number of items based on a ratio?

Back

If you know the number of items in one part of the ratio, you can find the total by using the formula: Total = (Number of known items / Number of parts in the ratio) * Total parts.

Front

How do you express a ratio in simplest form?

Back

To express a ratio in simplest form, divide both terms of the ratio by their greatest common divisor (GCD). For example, the ratio 6:8 can be simplified to 3:4.

Front

What is the relationship between ratios and fractions?

Back

Ratios can be expressed as fractions. For example, the ratio 3:4 can be written as the fraction 3/4.