Ratio and Proportional Relationships

Front

What is a unit rate?

Back

A unit rate is a comparison of two different quantities where one of the quantities is expressed as a single unit. For example, if a car travels 60 miles in 1 hour, the unit rate is 60 miles per hour.

Front

How do you calculate the unit cost of an item?

Back

To calculate the unit cost, divide the total cost by the number of units purchased. For example, if Gabby spent $44.10 for 14 gallons of gas, the unit cost is $44.10 ÷ 14 = $3.15 per gallon.

Front

What does a ratio of 5:3 represent in a group of items?

Back

A ratio of 5:3 means that for every 5 units of the first item, there are 3 units of the second item. For example, in an orchestra with 5 violin players and 3 flute players, the ratio indicates the relative number of each type of player.

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 10:15 can be simplified to 2:3 by dividing both terms by 5.

Front

What is the difference between a ratio and a rate?

Back

A ratio is a comparison of two quantities, while a rate is a specific type of ratio that compares two quantities with different units, such as miles per hour or price per item.

Front

How can you convert a ratio to a fraction?

Back

To convert a ratio to a fraction, write the first term as the numerator and the second term as the denominator. For example, the ratio 4:5 can be written as the fraction 4/5.

Front

What is the significance of unit rates in real-life applications?

Back

Unit rates help in making comparisons and informed decisions in real-life situations, such as determining the best price for products, understanding speed, or calculating efficiency.

Front

How do you find the total number of items from a ratio?

Back

To find the total number of items from a ratio, add the parts of the ratio together. For example, in a ratio of 5:3, the total is 5 + 3 = 8 parts.

Front

What is a proportional relationship?

Back

A proportional relationship is a relationship between two quantities where their ratio remains constant. For example, if you double one quantity, the other quantity also doubles.

Front

How do you determine if two ratios are equivalent?

Back

Two ratios are equivalent if they simplify to the same fraction or if their cross products are equal. For example, the ratios 1:2 and 2:4 are equivalent.