Question

Write the rate 42 ounces per 5 mugs as a unit rate. Write your answer as a decimal number. Write your answer in the box.

Short answer

8.4 ounces per mug

Step-by-step solution

Understand the Problem

The problem wants to convert the rate of 42 ounces per 5 mugs into a unit rate. A unit rate has a denominator of 1.

Set Up the Division

To find the unit rate, divide the number of ounces by the number of mugs. This can be written as a division problem: 42 ounces ÷ 5 mugs

Perform the Division

Now, perform the division: 42 ÷ 5 = 8.4

Interpret the Result

The unit rate is 8.4 ounces per mug.

Key concepts

Rates and Ratios

Rates and ratios are fundamental concepts in mathematics. A ratio compares two quantities, showing the relative size of one quantity to another. It tells us how many times one number contains another. For example, in the exercise, the ratio of 42 ounces to 5 mugs compares how much liquid fits into a certain number of mugs.
When dealing with ratios, it's essential to maintain the order of the quantities. A ratio of 42 ounces to 5 mugs is different from 5 mugs to 42 ounces, making this distinction critically important.
Rates are a specific type of ratio where the two compared quantities have different units, like ounces and mugs. In our exercise, we are provided a rate of 42 ounces per 5 mugs. A rate answers the question 'how much of something per one unit of something else?' Understanding rates makes it easier to work with and compare different kinds of quantities in real-life scenarios.

Unit Rates

A unit rate is a rate where the second quantity is one unit. This means it tells us how much of one quantity corresponds to a single unit of another quantity.
To find a unit rate, you divide the first quantity by the second. In our exercise, we want to find out how many ounces fit in one mug. The provided rate is 42 ounces per 5 mugs. To determine the unit rate, you perform the division: 42 ÷ 5.
After calculating, we find that one mug holds 8.4 ounces. The unit rate helps us understand the relationship in a simple, easy-to-use form. It simplifies comparisons and helps tackle problems efficiently.

Division

Division is a fundamental operation in mathematics used to split a quantity into equal parts. It provides the basis for finding unit rates. In our exercise, we are dividing 42 ounces by 5 mugs to find the amount of ounces per single mug.
Here's how to perform the division step-by-step:
- First, identify the numerator (top number) and the denominator (bottom number). Here, 42 is the numerator, and 5 is the denominator.
- Next, set up the division as 42 ÷ 5.
- Perform the division calculation. You can use long division, a calculator, or any other method that suits you. For this problem, 42 divided by 5 equals 8.4.
- The result, 8.4, is the unit rate. Hence, there are 8.4 ounces in one mug. Understanding division is critical because it allows us to break down ratios and rates into simpler, more accessible unit rates.