Problem 15 - Algebra 1: Concepts and Skills

Question

Find the unit rate. Round your answer to the nearest hundredth. 60 to 100

Step-by-Step Solution

Answer

The unit rate is 0.6.

Step 1: Understand the Given Ratio

The problem provided the ratio of 60 to 100. The task is to find the unit rate. The unit rate is the ratio of the first amount to 1 unit of the second amount.

Step 2: Compute for the Unit Rate

To calculate the unit rate, divide the first number by the second number. In this case, divide 60 by 100. Therefore, the unit rate is \( \frac{60}{100} = 0.6 \).

Step 3: Round Off to the Nearest Hundredth

The calculated unit rate is 0.6. Since this is already rounded to two decimal places, there is no need for further rounding action.

Key Concepts

Understanding Ratios

A ratio is a way to compare two numbers and express how much of one thing there is compared to another. When we talk about a ratio, we're usually interested in how much one part makes up of the whole. In the exercise, the given ratio is 60 to 100. Here, 60 can be thought of as 60 parts of a total where each whole consists of 100 such parts. This is similar to saying you have 60 out of 100 units of something, like 60 slices out of a pizza cut into 100 slices.

• The first number in the ratio (60) is known as the antecedent.
• The second number in the ratio (100) is called the consequent.

Ratio can be formatted in several ways: "60:100" or "60 to 100". They essentially mean the same thing, expressing the relationship between the two numbers.

Division for Unit Rate

Division is a mathematical operation where you split a quantity into equal parts. To find a unit rate, you will often use division to determine how much of one quantity corresponds to a single unit of another. For example, to find how many units of something one can make per unit of another thing. In our exercise, we are trying to find the unit rate for the ratio 60 to 100.
By dividing 60 by 100, we can find out how much one unit of the second number corresponds to:

• Perform the division: \( \frac{60}{100} = 0.6 \).
• Here, 0.6 is the result of the division and represents the unit rate.

This means for every 1 unit of the second quantity (consequent), there are 0.6 units of the first quantity (antecedent) present.

Rounding to the Nearest Hundredth

Rounding numbers is the process of adjusting them so that they are simpler to work with, whilst remaining close to the original value. Rounding to the nearest hundredth means you will round the number to two decimal places. This is a common requirement when we work with money or measurements where precision is required in hundredths. For example, if you have a number like 0.649, you check the third decimal place to decide rounding:

• If it is 5 or higher, increase the second decimal by 1.
• If it is less than 5, just keep the second decimal as is.

In our exercise, the unit rate calculated was 0.6, which has less than two decimal places. As it stands, 0.6 is equivalent to 0.60 and does not require further rounding, as it is already provided to the nearest hundredth.