Problem 16 - Algebra 1: Concepts and Skills

Question

Find the unit rate. Round your answer to the nearest hundredth. $$\frac{6}{8}$$

Step-by-Step Solution

Answer

The unit rate is approximately 0.75. This is the rate per 1 unit.

Step 1: Identify the Fraction

Look at the fraction given, which is \(\frac{6}{8}\). This represents a rate.

Step 2: Calculate the Division

The unit rate is found by dividing the numerator by the denominator. So, divide 6 by 8.

Step 3: Round to the Nearest Hundredth

After performing the division, the decimal result needs to be rounded to the nearest hundredth place.

Key Concepts

Understanding Fractions

Fractions are a way to express parts of a whole. They consist of two parts—a numerator and a denominator. In the fraction \( \frac{6}{8} \), 6 is the numerator, which tells us how many parts we have, and 8 is the denominator, which tells us into how many parts the whole is divided. So, \( \frac{6}{8} \) means we have 6 out of 8 equal parts. Understanding fractions is crucial when finding unit rates, as the unit rate is essentially the decimal form of the fraction.

Performing Division with Fractions

To find the unit rate from a fraction, you need to perform division. This involves dividing the numerator by the denominator. In our example, you take 6 and divide it by 8. Here's how it works step by step:

• Divide 6 by 8
• You can set this up as a long division problem
• The result will be a decimal

For \( \frac{6}{8} \), dividing gives us 0.75. Division helps us convert the fraction into a form that's easier to understand in the context of rates. Remember, understanding how to perform this operation is key to calculating unit rates and understanding proportionality.

Rounding Decimals to the Nearest Hundredth

Often, you'll need to round decimals, especially in real-world contexts, like when finding unit rates. Rounding helps simplify decimal numbers to make them easier to work with. To round a number to the nearest hundredth, you focus on the third decimal digit. If this digit is 5 or more, you round up the second decimal digit by one. If it's less than 5, you leave the second decimal digit as is. For our number, 0.75, there’s no need for further rounding, as it’s already exactly at the hundredth decimal point. This process of rounding ensures that numbers are both easier to read and understand.