Problem 70 - Prealgebra

Question

Express each ratio as a unit rate. Round to the nearest hundredth, if necessary. 120 miles on 4.3 gallons

Step-by-Step Solution

Answer

The unit rate is 27.91 miles per gallon.

Step 1: Understand the Problem

We are given a ratio of 120 miles to 4.3 gallons and need to express this as a unit rate, which is the ratio of miles per one gallon.

Step 2: Set Up the Division

To find the unit rate, divide the number of miles by the number of gallons. Write the division as: \( \frac{120}{4.3} \).

Step 3: Perform the Division

Perform the division: \( 120 \div 4.3 \approx 27.90697674 \).

Step 4: Round the Result

Round the quotient from the previous step to the nearest hundredth: 27.91.

Key Concepts

Ratio

A ratio is a mathematical expression that compares two quantities. In our exercise, the ratio is 120 miles to 4.3 gallons. This tells us how many miles are traveled for a given number of gallons. Ratios provide a sense of proportion and can be expressed in various ways, such as fractions or using a colon, like 120:4.3.

Understanding ratios helps us identify relationships between different quantities. In the context of our problem, the main goal is to convert this specific ratio into a unit rate, providing clear insight on the distance that can be covered per one gallon.

Division

Division is a crucial mathematical operation when working with ratios and unit rates. In our exercise, to find out how many miles can be driven per gallon, we divide the total miles (120) by the total gallons (4.3).

• Set up the division as a fraction: \( \frac{120}{4.3} \)
• This operation tells us the distance traveled for each gallon used.

Division allows us to break down a complex relationship into more understandable, smaller parts, enabling us to calculate and interpret unit rates effectively.

Rounding

Rounding is a mathematical method used to simplify numbers, making them easier to work with or understand. After performing division in our problem, we obtain a quotient of approximately 27.90697674. This number can be cumbersome in real-world applications, so we round it to make it more manageable.

• To round to the nearest hundredth, focus on the first two digits after the decimal point. In our case, we examine 90 and the third digit, which is 6, dictates rounding up.

Rounding makes the resulting unit rate 27.91 miles per gallon, providing a neat and practical figure for reports or calculations.

Problem Solving

Problem solving involves analyzing the given information and taking steps to find a solution. In the exercise, we first identified the ratio of miles to gallons. Then we used division to convert this ratio into a unit rate. Finally, we applied rounding to make the result more applicable.

• Step 1: Understand the problem by identifying given ratios and what needs to be determined.
• Step 2: Set up a division to calculate the unit rate.
• Step 3: Perform the division accurately.
• Step 4: Round to simplify the result.

This structured approach ensures you handle mathematical challenges efficiently and effectively.