Problem 13 - Algebra 1: Concepts and Skills

Question

Find the unit rate. Round your answer to the nearest hundredth. 30 to 120

Step-by-Step Solution

Answer

The unit rate of 30 to 120 is 4

Step 1: Understand the problem

To solve this problem, the instruction to 'find the unit rate' means converting the ratio 30 to 120 so that the second term is 1.

Step 2: Divide 120 by 30

To find the unit rate, calculate \( \frac{120}{30} \).

Step 3: Calculate and round off

Perform the calculation and round off your answer to the nearest hundredth if necessary.

Key Concepts

Understanding Ratios

Ratios are a way to compare two quantities by using division. They help us understand how one value relates to another. The ratio can be expressed in different forms, such as 30:120, 30 to 120, or \( \frac{30}{120} \).

To find a unit rate, we convert the ratio so that the second term is 1. This means we'll calculate how much of one thing exists per unit of another. For instance, with the ratio 30:120, our aim is to find out how much of the first number corresponds to just one unit of the second number.

Finding the unit rate involves dividing the first number by the second. Therefore, in our example, it means dividing 30 by 120. Once you have the result, the ratio becomes \( x:1 \).

The Importance of Rounding

Rounding helps simplify numbers, making them easier to use and understand. When dealing with decimals, rounding is a useful tool to deal with otherwise awkward figures.

In the case of ratios and unit rates, rounding to the nearest hundredth means looking at the first two decimal places. If the number in the third decimal place is 5 or greater, you round up the number in the second decimal place by one. If it's less than 5, you leave the second decimal place as it is.

For example, if you end up with a number like 0.2505, you round it to 0.25 because the third decimal, 0, is less than 5. This simplification helps maintain clarity and precision without complicating the results.

Exploring Fractions in Unit Rate

Fractions are another way to express ratios. They help us break down numbers into smaller, more manageable parts. When calculating a unit rate, using fractions lets us look at the relationship between the two quantities in a direct way.

In our ratio of 30:120, we express it as a fraction, \( \frac{30}{120} \). Simplifying this fraction involves dividing both the numerator and the denominator by their greatest common factor. Here, both 30 and 120 are divisible by 30.

Thus, \( \frac{30}{120} \) simplifies to \( \frac{1}{4} \), implying that for every 1 unit of measurement considered, there's a corresponding 1/4 of the initial value. Understanding fractions helps us get a clearer overview of the quantities in play and their relationship in a way that whole numbers or decimals might not show as clearly.