Problem 18 - Algebra 1: Concepts and Skills

Question

Find the unit rate. Round your answer to the nearest hundredth. $$\frac{15}{20}$$

Step-by-Step Solution

Answer

The unit rate of \( \frac{15}{20} \) is 0.75

Step 1: Understand the concept of unit rate

A unit rate compares a quantity to its unit of measure. A unit rate is a rate with 1 in the denominator.

Step 2: Perform Division

To get the unit rate, divide the numerator (15) by the denominator (20). The calculation is as follow: \( \frac{15}{20} = 0.75 \)

Step 3: Round to nearest hundredth

In this problem, since the outcome of the division is already at the hundredth place, there is no need to round off. Thus, the unit rate is 0.75.

Key Concepts

Understanding Ratios

When we talk about ratios, we're often comparing two numbers to understand the relationship between them. Imagine it as telling a story about how one quantity is related to another. For instance, if you have 15 apples and 20 oranges, the ratio of apples to oranges is 15:20. Ratios can be simplified just like fractions. This means you divide both sides of the ratio by their greatest common divisor to make it easier to understand. In our example, both 15 and 20 can be divided by 5, which simplifies our ratio to 3:4.
Ratios are powerful because they help us understand proportions, calculate, and compare things in everyday life. They can also be expressed as fractions or as a single number called a rate, where the second quantity is often set to one (unit rates). Understanding ratios is an essential step in problem solving and helps pave the way to deeper mathematical concepts.

Basics of Division

Division is a mathematical operation that lets us split a number into smaller, equal parts. It's much like sharing cookies among friends. To find out how many cookies each friend gets, you'd divide the total number of cookies by the number of friends. In the context of finding a unit rate, division helps us transform a fraction into a simpler form.
In our exercise, the fraction \( \frac{15}{20} \) needs to be simplified using division. By dividing 15 by 20, we are determining how many units of the first number exist per single unit of the second number. This process converts our ratio into a rate, which is more convenient when you need a comparison based on one. This operation nudges us closer to understanding and calculating the unit rate effortlessly, serving as a critical skill in various math problems.

Rounding Numbers

Rounding numbers is the process of simplifying a number while maintaining its value close to what it was. It's especially useful in real-world situations where precision isn't as vital, like estimating costs or time. When we round numbers to the nearest hundredth, we focus on the second decimal place.

• If the number in the third decimal place is 5 or greater, we increase the second decimal place by one.
• If it's less than 5, we leave the second decimal place unchanged.

In our example, the unit rate we calculated was 0.75. This rate already has its precision up to the hundredth place, making additional rounding unnecessary. Understanding how to round numbers is crucial because it often makes working with numbers easier, especially when dealing with money, measurements, and statistics. So next time you see a long decimal, you'll know exactly how to round it to suit your needs.