Fractions, Percents,and Decimals in Word Problems Study Guide
Find practice problems and solutions for these concepts at Fractions, Percents,and Decimals in Word Problems Practice Problems.
The word problems we've looked at so far have involved mostly integers. In this chapter, we'll look at word problems that involve fractions, percents, and decimals. We'll use the same strategies we used to solve integer word problems.
Fractions: Subject Review
To add two like fractions, add the numerators of the fractions and keep the denominator.
To add two unlike fractions, find common denominators and then add the numerators.
To subtract like fractions, subtract the numerator of the second fraction from the numerator of the first and keep the denominator.
To subtract unlike fractions, find common denominators, subtract the numerator of the second fraction from the numerator of the first, and keep the denominator.
To multiply two fractions, like or unlike, multiply the numerators and multiply the denominators.
To divide two fractions, like or unlike, multiply the first fraction by the reciprocal of the second fraction.
To convert an improper fraction into a mixed number, divide the numerator of the fraction by the denominator. The whole number part of that division is the whole number part of the mixed number. The remainder, if any, becomes the numerator of the fraction, and the denominator remains the same.
To reduce or simplify a fraction, find the greatest common factor of the numerator and denominator and divide the numerator and denominator by that number.
Fuel for Thought
Like fractions have the same denominator; and are like fractions. Unlike fractions have different denominators; and are unlike fractions. A proper fraction a value between 0 and 1 or between –1 and 0. The number in the numerator is usually less than the number in the denominator of the fraction. An improper fraction has a value greater than or equal to 1, or less than or equal to –1. A mixed number contains both an integer and a fraction. The greatest common factor of two numbers is the largest integer that both numbers can be divided by with no remainder.
Now that we've reviewed how to work with fractions, let's look at some fraction word problems. We can use any of the strategies we've learned to answer these questions.
DeDe pours 1 cup of cereal into a bowl. She adds cup of milk from a container that contains cups of milk. How many cups of milk are left in the container?
Let's use the eight-step process to answer this question.
Read the entire word problem.
We are given the amount of milk in the container and the amount that DeDe pours into her cereal bowl.
Identify the question being asked.
We are looking for how much milk is left in the container.
Underline the keywords.
The keyword left signals subtraction.
Cross out extra information and translate words into numbers.
We do not need to know that there is 1 cup of cereal in the bowl. That information will not help us solve this problem, so cross it out.
List the possible operations.
To find how much milk is left in the container, we have to subtract the original amount in the container from the amount that DeDe poured out.
Write number sentences for each operation.
Solve the number sentences and decide which answer is reasonable.
Convert one-half to fourths and subtract:
Since DeDe used only half a cup of milk, this answer seems reasonable.
Check your work.
We solved this problem using subtraction, so we must use addition to check our work. Add the number of cups of milk DeDe put in her cereal to the new amount of milk in the container. The sum should equal the original volume of milk in the container: + = . Our answer is correct.
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