Amy has a master's degree in secondary education and has taught math at a public charter high school.
Watch this video lesson to learn how to solve word problems with fractions in them easily by turning your fractions into whole numbers. Learn what you need to do to get rid of your fractions so you can easily solve your problem.
A Word Problem
We begin with a word problem. Sam and John are going to a party. Sam is bringing one-fifth of the food for the party. He's bringing things like fried chicken and potato salad. Together, Sam and John are bringing half of the food for the whole party. What part is John responsible for?
To solve this problem, we first need to label what we are looking for and the other important parts that we need. We are looking for the part that John is responsible for, so we will label that part x. It also tells us that Sam's part is one-fifth, or 1/5. We label Sam's part with 1/5. The problem says that Sam's part plus John's part equals one-half, or 1/2. We label Sam plus John's part with 1/2.
When labeling, we can either write our information below the problem in its own little section, or we can highlight the part of the problem that talks about it and then write the number or variable next to the highlighted part. Do whichever makes sense to you.
Now that we've labeled everything, let's write the equation. We know it is an addition problem because the problem says that 'together Sam and John are bringing half of the food.' We write Sam's part plus John's part equals a half, substituting in our numbers and variables. We get 1/5 + x = 1/2. Oh no, we have fractions!
Removing the Fractions
Let's make our problem-solving life easier by removing the fractions. How do we do that? We do that by multiplying everything by the least common denominator. Remember that when you want to add or subtract fractions, we look for the smallest number that all of our denominators can divide evenly into.
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In our case, our fractions are 1/5 and 1/2 with denominators of 5 and 2. What is the least common denominator? It is 10. Both 5 and 2 divide evenly into 10. So since 10 is our least common denominator, we multiply all of our terms by 10. Something really cool happens when we do this. Look. 1/5 times 10 equals 2. x times 10 equals 10x. 1/2 times 10 equals 5. We get 2 + 10x = 5. Look! No fractions! Woohoo!
Solving the Problem
Now we can go about solving our problem much more easily. We use our algebra skills in moving terms around from one side of an equation to the other and in isolating our variable. We move the 2 to the other side by subtracting it from both sides. We get 10x = 3. Then we divide by 10 on both sides to get the x by itself. We get x = 3/10. So this means that John is supplying three-tenths of the food for the whole party.
What have we learned? We learned that in order to solve word problems with fractions in them we first label all of our important pieces. Then we write our equation. To remove the fractions in our equation, we multiply all of our terms by the least common denominator, the smallest number that all of our denominators can divide evenly into. Doing this changes our fractions into whole numbers. Once we have an equation with only whole numbers, we can proceed by using our algebra skills to isolate our variable to find our answer.
The process of completing this lesson could help you to:
Identify the important parts of a word problem that contains fractions
Write an equation that includes the fractions
Multiply by the least common denominator to remove the fractions and solve the equation
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