Solving Fraction Problems: Help with Fractions

Solving Fraction Problems

To solve problems with fractions, it helps to understand what a fraction represents. Fractions are a handy way to show a portion of a whole. For instance, imagine that you have a whole pizza, and you'd like to share part of it with a friend. You would be sharing a fraction of your pizza. Likewise, if you bought a new pack of pencils and shared some with your friends, each friend would get a fraction of your pencils.

How to Write It

The first thing you'll learn about fractions is how to write them. Every fraction has a numerator and a denominator. The denominator is the number that's on the bottom of the fraction. It represents the total number of parts that the whole has. For example, if your pizza has five slices, the denominator of the fraction would be five.

The numerator goes on top of the fraction, and it tells you the number of parts that the fraction represents. If you gave your friend two out of your five slices of pizza, you could say that you gave away 2/5 of your pizza. In this fraction, the numerator is two.

Comparisons

Sometimes you'll solve problems that ask you to compare fractions. Let's say that you gave your friend 2/5 of your pizza, and you kept the remaining three slices for yourself (3/5). Who had more pizza, you or your friend? The correct answer is that you had more pizza, since 3/5 is larger than 2/5. You can figure this out by comparing the numerators of the two fractions. Since three is larger than two, you know that 3/5 represents a larger portion of the pizza than 2/5 does.

Adding and Subtracting

Imagine that instead of sharing pizza with just one friend, you were sharing with two friends. You gave one friend a single slice, or 1/5 of your pizza, and you gave your other friend two slices, or 2/5 of your pizza. What fraction of your pizza did you give away? To find out, you'd have to add the fractions 1/5 and 2/5. You know that you gave away a slice to one friend and two slices to the other friend, for a total of three slices (1 + 2 = 3). Three slices out of five is equal to the fraction 3/5, which is your answer. To add fractions with the same denominator, just add the numerators and keep the denominators the same.

You follow the same rule to subtract fractions. If you want to figure out how much pizza you had left for yourself after sharing with your friends, you would subtract the amount that your friends took, 3/5, from the total number of slices, 5/5. Since 5 - 3 = 2, this means that you had 2/5 of the pizza left for yourself.

Practice Problems

You have 17 pencils, and you decide to give three to Elisa, seven to Miguel and one to Angel. Answer the following questions:

1. What fraction of the pencils does each of your friends have?
2. What fraction of the pencils do you have left?
3. Who has the largest fraction of the pencils, and who has the smallest?
4. What fraction of the pencils do Angel and Miguel have altogether?

Solutions

1. Elisa has three pencils out of 17, so she has 3/17 of them. Miguel has 7/17, and Angel has 1/17.

2. To find out how many pencils are left, you first need to figure out how many pencils your friends have altogether. You add the fractions like this: 3/17 + 7/ 17 + 1/17. Since 3 + 7 + 1 = 11, your friends have 11/17 of the pencils. Now, to find out how many pencils you have left, you need to subtract 11/17 from 17/17. Since 17 - 11 = 6, you have 6/17 of the pencils left.

3. To put the fractions in order from largest to smallest, look at their numerators. The fraction 7/17 has the largest numerator, so Miguel has the most pencils. You have 6/17, which is the second-largest fraction. Next comes Elisa, with 3/17, and Angel has the fewest pencils, with just 1/17.

4. To answer this question, you need to add together the fractions of pencils that Miguel and Angel have. Miguel has 7/17 and Angel has 1/17, and 7 + 1 = 8, so they have 8/17 of the pencils altogether.