How to Do Word Problems Using Fractions
Even students who are gifted at mathematics sometimes struggle with the notorious and elusive word problem. When word problems include fractions, they become even trickier. Though it takes both effort and practice to get better at solving word problems involving fractions, translating a word problem into visual or numerical terms will help.
Read the word problem at least twice before you try to solve it. The first time, read it like a normal paragraph. The second time, read it more slowly, letting the words sink in. Don't try to solve the problem the first two times. Just try to understand the overall meaning.
Rewrite the last sentence of the word problem on a separate sheet of paper. The last sentence is the key to the problem. It tells you what you are trying to solve. If you can answer the last question, you can find the solution. For example, a word problem may say, "Sarah had three apples, but she gave one to Mark and shared half of one with Anna. Mary has two oranges. How many apples does Sarah have left?" The last sentence shows you what you need to find. You need to figure out how many apples are left after Sarah shares hers.
Cross out any information that seems unrelated to the last sentence. For example, in the word problem above, cross out the sentence "Mary has two oranges" because the question at the end does not ask about Mary or oranges.
Read the word problem once more, this time circling important clues. If you have not already crossed out a number, it is a clue. In the example, you would circle "three," "one" and "half of one." Write these hints on the same sheet of paper you used to write the last sentence; it is okay to write out the complete sentences. For example, you can write "Sarah had three apples" on one line, "she gave one to Mark" on the next, and "she shared half of one with Anna" on the third.
Look at the words near the hints and guess which operations go along with the numbers (subtraction, addition, multiplication or division). The operation will tell you what you need to do with the number, but it is not always given in clear, straightfoward terms. For example, the term "gave one" in the second hint describes subtraction because Sarah has less apples than when she started. For the same reason, the word "shared" in the third hint also describes subtraction.
Substitute the words that tell you which operation to do, such as "gave" and "shared," with actual mathematical symbols. The lengthy word problem will then become something like this: 3 - 1 = 2; then 2 - 1/2 = 1 1/2. Sarah is left with one and a half apples.
Draw sketches of the objects used in word problems to make solving problems involving fractions easier. This is especially useful if you are a visual learner. For example, you might write Sarah's name and draw a picture of three apples beneath it. Then shade one apple and write Mark's name in it to show that that Sarah gave one to Mark. Draw a line down the second apple to show the fraction one-half and write Anna's name in that half. All that is left is the one and a half apples still belonging to Sarah, which is your answer.
- Study key terms and translate them into mathematical operations. This will make solving word problems easier. For example, "combined, increased by or total of" generally means addition, "product of, factor of or times" generally means multiplication, and any "to be" verb or "yields or gives" generally means equals.
- Write clearly and legibly. By keeping your work organized, you are less likely to get confused.
- If drawing pictures does not work or if you are a hands-on learner, try using actual objects to solve the problem. In the example above, set up three chairs and stick papers with the names Sarah, Mark and Anna on each. Place three apples in front of Sarah and go through the word problem until you arrive at the correct answer.