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We're going to take a page and look at a few examples of word problems that use fractions. It will be good practice. We'll keep them pretty simple.

Addition

Question: The grocer gave you 5/9 of a bunch of bananas. You already had 2/9 of a bunch in your bag. Do you now have a whole bunch in your bag?

Strategy: This problem has two parts. You need to figure out how much of a bunch you now have and then you have to figure out if it is greater than a full bunch.

How much do you have?
5/9 + 2/9 = ?
• Common denominators: Yes.
• Add numerators: 5+2=7
• New fraction: 7/9
• Simplify: Not needed.
Answer: You have 7/9 of a bunch.

Do you have a whole bunch?
Is 7/9 of a bunch greater than 1 bunch?
Answer: No. 7/9 < 1

Subtraction

Question: You have a bag with 8 marbles. The bag can hold a maximum of 12 marbles. You let your friend borrow 3 marbles. What fraction of the bag do you have left?

Strategy: You weren't given a direct fraction in this problem. Can you see how you have 8/12 of a bag and you have to give up 3/12 of a bag? You were given two values: 8 and 3. The possible number of marbles is 12 for each value.

How much do you have left?
8/12 - 3/12 = ?
• Common denominators: Yes.
• Subtract numerators: 8-3=5
• New fraction: 5/12
• Simplify: Not needed.
Answer: You have 5/12 of a bag of marbles left.

Multiplication

Question: A carpenter is fixing a house. He needs to cut some beams. He will be sawing off 2/3 of a six and a half foot beam. How much will he be sawing off?

Strategy: Remember that multiplication word problems usually use the word "of". You might have "one half of six" or "2/3 of 9". That should help you figure out when you need to multiply. We're also using some words instead of numerals in the problem. You need to figure out how the numbers will look. The question is asking how much he will saw off. You have one fraction multiplied by a mixed number.

How many feet of the beam is he sawing off?
2/3 * 6 1/2 = ?
• Convert to improper fractions: 6 1/2 = 6 + 1/2 = 12/2 + 1/2 = 13/2
• Rewrite problem: 2/3 * 13/2 = ?
• Multiply numerators: 2*13=26
• Multiply denominators: 3*2=6
• New fraction: 26/6
• Convert to mixed number: 26/6 = 26÷6 = 4r2 = 4 2/6
• Simplify: 2 and 6 have the common factor 2. Divide the top and bottom by 2. 2/6 = 1/3
Answer: He will saw off 4 1/3 feet of the beam.

Division

Question: There are 12 kids at a birthday party. There are three and a half pies and everyone will get an equal amount of pie. How much pie does each kid get?

Strategy: This is a division problem. We are taking a big amount and dividing it up for a bunch of people. We have a mixed number being divided by a whole number. Try to convert the whole number and the mixed number into improper fractions. Then you can go through the normal steps of division for fractions.

How much pie does each kid get?
3 1/2 ÷ 12 = ?
• Convert:
3 1/2 = 3 + 1/2 = 6/2 + 1/2 = 7/2
12 = 12/1
• Rewrite: 7/2 ÷ 12/1 = ?
• Reciprocal of divisor: 1/12
• Rewrite as multiplication problem: 7/2 * 1/12 =?
• Multiply numerators: 7*1=7
• Multiply denominators: 2*12=24
• New fraction: 7/24
• Simplify: None needed. No common factors.
Answer: Each kid gets 7/24 of a pie.

While 7/24 is the right answer, can you see how that number is really close to 8/24? 8/24 is equivalent to 1/3. That answer means each kid almost gets one third of a pie. Sometimes it is easier to round numbers off. It's a lot easier to think about one third of a pie. Seven twenty-fourths isn't as easy to visualize as one third. When you are cutting up that pie, you can easily cut the pieces in thirds. It won't be exact, but it's a party! Your friends will understand.

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