How to Teach Kids to Solve Fraction Problems
Students may solve two different types of fraction problems. The first type includes straightforward drills involving addition, subtraction, multiplication and division. The second type requires logic and critical thinking to solving word problems. Both are addressed here.
Teaching Kids to Use Fractions
What Is a Fraction?
Before you begin teaching about fractions, you must teach about what a fraction is. The traditional way is to state that a fraction represents a certain part of a whole object. Fractions can be perceived in the following ways:
- Four people equally share one object, such as a pizza; each person gets ¼ (1 ÷ 4 = ¼)
- Four equal parts makes a whole
- Combining 1/4 from one pizza plus 1/4 from another is 2/4 (1/4 + 1/4 = 2/4)
- You can combine fractional units no matter how many you have: 1/4 + 1/4 + 1/4 + 1/4 + 1/4 + 1/4 + 1/4 = 7/4 (greater than one)
- The number line can illustrate fractional numbers: 3 1/4 pizzas is more than three pizzas but less than four pizzas
Once your students grasp all of these aspects, they will be ready to integrate them with the math skills they already have.
Relating Math Skills to Fractions
Before children begin to learn about fractions, they will have already learned how to add, subtract, multiply and divide. To teach them to add, subtract, multiply and divide fractions, you will simply teach them how to use those skills with fractions. The basics are listed here.
To add fractions, you must be sure the denominators are the same. Teach equivalent fractions with this rule:
- A common denominator is the smallest number that can be divided by all of the denominators in the problem.
Once all of the fractions have been changed to equivalent fractions with a common denominator, add the numerators, but keep the common denominator the same. Remember to reduce the fraction if necessary. Example: 1/4 + 1/4 = 2/4 = 1/2
To subtract fractions, you start the same as you do when adding them: be sure they have a common denominator. Subtract the second numerator from the first, and put the answer over the common denominator.
If the first number is a mixed number (a whole number and a fraction) and the fractional part is smaller than the second number, then you will have to teach your students to incorporate all or part of the whole number (depending on their grade) with the fraction. Finally, reduce the fraction if needed. Example: 1/4 - 1/8 = 2/8 - 1/8 = 1/8
No common denominators are needed when multiplying. Simply multiply the numerators with one another to find the numerator of the answer. Then multiply the two denominators. Reduce as necessary. Example: 3/8 x 1/2 = (3 x 1) / (8 x 2) = 3/16
Again, no common denominators need to be found. Simply turn the second fraction upside down (it is now called the reciprocal), and then multiply the two fractions. Example: 1/4 ÷1/6 = 1/4 x 6/1 = 6/4 = 1 2/4 = 1 1/2
Steps to Take
Word problems give students a chance to practice thinking logically. You can help by giving your students some steps to go through when solving the problem.
- 1. Read the problem until you understand it.
- This might include stating the problem in your own words, listing all of the questions you need to find answers for and eliminating any unnecessary information in the problem.
- 2. Make a plan.
- Figure out how you will find the answer. Will a drawing or a chart help? Are there words that tell you to add, subtract, multiply or divide? Can you make a formula? Use whatever you can think of to solve the problem.
- 3. Follow your plan.
- Patiently do everything that you need to do. In some problems, there will be only one simple step. In other problems, there will be a few, or even a lot of steps to go through.
- 4. Check your answer and review how you found it.
- See if the answer is logical. For example, if your answer is bigger than the numbers you started out with, you easily know you goofed somewhere. If you successfully found the correct answer, study what you did to find it so that you can repeat the process for a similar problem in the future.
Words that Help
Sometimes words in the story problem give a clue as to which mathematical methods to use. Some of the most common are:
- Add when you see words like added, greater, in addition, in excess, increased, more than and sum.
- Subtract if you see words like decreased by, difference, diminished, less than, reduced, remainder and subtract.
- Multiply if there are words such as times, product, percent of, interest on, as much and area.
- Divide when there are words like quotient, per, out of and divide.
Here is an example of a multi-step problem and how a sixth grade student might figure it out.
- Peter rode his bike 8 1/4 miles to Paul's house. It took him two hours and 35 minutes (2 7/12 hours) to get there, but he stopped for 45 minutes to talk to Philip. How fast did Peter go when he was riding his bike?
- 1. What I need to find out:
a) How long did Peter actually ride on his bike?
b) How fast did Peter go when he was on his bike?
- 2. Make a plan:
a) Subtract the time Peter talked to Philip from how long it took him to get to Paul's.
b) Divide the number of miles he traveled by the time he actually rode to find out how fast he went.
- 3. Follow your plan:
a) 2 7/12 hours - ¾ hours = 2 7/12 hours - 9/12 hours = 1 19/12 hours - 9/12 hours = 1 10/12 hours = 1 5/6 hours (1 hour 50 minutes)
b) 8 1/4 miles ÷1 5/6 hours = 33/4 miles ÷ 11/6 hours = 33/4 miles x 6/11 hours = 18/4 mph = 4 2/4 mph = 4 1/2 mph
- Check and review your answer: It makes sense that it would take just under two hours to get somewhere when riding at a speed of 4 ½ miles per hour.
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