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Performing Basic Operations with Fractions

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  • 0:04 Franco's Fraction Homework
  • 0:22 Adding and Subtracting…
  • 2:03 Multiplying Fractions
  • 3:07 Dividing Fractions
  • 4:00 Lesson Summary
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Lesson Transcript
Instructor: Bethany Calderwood

Bethany has taught special education in grades PK-5 and has a master's degree in special education.

You probably know how to perform basic operations for whole numbers, but do you know how to add, subtract, multiply, and divide fractions? This lesson introduces you to the rules for basic operations with fractions.

Franco's Fraction Homework

Franco grabs a bag of gummy bears and sits down to do his math homework. Franco just learned how to read and write fractions, and now he is learning how to use them in basic operations like addition, subtraction, multiplication, and division. Let's work with Franco and see how it's done.

Adding and Subtracting Fractions

What You Need to Know

Addition and subtraction of fractions both follow the same rule that says you can perform the operations on the numerator, but the denominator stays the same. For this reason, you can only add or subtract fractions with the same denominator, like 2/5 and 1/5. If you want to add fractions with different denominators, you must first find a common denominator.

Let's Try It

Franco dumps out a handful of gummy bears. 3/8 of the bears are red and 2/8 of the bears are yellow. If Franco adds the red and yellow bears, how many will he have?

  • We could write the problem like this: 3/8 + 2/8
  • Both fractions have the same denominator, so we can add them as they are
  • We add the numerators, so: 3 + 2 = 5
  • The denominator stays the same, so the denominator remains 8
  • We see that 3/8 + 2/8 = 5/8

Franco eats those gummy bears and gets a new handful. He wants to eat 7/10 of the gummy bears, but his sister walks in and asks for some. If Franco gives her 2/5 of the bears, how many will he have left?

  • This problem could be written: 7/10 - 2/5
  • The denominators are different! We know that 10 is a multiple of 5, so 2/5 can be converted to an equivalent fraction, which would be 4/10
  • Now the problem is: 7/10 - 4/10
  • We subtract the numerators, and the denominator stays the same
  • The final problem is: 7/10 - 4/10 = 3/10

Multiplying Fractions

What You Need to Know

Multiplying fractions is different from adding and subtracting them. The procedure is actually quite simple, as you multiply the two numerators to get the numerator for your answer, and then, you multiply the two denominators to get the denominator for your answer. There's no need to find a common denominator.

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