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Dividing Fractions by Fractions
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What you will learn from this videoWhat you will learn
- We'll learn how to divide fractions by fractions.
- We will also learn how to divide mixed numbers by mixed numbers.
- And we will see how this knowledge can help us throw a party, go for a run, and even make our own clothes!
- Discussion Questions
Before Video
What happens if you divide 1 pie by 4? What happens if you divide it by [ggfrac]1/4[/ggfrac]?ANSWERIf I divide 1 by 4, I am sharing 1 pie among 4 people, and each person gets [ggfrac]1/4[/ggfrac] of the pie. If I divide a pie by [ggfrac]1/4[/ggfrac], then I want to know how many [ggfrac]1/4[/ggfrac]-sized pieces there are in the pie. There are 4.
To multiply fractions, I multiply the numerators together and multiply the denominators together. Therefore, [ggfrac]1/4[/ggfrac] x [ggfrac]5/6[/ggfrac] = [ggfrac]5/24[/ggfrac].
I want to know how many groups of [ggfrac]2/3[/ggfrac] there are in 4 wholes. If I draw a model of the problem, I split each of 4 whole circles into 3 equal parts, and put 2 of those parts into each group. I count 6 groups of [ggfrac]2/3[/ggfrac]. Therefore 4 ÷ [ggfrac]2/3[/ggfrac] = 6. If I multiply 4 x [ggfrac]3/2[/ggfrac], I get [ggfrac]12/2[/ggfrac] = 6, so 4 ÷ [ggfrac]2/3[/ggfrac] is the same as 4 x [ggfrac]3/2[/ggfrac]. I keep the first number the same, change the operation to multiplication, and flip the fraction.
My answer is more than 3. If I divide by a number that is less than 1, that means I am making many little pieces and I want to know how many groups there are. If I divide 3 wholes into pieces of size [ggfrac]1/5[/ggfrac], I count 15 groups of [ggfrac]1/5[/ggfrac].
I can split 2 into fourths as indicated in the denominator, 4. So each of the 2 wholes is split into 4. I have 8 fourths, plus the 3 fourths from [ggfrac]3/4[/ggfrac]. In total, there are 11 fourths, so 2[ggfrac]3/4[/ggfrac] = [ggfrac]11/4[/ggfrac].
After Video
How can you turn [ggfrac]3/4[/ggfrac] ÷ [ggfrac]1/2[/ggfrac] into a multiplication problem?ANSWERI change the operation to multiplication and flip the second fraction. [ggfrac]3/4[/ggfrac] ÷ [ggfrac]1/2[/ggfrac] = [ggfrac]3/4[/ggfrac] x [ggfrac]2/1[/ggfrac].
No, I must keep the first fraction the same and flip the second fraction. The first fraction tells how much I have, and the second fraction tells the size of the groups I am trying to make.
No! To solve [ggfrac]3/4[/ggfrac] ÷ [ggfrac]1/2[/ggfrac], I want to know how many one-half-sized pieces there are in three-fourths. [ggfrac]3/4[/ggfrac] ÷ [ggfrac]1/2[/ggfrac] = [ggfrac]3/4[/ggfrac] x [ggfrac]2/1[/ggfrac] = [ggfrac]3/2[/ggfrac] = 1[ggfrac]1/2[/ggfrac]. To solve [ggfrac]1/2[/ggfrac] ÷ [ggfrac]3/4[/ggfrac], I want to know how many three-fourth-sized pieces there are in one half. [ggfrac]1/2[/ggfrac] ÷ [ggfrac]3/4[/ggfrac] = [ggfrac]1/2[/ggfrac] x [ggfrac]4/3[/ggfrac] = [ggfrac]2/3[/ggfrac]. I get two very different answers!
I need to turn 1[ggfrac]3/5[/ggfrac] into a mixed number. 1[ggfrac]3/5[/ggfrac] = [ggfrac]8/5[/ggfrac].
It should be less than [ggfrac]1/2[/ggfrac], because the number that I am dividing by, 1[ggfrac]3/5[/ggfrac] or [ggfrac]8/5[/ggfrac], is greater than 1.
- Vocabulary
- Fraction DEFINE
A number that expresses equal parts of a whole.
- Numerator DEFINE
The number on the top of the fraction, which tells us how many parts of the whole we have.
- Denominator DEFINE
The number on the bottom of the fraction, which tells us how many equal parts the whole has been cut into.
- Mixed number DEFINE
A number that combines whole numbers and fractions.
- Simplify DEFINE
Express a fraction using the smallest numbers possible, without changing the amount that the fraction represents.
- Keep-Change-Flip DEFINE
A method that helps us remember how to change a division problem into a multiplication problem.
- Fraction DEFINE
- Reading Material
- Practice Word Problems
- Practice Number Problems
- Lesson Plan
- Teacher Guide