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Multiplying Fractions by Fractions
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What you will learn from this videoWhat you will learn
- We'll learn how to multiply fractions by fractions.
- How to multiply fractions by MIXED numbers.
- And we'll see that this knowledge can help us make a model volcano, cook delicious pasta, and even prepare for a race!
- Discussion Questions
Before Video
How can you write [ggfrac]2/5[/ggfrac] + [ggfrac]2/5[/ggfrac] + [ggfrac]2/5[/ggfrac] as a multiplication problem? Find the product.ANSWER[ggfrac]2/5[/ggfrac] x 3, [ggfrac]2/5[/ggfrac] + [ggfrac]2/5[/ggfrac] + [ggfrac]2/5[/ggfrac] = [ggfrac]6/5[/ggfrac] = 1[ggfrac]1/5[/ggfrac], [ggfrac]2/5[/ggfrac] x 3 = [ggfrac]6/5[/ggfrac] = 1[ggfrac]1/5[/ggfrac]
Divide a square into 3 equal parts and shade 2 of those parts. Make 6 copies of that square. Count the thirds. There are 12 thirds, or [ggfrac]12/3[/ggfrac]. [ggfrac]12/3[/ggfrac] = 4, so [ggfrac]2/3[/ggfrac] x 6 = 4.
Multiply the numerator of the fraction by the whole number to get the numerator of the answer, and keep the denominator the same as the denominator in the fraction.
No. She multiplied both the numerator and the denominator by 3. She should have only multiplied the numerator by 3. The answer should be [ggfrac]9/5[/ggfrac], or 1[ggfrac]4/5[/ggfrac].
No. Mike added 4 and [ggfrac]1/5[/ggfrac]. The answer should be [ggfrac]4/5[/ggfrac].
After Video
How can you model [ggfrac]2/5[/ggfrac] x [ggfrac]3/4[/ggfrac]? Find the product.ANSWERDivide a square into fifths horizontally. Shade two of the fifths blue. Divide the square into fourths vertically. Shade three of the fourths yellow. The part of the square that is green (both blue and yellow) is the answer. [ggfrac]2/5[/ggfrac] x [ggfrac]3/4[/ggfrac] = [ggfrac]6/20[/ggfrac]
No. I think Safa used the rule for the addition of fractions rather than the rule for the multiplication of fractions. The correct product is [ggfrac]2/9[/ggfrac].
Multiply the numerators to get the numerator of the answer. Multiply the denominators to get the denominator of the answer. Example: [ggfrac]3/7[/ggfrac] x [ggfrac]1/2[/ggfrac] = [ggfrac]3/14[/ggfrac]
Convert both mixed numbers to fractions greater than 1. Then multiply using the rule for multiplying two fractions: multiply the numerators to get the numerator of the answer, and multiply the denominators to get the denominator of the answer. Example: 1[ggfrac]1/2[/ggfrac] x 3[ggfrac]2/3[/ggfrac] = [ggfrac]3/2[/ggfrac] x [ggfrac]11/3[/ggfrac] = [ggfrac]33/6[/ggfrac] = 5[ggfrac]3/6[/ggfrac] = 5[ggfrac]1/2[/ggfrac]
To multiply a fraction by a fraction we need to multiply the numerators and multiply the denominators. When one number is a whole number, we do not need to multiply the denominators. This is because a whole number has a denominator of 1.
- Vocabulary
- Fraction DEFINE
Represents a part of a whole.
- Mixed number DEFINE
A number made up of a whole number and a fraction.
- Numerator DEFINE
The number above the line in a fraction, which tells how many equal parts of the whole the fraction represents.
- Denominator DEFINE
The number below the line in a fraction, which tells how many equal parts are in the whole.
- Area model DEFINE
A shape (often a square) used to make a model of the whole and the operation used; in this case, multiplication of a fraction by a fraction.
- Convert DEFINE
Change the form of a mixed number to a fraction greater than 1 or a fraction greater than one to a mixed number.
- Fraction DEFINE
- Reading Material
- Practice Word Problems
- Practice Number Problems
- Lesson Plan
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Level 1
Find the product [ggfrac]1/4[/ggfrac] x [ggfrac]1/2[/ggfrac]
Level 2
Find the product [ggfrac]3/8[/ggfrac] x [ggfrac]5/6[/ggfrac]
Level 3
Find the product 1[ggfrac]2/3[/ggfrac] x 2[ggfrac]3/5[/ggfrac]
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