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Multiplying Fractions by Whole Numbers
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What you will learn from this videoWhat you will learn
- A fraction represents part of a whole.
- We can apply what we know about multiplication to fractions.
- Fractions greater than 1 can be simplified to a mixed number.
- Discussion Questions
Before Video
How are addition and multiplication connected?ANSWERMultiplication is a shorthand way of writing repeated addition. 3 + 3 + 3 + 3 = 4 x 3.
The denominator shows the total number of equal parts in the whole. The numerator shows how many of those equal parts we have or are talking about. In the fraction [ggfrac]2/3[/ggfrac] the 3 shows there are 3 equal parts, and this fraction represents 2 of the 3 equal parts.
[ggfrac]1/5[/ggfrac] + [ggfrac]1/5[/ggfrac] + [ggfrac]1/5[/ggfrac] = [ggfrac]3/5[/ggfrac]. I added the numerators and kept the same denominator, 5.
[ggfrac]1/3[/ggfrac] + [ggfrac]1/3[/ggfrac] + [ggfrac]1/3[/ggfrac] + [ggfrac]1/3[/ggfrac] + [ggfrac]1/3[/ggfrac] = [ggfrac]5/3[/ggfrac]. I added the numerators and kept the same denominator.
[ggfrac]2/5[/ggfrac] + [ggfrac]2/5[/ggfrac] + [ggfrac]2/5[/ggfrac] + [ggfrac]2/5[/ggfrac] = ? [ggfrac]1/4[/ggfrac] + [ggfrac]1/4[/ggfrac] +[ggfrac]1/4[/ggfrac] = ?
ANSWER[ggfrac]2/5[/ggfrac] + [ggfrac]2/5[/ggfrac] + [ggfrac]2/5[/ggfrac] + [ggfrac]2/5[/ggfrac] = [ggfrac]8/5[/ggfrac]. [ggfrac]5/5[/ggfrac] is equal to 1. [ggfrac]8/5[/ggfrac] has three more fifths than [ggfrac]5/5[/ggfrac] so [ggfrac]8/5[/ggfrac] is greater than 1.
After Video
How would you write [ggfrac]3/4[/ggfrac]+ [ggfrac]3/4[/ggfrac] + [ggfrac]3/4[/ggfrac] + [ggfrac]3/4[/ggfrac] + [ggfrac]3/4[/ggfrac] as a multiplication problem?ANSWER5 x [ggfrac]3/4[/ggfrac]
Yes it would be the same. Sample answer: I would multiply 20 x [ggfrac]2/9[/ggfrac] because I think it would take less time than adding.
Gita is wrong. She multiplied both the numerator and the denominator of the fraction by 4. She should have just multiplied the numerator by 4 and kept the denominator the same.
Husam is wrong. 6 x [ggfrac]1/3[/ggfrac] is [ggfrac]6/3[/ggfrac] or 2 and 2 is not less than 1.
Sample answer: 2; 9; 10
- Vocabulary
- Fraction DEFINE
A fraction represents a part of a whole.
- Denominator DEFINE
The denominator of a fraction is the number below the line. The denominator shows the total number of equal parts in the whole.
- Numerator DEFINE
The numerator of a fraction is the number above the line. The numerator shows how many equal parts of the whole the fraction represents.
- Unit Fraction DEFINE
A fraction where the numerator is 1.
- Fraction greater than 1 DEFINE
A fraction greater than 1 is a fraction where the numerator is greater than the denominator. A fraction greater than 1 represents an amount greater than one whole.
- Mixed Number DEFINE
A mixed number is a number that includes both a whole number and a fraction.
- Whole DEFINE
The whole is 1 of something such as 1 circle or 1 unit on a number line.
- Equal Parts DEFINE
Equal parts are parts of the same size that the whole is divided into.
- Fraction DEFINE
- Reading Material
- Practice Word Problems
- Practice Number Problems
- Lesson Plan
- Teacher Guide
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