Core Connections: Course 3
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2. Section 8.2
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Exercise 96 Page 369

Practice makes perfect
To multiply the given fractions, remember that the product of two fractions is equal to the product of the numerators over the product of the denominators.
- 9/5 * 8/15
- 9* 8/5* 15
- 72/75
- 72Ă· 3/75Ă· 3
- 24/25
When adding or subtracting fractions, they should have the same denominator. In this exercise, we are given three fractions with different denominators. 1/5 +( - 2/15) -(- 4/9) To add fractions, their denominators need to be the same. Since 45 is a common factor of 5, 15, and 9, we can multiply both the numerator and denominator of 15 by 9, - 215 by 3, and - 49 by 5 to create a common denominator. Let's start with the first fraction.
1/5
1* 9/5* 9
9/45
Let's continue with the second fraction.
- 2/15
- 2* 3/15* 3
- 6/45
Finally, let's expand the last fraction.
- 4/9
- 4* 5/9* 5
- 20/45
Now that we have a common denominator, we can proceed to simplifying the expression.
9/45 +( - 6/45) -(- 20/45)
9/45 +( - 6/45) + 20/45
9/45 +- 6/45 + 20/45
9+(- 6)+20/45
9-6+20/45
23/45
To multiply the given fractions, remember that the product of two fractions is equal to the product of the numerators over the product of the denominators.
- 4/8 * 3/7* ( - 2/5)
- 4/8 * ( - 2/5)* 3/7
4/8 * 2/5* 3/7
4* 2* 3/8* 5* 7
8* 3/8* 35
8* 3/8* 35
3/35
We want to simplify the following expression. 3/5* (- 2/7)+(- 5/7)(3/10) According to the order of operations, we need to start by performing the multiplications. Remember that the product of two fractions is equal to the product of the numerators over the product of the denominators.
3/5* (- 2/7)+(- 5/7)(3/10)
(-3/5* 2/7)+(- 5/7)(3/10)
(-3/5* 2/7)+(- 5/7 * 3/10)
(-3* 2/5* 7)+(- 5* 3/7* 10)
(- 6/35)+(- 15/70)
Next, we will do the addition. To add fractions, their denominators need to be the same. Since 70 is a multiple of 35, we can multiply both the numerator and denominator of - 635 by 2 to create a common denominator. Let's do it!
(- 6/35)+(- 15/70)
(- 6* 2/35* 2)+(- 15/70)
(- 12/70)+(- 15/70)
Now that we have a common denominator, we can proceed to simplifying the expression.
(- 12/70)+(- 15/70)
- 12/70+- 15/70
- 12+(- 15)/70
- 12-15/70
- 27/70
- 27/70
Before we evaluate the expression, let's first rewrite it so that all of the numbers are fractions.
- 8 19+ 3 56
- 8* 9+1/9+3* 6+5/6
- 72+1/9+18+5/6
- 73/9+23/6
When adding or subtracting fractions, they should have the same denominator. In this case, we have two fractions with different denominators. - 73/9+23/6 Since 18 is a multiple of both 9 and 6, we can multiply both the numerator and denominator of - 739 by 2 to create a common denominator.
- 73/9+23/6
- 73* 2/9* 2+23/6
- 146/18+23/6
Next, let's multiply both the numerator and denominator of 236 by 3 to create a common denominator.
- 146/18+23/6
- 146/18+23* 3/6* 3
- 146/18+69/18
Now that we have a common denominator, we can proceed to simplifying the expression.
- 146/18+69/18
- 146/18+69/18
- 146+69/18
- 77/18
- 77/18
We can also write the result as a mixed number.
- 77/18
- (72+5/18)
- (72/18+5/18)
- (4+5/18)
- 4 518
Before we evaluate the given expression, let's first rewrite the expression so that all of the numbers are fractions.
2 12 * 4 15
2* 2+1/2 * 4* 5+1/5
4+1/2 * 20+1/5
5/2 * 21/5
When multiplying fractions, remember that the product of two fractions is equal to the product of the numerators over the product of the denominators.
5/2 * 21/5
5* 21/2* 5
5* 21/2* 5
21/2
We can also write the result as a mixed number.
21/2
(20+1/2)
20/2+1/2
10+1/2
10 12