Core Connections: Course 2
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1. Section 6.1
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Exercise 8 Page 323

Practice makes perfect
When adding or subtracting fractions, they should have the same denominator. In this exercise, we have two fractions with different denominators. - 3/4 - 2/5 Since 20 is a multiple of both 4 and 5, we can first multiply both the numerator and denominator of - 34 by 5 to create a common denominator.

- 3/4 - 2/5
- 3* 5/4* 5 - 2/5
- 15/20 - 2/5

Next, we can multiply both the numerator and denominator of 25 by 4 to create a common denominator.

- 15/20 - 2/5
- 15/20 - 2* 4/5* 4
- 15/20 - 8/20

Now that we have a common denominator, we can proceed to simplifying the expression.

- 15/20 - 8/20
- 15/20 - 8/20
- 15-8/20
- 23/20
- 23/20

The simplified expression is equal to - 2320.

When adding or subtracting fractions, they should have the same denominator. In this exercise, we have two fractions with different denominators. 7/8 - 2/3 Since 24 is a multiple of both 8 and 3, we can first multiply both the numerator and denominator of 78 by 3 to create a common denominator.

7/8 - 2/3
7* 3/8* 3 - 2/3
21/24 - 2/3

Next, we can multiply both the numerator and denominator of 23 by 8 to create a common denominator.

21/24 - 2/3
21/24 - 2* 8/3* 8
21/24 -16/24

Now that we have a common denominator, we can proceed to simplifying the expression.

21/24 -16/24
21-16/24
5/24

The simplified expression is equal to 524.

When adding or subtracting fractions, they should have the same denominator. In this exercise, we have two fractions with different denominators. 1/3 - 5/6Since 6 is a multiple of 3, we can multiply both the numerator and denominator of 13 by 2 to create a common denominator.

1/3 -5/6
1* 2/3* 2 -5/6
2/6 -5/6

Now that we have a common denominator, we can proceed to simplifying the expression.

2/6 -5/6
2-5/6
- 3/6
- 3/6
- 1/2

The simplified expression is equal to - 12.

Before we can evaluate a sum or difference involving mixed numbers, the mixed numbers must first be rewritten as fractions.

a bc a* c+b/c Simplify
1 23 1* 3+2/3 5/3

When adding or subtracting fractions, they should have the same denominator. In this exercise, we have two fractions with different denominators. 1 23 + (- 2/5) ⇔ 5/3 + (- 2/5) Since 15 is a multiple of both 3 and 5, we can first multiply both the numerator and denominator of 53 by 5 to create a common denominator.

5/3+(- 2/5)
5* 5/3* 5+(- 2/5)
25/15+(- 2/5)

Next, we can multiply both the numerator and denominator of - 25 by 3 to create a common denominator.

25/15+(- 2/5)
25/15+(- 2* 3/5* 3)
25/15+(- 6/15)

Now that we have a common denominator, we can proceed to simplifying the expression.

25/15+(- 6/15)
25/15-6/15
25-6/15
19/15

The simplified expression is equal to 1915.

When adding or subtracting fractions, they should have the same denominator. In this exercise, we have two fractions with different denominators. 4/7 - (- 3/8) Since 56 is a multiple of both 7 and 8, we can first multiply both the numerator and denominator of 47 by 8 to create a common denominator.

4/7-(- 3/8)
4* 8/7* 8-(- 3/8)
32/56-(- 3/8)

Next, we can multiply both the numerator and denominator of - 38 by 7 to create a common denominator.

32/56-(- 3/8)
32/56-(- 3* 7/8* 7)
32/56-(- 21/56)

Now that we have a common denominator, we can proceed to simplifying the expression.

32/56-(- 21/56)
32/56+21/56
32+21/56
53/56

The simplified expression is equal to 5356.

Before we can evaluate a sum or difference involving mixed numbers, the mixed numbers must first be rewritten as fractions.

a bc a* c+b/c Simplify
- 4 12 - (4* 2+1/2) - 9/2
3 19 3* 9+1/9 28/9

When adding or subtracting fractions, they should have the same denominator. In this exercise, we have two fractions with different denominators. - 4 12 + 3 19 ⇔ - 9/2 + 28/9 Since 18 is a multiple of both 2 and 9, we can first multiply both the numerator and denominator of - 92 by 9 to create a common denominator.

- 9/2+28/9
- 9* 9/2* 9+28/9
- 81/18+28/9

Next, let's multiply both the numerator and denominator of 289 by 2 to create a common denominator.

- 81/18+28/9
- 81/18+28* 2/9* 2
- 81/18+56/18

Now that we have a common denominator, we can proceed to simplifying the expression.

- 81/18+56/18
- 81/18+56/18
- 81+56/18
- 25/18
- 25/18

The simplified expression is equal to - 2518.