Core Connections: Course 1
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2. Section 5.2
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Exercise 64 Page 234

Practice makes perfect
When adding or subtracting fractions, they should have the same denominator. In this exercise, we have two fractions with different denominators. 5/6 + 2/3Since 6 is a multiple of 3, we can multiply both the numerator and denominator of 23 by 2 to create a common denominator.
5/6+2/3
5/6+2*2/3*2
5/6+4/6
Now that we have a common denominator, we can proceed to simplifying the expression.
5/6+4/6
5+4/6
9/6
3/2
1 12
When adding or subtracting fractions, they should have the same denominator. In this exercise, we have two fractions with different denominators. 7/8 - 1/2Since 8 is a multiple of 2, we can multiply both the numerator and denominator of 12 by 4 to create a common denominator.
7/8 - 1/2
7/8 - 1* 4/2* 4
7/8 - 4/8
Now that we have a common denominator, we can proceed to simplifying the expression.
7/8 - 4/8
7-4/8
3/8

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
1 14 1* 4+1/4 5/4
When adding or subtracting fractions, they should have the same denominator. In this exercise, we have two fractions with different denominators. 1 23 + 1 14 ⇔ 5/3 + 5/4 Since 12 is a multiple of both 3 and 4, we can first multiply both the numerator and denominator of 53 by 4 to create a common denominator.
5/3+5/4
5* 4/3* 4+5/4
20/12+5/4
Next, we can multiply both the numerator and denominator of 54 by 3 to create a common denominator.
20/12+5/4
20/12+5* 3/4* 3
20/12+15/12
Now that we have a common denominator, we can proceed to simplifying the expression.
20/12+15/12
20+15/12
35/12
2 1112

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
2 13 2* 3+1/3 7/3
1 56 1* 6+5/6 11/6
When adding or subtracting fractions, they should have the same denominator. In this exercise, we have two fractions with different denominators. 2 13 - 1 56 ⇔ 7/3 - 11/6 Since 6 is a multiple of 3, we can multiply both the numerator and denominator of 73 by 2 to create a common denominator.
7/3- 11/6
7* 2/3* 2- 11/6
14/6- 11/6
Now that we have a common denominator, we can proceed to simplifying the expression.
14/6- 11/6
14-11/6
3/6
1/2