Core Connections: Course 2
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2. Section 5.2
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Exercise 87 Page 285

Practice makes perfect
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 12 1* 2+1/2 3/2
2 18 2* 8+1/8 17/8

When adding or subtracting fractions, they should have the same denominator. In this exercise, we have two fractions with different denominators. 3/2 + 17/8 Since 8 is a multiple of 2, we can multiply both the numerator and denominator of 32 by 4 to create a common denominator.

3/2 + 17/8
3* 4/2* 4 + 17/8
12/8 + 17/8

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

12/8 + 17/8
12+17/8
29/8
3 58

When adding or subtracting fractions, they should have the same denominator. In this exercise, we have three fractions with different denominators. 4/5 - 2/3 + 1/6 First, we can list the multiples of 5, 3, and 6. Multiples of $5$:&5, 10, 15, 25, 30, ... Multiples of $3$:&3, 6, 9, 12, 15, 18, &21, 24, 27, 30, ... Multiples of $6$:&6, 12, 18, 24, 30, ... Since 30 is a multiple of both 5, 3, and 6, we can first multiply both the numerator and denominator of 45 by 6 to create a common denominator.

4/5 - 2/3 + 1/6
4* 6/5* 6 - 2/3 + 1/6
24/30 - 2/3 + 1/6

Next, we can multiply both the numerator and denominator of 23 by 10 to create a common denominator.

24/30 - 2/3 + 1/6
24/30 - 2* 10/3* 10 + 1/6
24/30 - 20/30 + 1/6

Finally, we can multiply both the numerator and denominator of 16 by 5 to create a common denominator.

24/30 - 20/30 + 1/6
24/30 - 20/30 + 1* 5/6* 5
24/30 - 20/30 + 5/30

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

24/30 - 20/30 + 5/30
24-20+5/30

\AddSubTerm

9/30
3/10

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
5 35 5* 5+3/5 28/5
1 45 1* 5+4/5 9/5
When adding or subtracting fractions, they should have the same denominator. In this exercise, we have two fractions with the same denominator. 28/5-9/5 Let's simplify the expression!

28/5-9/5
28-9/5
19/5
3 45