Exercise 155 Page 311

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
2 310	2* 10+3/10	23/10
1 25	1* 5+2/5	7/5

When adding or subtracting fractions, they should have the same denominator. In this case, we have two fractions with different denominators. 2 310-1 25 ⇔ 23/10-7/5 Since 10 is a multiple of 5, we can multiply both the numerator and denominator of 75 by 2 to create a common denominator.

23/10-7/5

ExpandFrac

a/b=a * 2/b * 2

23/10-7* 2/5* 2

Multiply

23/10-14/10

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

23/10-14/10

SubFrac

Subtract fractions

23-14/10

SubTerm

Subtract term

9/10

WriteDec

Write as a decimal

0.9

When multiplying real numbers, the product will be positive if the signs are the same and it will be negative if the signs are different. cc Same Sign & Different Signs (+)(+)=(+) & (+)(-)=(-) (-)(-)=(+) & (-)(+)=(-) In our case both numbers are positive, so the product will be positive.

9/3* 4/5

MultFrac

Multiply fractions

9* 4/3* 5

Multiply

36/15

ReduceFrac

a/b=.a /3./.b /3.

12/5

WriteDec

Write as a decimal

1.4

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 78	5* 8+7/8	47/8

When adding or subtracting fractions, they should have the same denominator. In this case, we have two fractions with different denominators. 3/4+5 78 ⇔ 3/4+47/8 Since 8 is a multiple of 4, we can multiply both the numerator and denominator of 34 by 2 to create a common denominator.

3/4+47/8

ExpandFrac

a/b=a * 2/b * 2

3* 2/4* 2+47/8

Multiply

6/8+47/8

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

6/8+47/8

AddFrac

Add fractions

6+47/8

SubTerm

Subtract term

53/8

FracToMixed

Write fraction as a mixed number

6 58

WriteDec

Write as a decimal

6.625

When multiplying real numbers, the product of two numbers will be positive if the signs are the same and it will be negative if the signs are different. cc Same Sign & Different Signs (+)(+)=(+) & (+)(-)=(-) (-)(-)=(+) & (-)(+)=(-) In our case two numbers are positive and one number is negative, so the product will be negative.

2/9* (- 3/7)(14/5)

MultPosNeg

a(- b)=- a * b

- 2/9* 3/7(14/5)

MultFrac

Multiply fractions

- 2* 3/9* 7 (14/5)

Multiply

- 6/63 (14/5)

MultFrac

Multiply fractions

- 6* 14/63* 5

Multiply

- 84/315

ReduceFrac

a/b=.a /21./.b /21.

- 4/15

When adding or subtracting fractions, they should have the same denominator. In this case, we have two fractions with different denominators. - 9/15-(- 26/45) Since 45 is a multiple of 15, we can multiply both the numerator and denominator of - 915 by 3 to create a common denominator.

- 9/15-(- 26/45)

ExpandFrac

a/b=a * 3/b * 3

- 9* 3/15* 3-(- 26/45)

Multiply

- 27/45-(- 26/45)

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

- 27/45-(- 26/45)

SubNeg

a-(- b)=a+b

- 27/45+26/45

MoveNegFracToNum

Put minus sign in numerator

- 27/45+26/45

AddFrac

Add fractions

- 27+26/45

AddTerms

Add terms

- 1/45

MoveNegNumToFrac

Put minus sign in front of fraction

- 1/45

Before we can evaluate our expression involving mixed numbers, the mixed numbers must first be rewritten as fractions.

a bc	a* c+b/c	Simplify
5 16	5* 6+1/6	31/6

Now, we can rewrite our expression. 5 16* (- 7/9) ⇔ 31/6* (- 7/9) When multiplying real numbers, the product will be positive if the signs are the same and it will be negative if the signs are different. cc Same Sign & Different Signs (+)(+)=(+) & (+)(-)=(-) (-)(-)=(+) & (-)(+)=(-) In our case one number is positive and one number is negative, so the product will be negative.

31/6* (- 7/9)

MultPosNeg

a(- b)=- a * b

- 31/6* 7/9

MultFrac

Multiply fractions

- 31* 7/6* 9

Multiply

- 217/54

FracToMixed

Write fraction as a mixed number

- 4 154