Exercise 31 Page 235

Practice makes perfect

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 (+)(+)=(+) & (+)(-)=(-) (-)(-)=(+) & (-)(+)=(-) Here one number is positive and one number is negative, so the product will be negative.

73/100*(- 2/7)

MultPosNeg

a(- b)=- a * b

- (73/100*2/7)

MultFrac

Multiply fractions

- 73* 2/100 * 7

Multiply

- 146/700

ReduceFrac

a/b=.a /2./.b /2.

- 146÷ 2/700÷ 2

SimpQuot

Simplify quotient

- 73/350

Before we evaluate the expression, let's first rewrite the expression so that all of the numbers are fractions.

0.4* 0.3

WriteAsFrac

Write as a fraction

4/10* 3/10

ReduceFrac

a/b=.a /2./.b /2.

4÷ 2/10÷ 2* 3/10

SimpQuot

Simplify quotient

2/5* 3/10

Now we can multiply the numerators and the denominators of the fractions. Let's do it!

2/5* 3/10

MultFrac

Multiply fractions

2* 3/5* 10

Multiply

6/50

ReduceFrac

a/b=.a /2./.b /2.

6÷ 2/50÷ 2

SimpQuot

Simplify quotient

3/25

We can also write this fraction as decimal.

3/25

ExpandFrac

a/b=a * 4/b * 4

3* 4/25* 4

Multiply

12/100

WriteDec

Write as a decimal

0.12

We found that the expression is equal to 325, which can be written as 0.12.

We are asked to find the sum of the given mixed numbers. Let's do it! First, we will split the integer parts from the fraction parts of the numbers.

5 19+8 25

WriteSum

Write as a sum

5+1/9+8+2/5

CommutativePropAdd

Commutative Property of Addition

5+8+2/5+1/9

AddTerms

Add terms

13+2/5+1/9

Now, to add the two fractions, they need to have the same denominator. Let's try to create a common denominator! We can multiply the numerator and denominator of the first fraction by 9 and the numerator and denominator of the second fraction by 5.

13+2/5+1/9

ExpandFrac

a/b=a * 9/b * 9

13+2* 9/5* 9+1/9

ExpandFrac

a/b=a * 5/b * 5

13+2* 9/5* 9+1* 5/9* 5

Multiply

13+18/45+5/45

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

13+18/45+5/45

AddFrac