Pre-Algebra 3-3 Multiplying Rational Numbers 3-3 Multiplying Rational Numbers Pre-Algebra Warm Up...

Pre-Algebra

3-3 Multiplying Rational Numbers


Pre-Algebra

Warm Up

Problem of the Day

Lesson Presentation

Pre-Algebra


Warm UpWrite each number as an improper fraction.

Pre-Algebra


1. 13

2 73

2. 78

1 15 8

3. 25

3 17 5

4. 23

6 203

5. 38

5 438

Pre-Algebra


Problem of the Day

The sum of three consecutive integers is 168. What are the three integers?

55, 56, and 57

Pre-Algebra


Learn to multiply fractions, decimals, and mixed numbers.

Pre-Algebra


Kendall invited 36 people to a party. She needs to triple the recipe for a dip, or multiply the amount of each ingredient by 3. Remember that multiplication by a whole number can be written as repeated addition.

Notice that multiplying a fraction by a whole number is the same as multiplying the whole number by just the numerator of the fraction and keeping the same denominator.

1 4

3 4

1 4

+ + =

Repeated

addition1 4 3 3

4= =

Multiplication3 • 1

414

Pre-Algebra


RULES FOR MULTIPLYING TWO RATIONAL NUMBERS

If the signs of the factors are the same, the product is positive.

If the signs of the factors are different, the product is negative.

(+) • (+) = (+) or (–) • (–) = (+)

(+) • (–) = (–) or (–) • (+) = (–)

Pre-Algebra


–8 6 7

Multiply. Write the answer in simplest form.

Multiply

Simplify

–48 7

=

–6 6 7

=

–8 • 6 7

=

To write as a mixed

number, divide:

Helpful Hint

12 5

125 = 2 R2

2 5= 2

Additional Example 1A: Multiplying a Fraction and an Integer

A.

Pre-Algebra


2 1 3

Multiply

Simplify 10 2 3=

16 3=2

32 3=

5

5(3) + 1 3= =1 35 16

3


Additional Example 1B: Multiplying a Fraction and an Integer

B.

Pre-Algebra


–3 5 8


Multiply

Simplify

–15 8

=

–1 7 8

=

–3 • 5 8

=

Try This: Example 1A

A.

Pre-Algebra


4 2 5

Multiply

Simplify 37 3 5

=

47 5

= 4

188 5

=

9

9(5) + 2 5

= =2 5

9 47 5

Try This: Example 1B

B.


Pre-Algebra


A model of is shown. Notice that to multiply fractions, you multiply the numerators and multiply the denominators.

3 5 • 2

3

35

•

•

=

= 6 15

23

If you place the first rectangle on top of the second, the number of green squares represents the numerator, and the number of total squares represents the denominator.

Pre-Algebra


To simplify the product, rearrange the six green squares into the first two columns. You can see that this is .2

5

=

= 2 5

6 15

A fraction is in lowest terms, or simplest form, when the numerator and denominator have no common factors.

Helpful Hint

Pre-Algebra


1(6) 8(7)=


6 7

Simplest form3 28

=

1 8

=1(6) 8(7)

Multiply numerators.

Multiply denominators.

Look for common factors: 2.3

4

Additional Example 2A: Multiplying Fractions

A.

Pre-Algebra


–2(9) 3(2)=

=–2(9) 3(2)

3

1

Simplest form–3=

Multiply numerators.

Multiply denominators.

Look for common factors: 2, 3.

9 2

2 3

–

1

–1

Additional Example 2B: Multiplying Fractions

B.


Pre-Algebra


Multiply numerators. Multiply denominators.

1 2

3 7

4

Write as an improper fraction.

= 31(1) 7(2)

31 ÷ 14 = 2 R3 = or 231 14

3 14

Additional Example 2C: Multiplying Fractions

C.


1 2

3 7

4 = 31 17 2

Pre-Algebra


3(5) 5(8)=


5 8

Simplest form3 8

=

3 5

=3(5) 5(8)

Multiply numerators.Multiply denominators.

Look for common factors: 5.1

1


A.

Pre-Algebra


–7(4) 8(7)=

=–7(4) 8(7)

1

2

Simplest form

Multiply numerators.Multiply denominators.

Look for common factors: 4, 7.

4 7

7 8

–

1

–1

1 2= –

B.



Pre-Algebra


7 9

3 5

2C.


Try This: Example 2C

Multiply numerators. Multiply denominators.


= 13(7) 5(9)

91 ÷ 45 = 2 R 1 = or 291 45

1 45

7 9

3 5

2 = 13 75 9

Pre-Algebra


2(–0.51)

Multiply.

Product is negative with 2 decimal places.

2 • (–0.51) = –1.02

(–0.4)(–3.75)Product is positive with 3 decimal places.

(–0.4) • (–3.75) = 1.500

You can drop the zeros after the decimal point.

= 1.5

Additional Example 3: Multiplying Decimals

A.

B.

00

Pre-Algebra


3.1 (0.28)

Multiply.

Product is positive with 3 decimal places.

3.1 • (0.28) = 0.868

(–0.4)(–2.53)Product is positive with 3 decimal places.

(–0.4) • (–2.53) = 1.012

Try This: Example 3

A.

B.

Pre-Algebra


A. x = 5

Evaluate –3 x for the value of x.1 8

Substitute 5 for x.

–3 x 18

–125 8

=

= –15 5 8

–125 ÷ 8 = –15 R5

Additional Example 4A: Evaluating Expressions with Rational Numbers

–25 8

= (5)

–3 (5) 18=


Pre-Algebra


–25 • 2 8 • 7

=

= – 25 28

27


Substitute for x.2 7

1

4

27

Additional Example 4B: Evaluating Expressions with Rational Numbers Continued

B. x = –3 x 18

27

–25 8=

–3= 18

Look for common factors: 2.

Evaluate –3 x for the value of x.1 8

Pre-Algebra


A. y =

–28 • 6 5 • 7=

67


1

–4

–28 5

= 67

35–5= 6

7

–5 y 35


Look for common factors: 7.

= – 24 5 , or – 4 4

5

Evaluate –5 y for the value of y.3 5

Substitute for x.6 7

Pre-Algebra


B. y = 3

Substitute 3 for y.

–5 y 35

–84 5=

= –16 4 5

–84 ÷ 5 = –16 R4

–28 5= (3)


Evaluate –5 y for the value of y.3 5


35–5 (3)=

Pre-Algebra


4. Evaluate 2 (x) for x = .

1.

Lesson Quiz: Part 1

Multiply.

–1.034

2. 5 8

2 3

–

1 7

9

3. –0.47(2.2)

1 2 24

5

– 5 12

1 2 7

Pre-Algebra


Teri is shopping for new shoes. Her mom has agreed to pay half the cost (and all the sales tax). The shoes that Teri likes are normally $30 a pair but are on sale for off. How much money does Teri need to buy the shoes?

Lesson Quiz: Part 2

5.

$10

1 3

Pre-Algebra 3-3 Multiplying Rational Numbers 3-3 Multiplying Rational Numbers Pre-Algebra Warm Up...

Documents

Transcript of Pre-Algebra 3-3 Multiplying Rational Numbers 3-3 Multiplying Rational Numbers Pre-Algebra Warm Up...