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Session 3

- Common Fractions
- Multiplication and
- Division

Session 3 - Objectives

- After studying this unit you should be able to
- multiply and divide fractions.
- multiply and divide combinations of fractions,

mixed numbers, and whole numbers. - solve practical problems by combining addition,

subtraction, multiplication, and division. - simplify arithmetic expressions with combined

operations by applying the proper order of

operations. - solve practical combined operations problems

involving formulas by applying the proper order

of operations.

Session 3

- 213 Multiplication of Common Fractions 60
- 214 Multiplying Common Fractions in Practical

Applications 64 - 215 Division of Common Fractions 67
- 216 Dividing Common Fractions in Practical

Applications 70 - 217 Combined Operations with Common Fractions

73 - 218 Combined Operations of Common Fractions in

Practical Applications 75 - UNIT EXERCISE AND PROBLEM REVIEW 77

MULTIPLICATION OF FRACTIONS

Just as with whole numbers, multiplication of

fractions is a short method of adding equal

amounts. It is important to understand the

meaning of multiplication of fractions. For

example, 6 x ¼ means ¼ is added 6 times

¼ ¼ ¼ ¼ ¼ ¼

Adding the fractions gives the sum or

MULTIPLICATION OF FRACTIONS

The enlarged 1-inch scale in Figure 220 shows

six -inch parts.

MULTIPLICATION OF FRACTIONS

Recall that multiplication of whole numbers can

be done in any order. Multiplication of fractions

can also be done in any order. The expression 6 x

¼ is the same as ¼ x 6. Six divided into 4 equal

units is written as ¼ of 6 or 6 x ¼ . The 6-inch

scale shows 6 inches divided into 4 equal parts

and 1 of the 4 parts is taken.

MULTIPLICATION OF FRACTIONS

- To multiply two or more fractions, multiply the

numerators. - 2. Multiply the denominators.
- 3. Write as a fraction with the product of the

numerators over the product of the

denominators. - 4. Always express the answer in lowest terms.

MULTIPLICATION OF FRACTIONS

- Example
- Multiply the numerators and denominators

(No Transcript)

EXERCISE 2-13B Page 62

2.

4.

6.

EXERCISE 2-13B Page 62

10.

12.

MULTIPLICATION OF FRACTIONS

- To multiply any combination of fractions, mixed

numbers, and whole numbers, write the mixed

numbers as fractions. - Write whole numbers over the denominator 1.
- Multiply numerators.
- 4. Multiply denominators.
- 5. Express the answer in lowest terms.

MULTIPLICATION OF FRACTIONS

- Example
- Multiply numerators and denominators
- Express as mixed number in lowest terms

EXERCISE 2-13C Page 64

2.

4.

6.

8.

EXERCISE 2-13C Page 64

10.

12.

14.

16.

Cancellation(DIVIDING BY COMMON FACTORS)

- Problems involving multiplication of fractions

are generally solved more quickly if a numerator

and denominator are divided by any common factors

before the fractions are multiplied - This process is called cancellation

Cancellation

- Example
- The factor 3 is common to both the numerator 3

and the denominator 9 so divide - The factor 4 is common to both the numerator 4

and the denominator 8 so divide - Multiply the numerators and denominators

DIVISION OF FRACTIONS

- Division is the inverse of multiplication
- Dividing by 2 is the same as multiplying by

or ½. ½ is the multiplicative inverse of 2 - To divide fractions, invert the divisor, change

to the inverse operation (multiplication), and

multiply

DIVISION OF FRACTIONS

- Example
- Invert the divisor, multiply, and reduce

EXERCISE 2-15A Page 69

2.

10.

4.

12.

6.

8.

DIVISION OF FRACTIONS

- To divide any combination of fractions, mixed

numbers, and whole numbers - Write mixed numbers as fractions
- Write whole numbers over the denominator of 1
- Invert the divisor
- Change to the inverse operation
- Multiply

DIVISION OF FRACTIONS

- Example
- Write
- Invert the divisor
- Change to the inverse operation and multiply

EXERCISE 2-15B Page 70

2.

10.

4.

12.

6.

8.

Practical Applications

- The machine bolt shown in Figure 229 has a

thread pitch of inch. The pitch is the

distance between 2 adjacent threads or the

thickness of 1 thread. Find the number of threads

in ? inch. - The number of threads is found by dividing the

total threaded length (?) by the pitch or

thickness of 1 thread ( ) .

ORDER OF OPERATIONS

- As with any arithmetic expression, the order of

operations must be followed. The operations are - Parentheses
- Exponents and roots
- Multiplication and division from left to right
- Addition and subtraction from left to right

ORDER OF OPERATIONS

- First, add the fractions in ( )
- Next, multiply and divide
- Finally, subtract

EXERCISE 2-17 Pages 74-75

2.

8.

4.

10.

6.

EXERCISE 2-17 Pages 74-75

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16.

14.

EXERCISE 2-18 Pages 76-77

4. A simple parallel electrical circuit is shown

in Figure 239. An environmental systems

technician finds the total resistance of the

circuit.

where R1, R2, R3, and R4 are the

individual resistors and RT is the total

resistance.

Homework Assignment

- Review this presentation on-line as needed.
- Do odd numbered problems as needed from
- Exercises 2-13B, 2-13C, 2-15A, 2-15B, 2-17, 2-18
- Concentrate your efforts on reviewing problems

and examples in this presentation. Also do odd

numbered problems of Unit Exercise and Problem

Review Pages 79-80 - Problems 51-80, 85, and 87