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Common Fractions

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Session 3 Common Fractions Multiplication and Division After studying this unit you should be able to: multiply and divide fractions. multiply and divide combinations ... – PowerPoint PPT presentation

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Title: Common Fractions


1
Session 3
  • Common Fractions
  • Multiplication and
  • Division

2
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.

3
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

4
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

5
MULTIPLICATION OF FRACTIONS
The enlarged 1-inch scale in Figure 220 shows
six -inch parts.
6
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.
7
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.

8
MULTIPLICATION OF FRACTIONS
  • Example
  • Multiply the numerators and denominators

9
(No Transcript)
10
EXERCISE 2-13B Page 62
2.
4.
6.
11
EXERCISE 2-13B Page 62
10.
12.
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.

13
MULTIPLICATION OF FRACTIONS
  • Example
  • Multiply numerators and denominators
  • Express as mixed number in lowest terms

14
EXERCISE 2-13C Page 64
2.
4.
6.
8.
15
EXERCISE 2-13C Page 64
10.
12.
14.
16.
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

17
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

18
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

19
DIVISION OF FRACTIONS
  • Example
  • Invert the divisor, multiply, and reduce

20
EXERCISE 2-15A Page 69
2.
10.
4.
12.
6.
8.
21
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

22
DIVISION OF FRACTIONS
  • Example
  • Write
  • Invert the divisor
  • Change to the inverse operation and multiply

23
EXERCISE 2-15B Page 70
2.
10.
4.
12.
6.
8.
24
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 ( ) .

25
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

26
ORDER OF OPERATIONS
  • First, add the fractions in ( )
  • Next, multiply and divide
  • Finally, subtract

27
EXERCISE 2-17 Pages 74-75
2.
8.
4.
10.
6.
28
EXERCISE 2-17 Pages 74-75
12.
16.
14.
29
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.
30
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
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