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Whole Numbers How To Dissect And Solve Word Problems

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Subtract like and unlike fractions. Add and subtract mixed numbers with ... Adding Like Fractions. Add the numerators and place the total over the denominator ... – PowerPoint PPT presentation

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Title: Whole Numbers How To Dissect And Solve Word Problems


1
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2
Chapter 2
  • Fractions

3
Fractions
2
Learning Unit Objectives
Types of Fractions and Conversion Procedures
LU2.1
  • Recognize the three types of fractions
  • Convert improper fractions to whole or mixed
    numbers and mixed numbers to improper fractions
  • Convert fractions to lowest and highest terms

4
Fractions
2
Learning Unit Objectives
Adding and Subtraction of Fractions
LU2.2
  • Add like and unlike fractions
  • Find the least common denominator (LCD) by
    inspection and prime numbers
  • Subtract like and unlike fractions
  • Add and subtract mixed numbers with the same or
    different denominators

5
Fractions
2
Learning Unit Objectives
Multiplying and Dividing Fractions
LU2.3
  • Multiply and divide proper fractions and mixed
    numbers
  • Use the cancellation method in the multiplication
    and division of fractions

6
Types of Fractions
Improper
Proper
Numerator
3, 4, 12, 11 15 8 26 35
19, 9, 13, 42 19 4 10 29
Mixed Numbers
Denominator
5, 3, 2, 1 8 17 9 8
4
2
9
15
7
Converting Improper Fractions to Whole or Mixed
Numbers
  • 24
  • 24
  • 2 Steps
  • 1. Divide the numerator by the denominator
  • 2. a.If you have no remainder, the quotient is a
    whole number
  • 2 b.If you have a remainder, the quotient is a
    mixed number

1
21 1 4 4 5 R
1 4 21 20 1
5
8
Converting Improper Fractions to Whole or Mixed
Numbers
  • 3 Steps
  • 1. Multiply the denominator of the fraction by
    the whole number.
  • 2. Add the product from Step 1 to the numerator
    of the old fraction.
  • 3 Place the total from Step 2 over the
    denominator of the old fraction to get the
    improper fraction.

1 8
6
  • (8 x 6) 48

(8 x 6) 48 48 1 49
49 8
9
Reducing Fractions to Lowest Terms by Inspection
24 24 / 6 4 30 30 / 6 5
Find the lowest whole number that will divide
evenly into the numerator and denominator


10
Finding the Greatest Common Divisor
12 30
2 12 30 24 6
Step 1. Divide the numerator into the
denominator
2 6 12 12 0
Step 2. Divide the remainder in Step 1 into the
divisor of Step 1
Step 3. Divide the remainder of Step 2 into the
divisor of Step 2. Continue until the remainder
is 0
12 / 6 2 30 / 6 5

11
Divisibility Tests
Sum of the digits is divisible by 3
Last two digits can be divided by 4
The number is even and 3 will divide into the sum
of the digits
Last digit is 0,2,4,6,8
Last digit is 0 or 5
The last digit is 0
12 6 14 7
36 12 69 23
140 1(40) 160 1(60)
15 3 20 4
12 2 18 3
90 9 100 10






3 6 9 / 3 3 6 9 15 / 3 5
35 7 40 8

12
Raising Fractions to Higher Terms When
Denominator is Known
  • 2 Steps
  • 1. Divide the new denominator by the old
    denominator to get the common number that raises
    the fraction to higher terms.
  • 2. Multiply the common number from Step 1 by the
    old numerator and place it as the new numerator
    over the new denominator.

4 ? 7 28
  • 4
  • 7 28
  • 28
  • 0

4 x 4 16
16 28
13
Least Common Denominator (LCD)
  • The smallest nonzero whole number into which ALL
    denominators will divide evenly.

5 16 20 10

40 60 20
  • What is the least common denominator?

14
Adding Like Fractions
  • Add the numerators and place the total over the
    denominator
  • If the total of your numerators is the same as
    your original denominator, convert your answer to
    a whole number if the total is larger than your
    original denominator, convert your answer to a
    mixed number

2 3 5 9 9 9


-b
5 6 11 2 9 9 9 9



1
15
Adding Unlike Fractions
  • 4 Steps
  • 1. Find the LCD
  • 2. Change each fraction to a like fraction with
    the LCD.
  • 3. Add the numerators and place the total over
    the LCD.
  • 4. If necessary, reduce the answer to lowest
    terms.

1 1 1 1 3 8 9 12



24 9 8 6 47 72 72 72
72 72
16
Prime Numbers
A whole number greater than 1 that is only
divisible by itself and 1. The number 1 is not a
prime number.
Examples 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31,
37, 41, 43
17
Adding Mixed Numbers
7 7 20 20 3 12 5
20 1 5 4 20
24 4 20
20 17 .
4 1
20 5
4
4
  • 3 Steps
  • 1. Add the fractions.
  • 2. Add the whole numbers.
  • 3. Combine steps 1 2. Be sure you do not have
    an improper fraction in your final answer. If
    necessary, reduce the answer to lowest terms.

6
6
7
7


1

Step 1

Step 2
18
18

Step 3
18
Subtracting Like Fractions
  • Subtract the numerators and place the total over
    the denominator
  • If necessary, reduce the answer to lowest terms

7 1 6 / 2 3 12 12 12 / 2
6
-


19
Subtracting Unlike Fractions
  • 4 Steps
  • 1. Find the LCD
  • 2. Raise the fraction to its equivalent value.
  • 3. Subtract the numerators and place the answer
    over the LCD.
  • 4. If necessary, reduce the answer to lowest
    terms.

5 2 8 64
-
5 40 8 64 2 - 2 64
64 38 19 64 32
-
20
Subtracting Mixed Numbers
When Borrowing is Not Necessary
  • 3 Steps
  • 1. Subtract fractions, making sure to find the
    LCD.
  • 2. Subtract whole numbers.
  • 3. Reduce the fractions to lowest terms.

1 4 2 8 - 3 - 3
8 8 1 8
6
6
6
21
Subtracting Mixed Numbers
When Borrowing is Necessary
  • 4 Steps
  • 1. Make sure the fractions have the LCD.
  • 2. Borrow from the whole number.
  • 3. Subtract whole numbers and fractions.
  • 4. Reduce the fractions to lowest terms.

1 2 6 2 4
4 3 3 3 4 4
4 3
4
3
3
2
-1
-1
-1
1
22
Subtracting Unlike Fractions
  • 4 Steps
  • 1. Find the LCD
  • 2. Raise the fraction to its equivalent value.
  • 3. Subtract the numerators and place the answer
    over the LCD.
  • 4. If necessary, reduce the answer to lowest
    terms.

5 2 8 64
-
5 40 8 64 - 2 2
64 64 38 19 64 32
-
23
Multiplying Proper Fractions
2 Steps 1. Multiply the numerator and the
denominators 2. Reduce the answer to lowest
terms
5 2 4 40 20 2 5 7 70
35


x
x
24
Multiplying Mixed Numbers
Multiply the numerator and denominators
  • Convert the mixed numbers to improper fractions

Reduce the answer to lowest terms
1
1 1 7 3 7 1 3
2 3 2 2 2
3



1
2
X
X
1
25
Dividing Proper Fractions
Invert (turn upside down) the divisor (the second
fraction)
Multiply the fractions
Reduce the answer to lowest terms
.
1 2 1 3 3 8 3 8
2 16
.


X
26
Dividing Mixed Numbers
  • Convert all mixed numbers to improper fractions

Invert the divisor and multiply
Reduce the answer to lowest terms
3 5 35 6 105 3 4
6 4 17 34 34


3

2
8
X
X
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