Title: Whole Numbers How To Dissect And Solve Word Problems
1(No Transcript)
2Chapter 2
3Fractions
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
4Fractions
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
5Fractions
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
6Types 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
7Converting Improper Fractions to Whole or Mixed
Numbers
- 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
8Converting 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 48 1 49
49 8
9Reducing 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
10Finding 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
11Divisibility 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
12Raising 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 x 4 16
16 28
13Least 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?
14Adding 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
15Adding 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
16Prime 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
17Adding 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
18Subtracting 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
-
19Subtracting 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
-
20Subtracting 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
21Subtracting 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
22Subtracting 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
-
23Multiplying 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
24Multiplying 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
25Dividing 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
26Dividing 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