Download MAT001 – Chapter 2 - Fractions 1 of 15 Understanding Fractions

MAT001 – Chapter 2 - Fractions
Representing Part of a Whole
2.1
A fraction represents parts of a whole.
The whole is the circle on the left.
1
Understanding
Fractions
The fraction represents the
4
shaded part of the circle. 1 out of
1
4 pieces is shaded. is read “one4
fourth.”
numerator
1
denominator
4
1
Representing Part of a Whole
2
CQ2-01. Write a fraction that represents
the portion of the box that is shaded.
The fraction 85 represents the
portion of the box that is shaded.
1. .
2. .
3. .
4. .
We can also think of a fraction as a division problem.
5
8
5 8
and
5 8
5
8
3
1
2
3
7
10
4
7
4
6
11
0%
7
11
5
0%
0%
2
3
1
6
7
8
9
10
11
12
13
14
15
16
0%
4
17
4
CQ2-02. Use a fraction to describe the
situation.
3 out of 25 students don’t have the
computer at home.
Representing Part of a Whole
Example:
Use a fraction to describe the situation.
1. 11 out of 15 of the math students received an
“A” for the semester.
1. .
2. .
3. .
4. .
11
15
2. Patty needed three-fourths of a yard of material
to make the doll.
3
4
5
1
2
3
22
25
3
25
4
25
3
0%
25
28
5
0%
0%
2
3
1
6
7
8
9
10
11
12
13
14
15
16
0%
4
17
6
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MAT001 – Chapter 2 - Fractions
Prime Numbers
A prime number is a whole number greater than 1
that cannot be evenly divided except by 1 and itself.
2.2
2, 3, 5, 7, 11, 13, 17, 19, 23, 29
Simplifying
Fractions
The first 10 prime numbers
A composite number is a whole number greater
than 1 that can be evenly divided by whole numbers
other than 1 and itself.
24 = 2
12
24 = 3
8
24 = 4
6
7
8
Prime Factorization
Divisibility Tests
Example:
Write the number 24 as a product of primes.
1. A number is divisible by 2 if the last digit is 0, 2,
4, 6, or 8.
2. A number is divisible by 3 if the sum of the digits
is divisible by 3.
3. A number is divisible by 5 if the last digit is 0 or 5.
24 = 4
2
Example:
The number 450 is divisible by 2. (It ends in 0.)
24 = 2
The number 450 is divisible by 3. (4 + 5 + 0 = 9 and 9 is
divisible by 3.)
6
Write 24 as the product of any two factors.
2 2
3
2
2
Instead of writing 2
If the factors are not prime, they must
be factored.
3
When all of the factors are prime, the
number has been completely factored.
2
2
3, we can also write 23
3.
The number 450 is divisible by 5. (It ends in 0.)
9
The Fundamental Theorem of Arithmetic
Equivalent Fractions
The Fundamental Theorem of Arithmetic
Every composite number can be written in exactly
one way as a product of primes.
24 = 4
2
6
2 2
24 = 3
2
2
3
3
2
24 = 3
Equivalent fractions can be written in more than one
way. The value of the fractions is the same.
8
4
2
24 = 2
10
2
2
3 is shaded.
6
2
2
1 is shaded.
2
Equivalent fractions
The order of the prime factors is not important
because multiplication is commutative.
11
12
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MAT001 – Chapter 2 - Fractions
3
CQ2-03. Write
as an equivalent
7
fraction with a denominator of 35.
Equal Fractions
If two fractions are equivalent, their diagonal products or
cross products will be equal.
2
1
1=4
?
2 8
4
8
31
1. . 35
2. .
15
3. . 35
4. .
The products are equal,
1 4
therefore
.
2 8
8
8
Equality Test for Fractions
For any two fractions where a, b, and c are whole
c then a d = b
numbers and b 0, d 0, if a
,
b
d
3
35
18
35
0%
c.
0%
0%
2
3
1
13
1
2
3
4
5
6
2
7
8
9
10
11
12
13
14
15
16
0%
4
17
14
Simplest Form
CQ2-04. Write
as an equivalent
9
fraction with a numerator of 12.
Any nonzero number divided by itself is equal to 1.
12
21
1. .
2. .
12
3. . 49
4. .
2
2
12
54
1
2
2
3
4
5
3
6
1
2
4
4
0%
0%
0%
2
3
4
8
6
7
8
9
10
11
12
13
14
15
16
4
1
2
50
50
50
100
17
15
A fraction is in simplest form when the numerator
and denominator have no common factors (other
than 1).
CQ2-05. Simplify
When a fraction is not in simplest form, it can be reduced.
21
1. . 49
2. .
7
3. . 11
4. .
To reduce a fraction, find a common factor in the
numerator and the denominator and divide it out.
5
5
1
0%
Common Factors
25
40
b
b
1 3 4
50
are equivalent fractions.
, , , and
2 6 8
100
12
19
1
1
3
3
43
43
5
8
25
40
5
8
5 is the common factor.
63
to lowest terms.
147
9
21
3
7
A fraction is called simplified, reduced, or in lowest
terms if the numerator and the denominator only
have 1 as a common factor.
0%
0%
0%
2
3
1
17
1
2
3
4
16
5
6
7
8
9
10
11
12
13
14
15
16
0%
4
17
18
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MAT001 – Chapter 2 - Fractions
Proper and Improper Fractions
If the value of a fraction is less than 1 (the numerator is
less than the denominator), the fraction is proper.
2.3
3 5 1 27
, , ,
4 9 2 40
Converting Between
Improper Fractions and
Mixed Numbers
If the value of a fraction is greater than or equal to 1 (the
numerator is greater than or equal to the denominator),
the fraction is improper.
The numerator is
greater than or equal
to the denominator.
9 5 18 27
, ,
,
5 2 13 27
19
6
CQ2-06. What is the name of a fraction
CQ2-07. The fraction
is best
7
described to by which word.
with a numerator that is greater than or
equal to its denominator?
1. Improper
2. Mixed
3. Proper
4. Unmixed
0%
0%
0%
2
3
1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
1. Proper
2. Improper
3. Simplified
4. Factored
0%
0%
4
17
21
0%
2
3
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
0%
4
17
22
Mixed Numbers to Improper Fractions
Changing a Mixed Number to an Improper Fraction
A mixed number is the sum of a whole number
greater than zero and a proper fraction.
1. Multiply the whole number by the denominator of the fraction.
2. Add the numerator of the fraction to the product found in step 1.
3. Write the sum found in step 2 over the denominator of the
fraction.
3 5
1
, 1 , 22
4 9
2
Example: Change 4
2
into an improper fraction.
3
Multiply the whole number
by the denominator.
4
3
2
4
0%
1
Mixed Numbers
2
20
23
3
3
2
Add the numerator
to the product.
12
2
3
14
3
Write the sum over
the denominator.
24
4 of 15
MAT001 – Chapter 2 - Fractions
5
2
CQ2-08. Write 2 as an improper
7
fraction.
1. . 147
2. .
19
3. . 7
4. .
2
3
4
1. . 103
2. .
16
3. . 3
4. .
37
7
19
5
0%
0%
0%
2
3
1
1
CQ2-09. Write 5
as an improper
3
fraction.
5
6
7
8
9
10
11
12
13
14
15
16
0%
30
3
17
3
0%
4
17
25
Improper Fractions to Mixed Numbers
1
2
3
4
5
6
7
8
CQ2-10. Write
Changing an Improper Fraction to a Mixed Number
1. Divide the numerator by the denominator.
2. Write the quotient followed by the fraction with the
remainder over the denominator.
quotient
Example: Change
remainder
denominator
21
into a mixed number.
4
4 21
21
4
5
1
4
9
10
11
0%
2
3
12
13
14
15
16
0%
4
17
26
45
as a mixed number.
7
1. . 7 74
38
2. .
3
3. . 6 7
3
4. . 42 7
quotient
5 R1
0%
1
0%
0%
0%
2
3
0%
remainder
1
4
denominator
27
1
125
15
5
5
3
5
51
25
3
1
11
4
11
1
6
4
1. . 26
22
2. .
13
3. . 11
4. .
common factors
11
4
66
3
5
6
7
8
9
10
11
12
13
14
15
16
17
28
CQ2-11. Simplify 44 to lowest terms.
Write the result as a mixed number if
possible.
125
.
15
Example: Reduce the mixed number fraction 4
2
52
Reducing a Mixed Number
Example: Reduce the improper fraction
1
11
.
66
1
4
6
1
2
11
1
8
44
0%
0%
0%
2
3
1
0%
4
1
29
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
30
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MAT001 – Chapter 2 - Fractions
Multiplying Fractions
2.4
Multiplication of fractions is used when we want to
take a fractional part of something.
1
2
Multiplying Fractions
and Mixed Numbers
5
9
5
18
1
5
of
2
9
5
9
yields 5 out of 18
squares.
1
2
31
32
Multiplying Fractions
Multiplying Proper or Improper Fractions
To multiply two fractions, we multiply the
numerators and multiply the denominators.
3
7
2
5
Example: Multiply
12
17
3 2 6
7 5 35
6
35
c
d
a
b
12
17
3
.
24
3
24
36
408
12
17
c
d
3
3
24
4
17
2
1
(when b and d are not 0).
4
2
3 5
7 8
24
35
35
24
0%
0%
0%
2
3
1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
0%
4
17
1
34
1
3
13
39
0%
0%
0%
2
3
1
35
1
2
3
4
3
34
2
11 13
39 11
4
17
4
3
1
CQ2-13. Multiply:
1. . 143
429
2. .
121
3. . 507
4. .
3
3
3
3
33
1. . 15
56
2. .
8
3. . 15
4. .
Simplify the
fraction.
1
3
17
CQ2-12. Multiply:
3
34
To make multiplying easier, the fractions may be
simplified before multiplying.
In general, for all positive whole numbers a, b, c, and d,
a
b
3
24
12
17
5
6
7
8
9
10
11
12
13
14
15
16
0%
4
17
36
6 of 15
MAT001 – Chapter 2 - Fractions
5
7
CQ2-14. Simplify:
1. . 79
2. .
10
3. . 14
4. .
2
3
4
CQ2-15. What do we call two numbers
which have a product of one?
25
49
0%
0%
0%
2
3
5
6
7
8
9
10
11
12
13
14
15
16
2
3
6
0%
7
8
9
10
11
12
13
0%
0%
2
3
14
0%
4
5
6
7
8
9
10
11
12
15
16
2
3
4
5
3
6
7
8
9
10
11
12
13
14
15
16
0%
4
17
38
Multiplying Mixed Numbers
Example: Multiply 2 4
0%
13
4
.
7
1
0%
3
15
16
1
2
4
7
14
5
11
7
1
22
2
or 4
5
5
39
40
6
CQ2-18. Simplify:
2
14
4
5
4
17
0%
1
3
1
7
.
9
2
3
3
3 5
6
1. . 18 52
1
2. . 33 3
5
3. . 9 8
24
4. .
2
37
2
CQ2-17. Simplify:
1
0%
2
To multiply mixed numbers, first change each mixed
number into an improper fraction.
1
63
5
0%
1
7
9
1
2
4
0%
4
5
9
7
1
1
0%
17
CQ2-16. Find the reciprocal of
1. .
2. .
3. .
4. .
1. Opposites
2. Factors
3. Quotients
4. Reciprocals
52
72
1
1
2
1. . 9 421
1
2. . 5 9
1
3. .19 3
1
4. . 18 42
0%
0%
4
17
3
1
3
14 9
0%
0%
2
3
1
41
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
0%
4
17
42
7 of 15
MAT001 – Chapter 2 - Fractions
Dividing Fractions
A cup of lemonade that is 3 full must be divided
2.5
4
into 14 -cup servings. How many cups of lemonade
will there be?
Dividing Fractions and
Mixed Numbers
3
4
How many
1
3
's are in ?
4
4
1
4
There are three
1
4
1
4
1
4
1
3
's in .
4
4
1
There will be three 4 -cup servings in the cup.
43
Dividing Proper or Improper Fractions
44
When fractions are divided, we invert the second
fraction and multiply.
1. . 256
2. .
25
3. . 6
4. .
1
3
4
1
4
3
41
4
1
3
or 3.
1
Rules for Division of Fractions
To divide two fractions, we invert the second fraction and multiply.
a
b
c
d
a
b
4 3
5 10
CQ2-19. Simplify:
d
c
3
8
8
3
0%
0%
0%
2
3
1
0%
4
(when b, c, and d are not 0).
45
6 12
10 7
CQ2-20. Simplify:
1
2
3
4
5
6
7
8
9
10
1. .
2. .
15
3. . 35
4. .
Example: Divide 2 4
2
7
20
0%
0%
0%
2
3
4
5
1
7
10
3
4
5
6
1
14
15
16
17
46
7
.
10
14
5
17
10
14
5
10
17
0%
2
4
1
2
13
To divide mixed numbers, first change each mixed
number into an improper fraction.
20
7
1
1
12
Dividing Mixed Numbers
5
36
35
11
7
8
9
10
11
12
13
14
15
16
17
47
28
11
or 1
17
17
48
8 of 15
MAT001 – Chapter 2 - Fractions
Dividing Mixed Numbers
3
1
2
7
3
4
CQ2-21. Simplify:
5
Example: Divide 5 6
.
1. . 10 13
44
2. . 1 49
1
3. . 8 7
1
2
4. .
7
7
5
5
6
7
5
5
6
7
1
35
6
7
1
5
35
6
5
6
1
71
0%
0%
0%
2
3
1
49
7
CQ2-22. Simplify:
1. . 1 68
93
8
2. . 5 27
14
3. .18 27
4
4. . 3 15
7
8
2
9
21
0%
0%
0%
2
3
1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
1
2
3
4
5
6
7
8
9
10
11
12
CQ2-23. Simplify:
1. . 8
2. .
3. . 36
4. .
0%
9
15
16
18 2
1
4
14
40
1
2
0%
1
2
3
4
5
17
0%
0%
2
3
1
51
4
50
1
4
4
17
13
0%
6
7
8
9
10
11
12
13
14
15
16
0%
4
17
52
Least Common Multiple (LCM)
2.6
A multiples of a number are the products of that
number and the numbers 1, 2, 3, 4, 5, …
The Least Common
Denominator and
Creating Equivalent
Fractions
The multiples of 3 are 3, 6, 9, 12, 15, …
3
1
3
2
3
3
The least common multiple, or LCM, of two
natural numbers is the smallest number that is
a multiple of both.
53
54
9 of 15
MAT001 – Chapter 2 - Fractions
Least Common Multiple (LCM)
Least Common Denominator (LCD)
A least common denominator (LCD) of two or more
fractions is the smallest number that can be divided
evenly by each of the fractions’ denominators.
Example: Find the LCM of 4 and 6.
The multiples of 4 are
4, 8, 12, 16, 20, 24 …
The multiples of 6 are
6, 12, 18, 24, 30, 36 …
7
3
and
12
4
The first number that appears on both lists is the LCM.
Since 4 can be divided into 12, the LCD of
7
3 is 12.
and
12
4
12 is the least common multiple of 4 and 6.
55
Least Common Denominator (LCD)
Example: Find the LCD for
4
56
Finding the Least Common Denominator
Three-Step Procedure for Finding the LCD
3
4
and .
4
5
1. Write each denominator as the product of prime factors.
2. List all the prime factors that appear in either product.
3. Form a product of those prime factors, using each factor the
greatest number of times it appears in any one denominator.
5 = 20
20 is also the smallest number that can be divided
by 4 and 5 without a remainder.
Example: Find the LCD for
5
7
and
.
12
30
Product of primes
2
3
4
and
The LCD of
is 20.
4
5
2 3
Prime factors in either product: 2
The LCD is 60.
2
2
3 5
3
5
57
58
Creating Equivalent Fractions
Building Fraction Property
Fractions with unlike denominators cannot be added.
Building Fraction Property
3
4
+
4
5
For whole numbers a, b, and c where b
The LCD is 20.
a
b
To change the denominators and make them the same,
1) find the LCD and
2) build up the addends into equivalent fractions that
have the LCD as the denominator.
3
4
c
c
?
20
4
5
c
c
?
20
c
5
5,
5
1
c
4
4,
4
1
a
b
1
a
b
c
c
a
b
0, c
0,
c
.
c
Example:
Build 3 to an equivalent fraction with a LCD of 20.
4
3
c
?
3
15
and
are
4
c
20
4
20
The building
fraction property
3
4
59
5
5
15
20
equivalent fractions.
60
10 of 15
MAT001 – Chapter 2 - Fractions
Fractions with Common Denominators
Fractions must have common denominators before
they can be added or subtracted.
2.7
2
4
Adding and Subtracting
Fractions
1
4
3
4
+
=
2
4
3
4
1
4
61
4
9
CQ2-24. Simplify:
12
18
1. .
2. .
12
3. . 9
4. .
8
9
2
3
4
4
3
5
6
5
10
2
3
4
7
8
9
10
11
0%
0%
2
3
12
13
14
15
1
3
4
21
5
6
1
.
6
LCD = 24
0%
16
0%
17
0%
7
8
9
10
11
12
13
9
24
1
6
4
4
4
24
4
24
13
24
64
1. . 17
2. .
12
3. . 7
4. .
0%
2
3
16
0%
31
7
25
7
0%
4
17
3
7
4
CQ2-26. Simplify:
0%
15
3
3
63
4
7
14
3
8
9
24
4
19
21
1
2
3
8
Add
1
1
If fractions have different denominators, find the
LCD and build up each fraction so that its
denominator is the LCD.
Example:
CQ2-25. Simplify:
1. .
2. .
3. .
4. .
Fractions with Different Denominators
2
3
1
1
62
0%
0%
2
3
1
65
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
0%
4
17
66
11 of 15
MAT001 – Chapter 2 - Fractions
Fractions with Different Denominators
Example:
5
12
Subtract
7
.
30
LCD = 60
5
12
5
5
25
60
7
30
2
2
14
60
14
60
11
60
25
60
13 7
18 12
CQ2-27. Simplify:
1. . 1
2. .
5
3. . 36
4. .
1
1
6
57
36
0%
0%
0%
2
3
1
67
7
8
CQ2-28. Simplify:
5
40
1. .
2. .
19
3. . 40
4. .
0%
2
3
4
5
6
7
8
9
10
11
12
13
0%
0%
2
3
14
15
16
0%
17
LCD = 6
2
1
6
2
2
3
9
Add the whole
numbers.
2
3
2
2
1
6
4
2
6
5
11
6
9
2
6
7
8
9
10
11
12
13
14
15
16
17
68
69
70
3
CQ2-29. Simplify:
1. . 5 13
21
3
2. . 5 10
2
3. .6 21
3
4. . 6 10
Example:
2
.
3
5
4
When adding mixed numbers, it is best to add the
fractions together and then add the whole
numbers together.
2
4
Adding and Subtracting
Mixed Numbers and the
Order of Operations
Adding Mixed Numbers
Add 9 1
6
3
4
2.8
5
8
5
3
2
2
5
1
1
1
0%
4
6
Add the
fractions
first.
2
1
2
7
3
0%
0%
0%
2
3
1
71
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
0%
4
17
72
12 of 15
MAT001 – Chapter 2 - Fractions
5
13
82
12
18
CQ2-30. Simplify: 38
5
.12136
3
. 120 5
65
120
. 216
3
. 151 5
1.
2.
3.
4.
Subtracting Mixed Numbers
Subtracting mixed numbers is like adding mixed
numbers.
Example:
Add 9 2
3
1
7 .
8
LCD = 24
2
3
1
7
8
0%
0%
2
3
1
0%
4
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
Add 5 1
12
LCD = 36
3
We cannot subtract
36
so we need to borrow.
3
36
14
3
36
14
36
1
12
3
3
5
7
3
18
2
2
14
3
36
5
7
3 .
18
39
36
14
3
36
25
1
36
5
5
0%
4
1. . 6 23
2. .
1
3. . 5 8
4. .
39
.
36
2
3
4
5
6
7
8
9
10
11
12
13
1
4
3
3
7
3
24
6
1
8
6
1
4
Subtract the
fractions
first.
5
1
6
8
2
0%
0%
2
3
14
15
16
1
2
3
4
5
6
7
8
9
10
11
12
13
CQ2-33. Simplify: 113
0%
1
1
1
8
0%
0%
2
3
1
18 7
1. . 11 14
1
2. . 10 4
3
3. .11 4
3
4. . 10 4
7
12
CQ2-31. Simplify:
75
CQ2-32. Simplify:
16
24
74
3
36
We borrow 1 from 5 to obtain
3
3
39
4 1
4
36
36
36
4
9
73
Subtracting Mixed Numbers
Example:
8
8
9
Subtract the whole
numbers.
1
2
3
16
24
3
7
24
13
2
24
9
0%
9
11
1. . 26 15
8
2. . 25 15
11
3. .26 20
1
4. . 26 10
0%
17
1
2
3
4
5
6
7
8
9
10
11
12
16
17
0%
0%
2
3
1
77
15
4
76
2
13
87
5
15
0%
4
14
0%
13
14
15
16
0%
4
17
78
13 of 15
MAT001 – Chapter 2 - Fractions
Order of Operations
Order of Operations
Order of Operations
1.
2.
3.
4.
Do first
Do last
Example: Evaluate 3
Perform operations inside any parentheses.
Simplify any expressions with exponents.
Multiply or divide from left to right.
Add or subtract from left to right.
Example: Evaluate 85
2
5
1
4
4
3
4
1
4
5
3
2
3
4
1
4
3
4
3
20
5
.
3
3
5
Express division
as multiplication.
Multiply.
Exponents
.
15
20
3
20
Rewrite fractions
using the LCD.
18
20
9
10
Add and simplify.
Multiplication
5
8
4
25
1
2
1
5
1
10
79
41
1. . 135
121
2. . 135
49
3. . 135
11
4. .
72
0%
0%
2
3
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
1. . 3 859
2. .
46
3. .2 85
4. .
0%
1
3
5
6
CQ2-35. Simplify:
0%
1
1
2
3 8 1
5 3 3
CQ2-34. Simplify:
80
24
85
0%
0%
0%
2
3
1
81
1
2
3
4
5
1
8
4
5
4
17
2
6
7
8
9
10
11
12
13
14
15
16
0%
4
17
82
Problem Solving Steps
1. Understand the problem.
2.9
2.
Solving Applied Problems
Involving Fractions
a) Read the problem carefully.
Draw a picture if it is helpful.
a) Fill in the Mathematics Blueprint so that you have the
facts and a method of proceeding in this situation.
3. Solve and state the answer.
a) Perform the calculations.
b) State the answer and include the unit of measure.
4. Check.
a) Estimate the answer.
b) Compare the exact answer with the estimate to see if
your answer is reasonable.
83
84
14 of 15
MAT001 – Chapter 2 - Fractions
Mathematics Blueprint
Mathematics Blueprint
Example:
The Mathematical Blueprint is simply a sheet of paper with
four columns. Each column tells you something to do.
A carpenter is using an 8-foot length of wood for a frame. He needs to cut a
notch in the wood that is 12feet from one end and 47feet from the other
3
8
end. How long does the notch need to be?
Mathematics Blueprint for Problem Solving
Gather the
Facts
What Am I
Asked to Do?
How Do I
Proceed?
Key Points to
Remember
Mathematics Blueprint for Problem Solving
Gather the
Facts
What Am I
Asked to Do?
How Do I
Proceed?
The board is 8 ft.
long. There is a
cut from each
side of the board.
Find the length of Add the fractions
the notch.
and subtract the
total from 8.
Key Points to
Remember
All fractions must
use the LCD = 24.
Example continues.
85
86
Mathematics Blueprint
Mathematics Blueprint
Example:
Example:
A carpenter is using an 8-foot length of wood for a frame. He needs to cut a
notch in the wood that is 12feet from one end and 47feet from the other
3
8
end. How long does the notch need to be?
withheld for medical coverage. How much money per week is left for Patty
Patty earns $450 per week. She has 1 of her income withheld for federal
5
1
taxes, 1 of her income withheld for state taxes, and
of her income
25
15
after those three deductions?
2
1
3
8
4
6
7
8
13
24
16
1
24
37
5
24
7
24
24
21
24
13
6
24
4
6
13
24
This is the part of the
board that is not
notched.
11
1
24
Mathematics Blueprint for Problem Solving
The length of the
11
notch is 1 feet.
24
Gather the
Facts
What Am I
Asked to Do?
How Do I
Proceed?
Key Points to
Remember
The total income
is $450.There are
three deductions
to be subtracted
from the 450.
Find how much
money Patty has
after the
deductions.
Multiply each
fraction by 450,
then subtract the
three products
from 450.
“of” means to
multiply.
Example continues.
87
88
Mathematics Blueprint
Example:
Patty earns $450 per week. She has 1 of her income withheld for federal
5
1
taxes, 1 of her income withheld for state taxes, and
of her income
25
15
withheld for medical coverage. How much money per week is left for Patty
after those three deductions?
1
450
5
1
450
15
1
450
25
450
5
450
15
450
25
90
30
The total of the deductions is 138.
450 – 138 = 312
18
Patty has $312 left
after deductions.`
89
15 of 15