Chapter 0:
Fundamental Review
Selected Worked Homework Problems
Reduce each fraction completely.
14
!
32
1.
2 divides into
both numbers
1/ 4/ 7
!
4 divides into
both numbers
!
3/ 2/ 16
=
32
60
2.
3/ 2/ 8
!
6/ 0/ 15
7
16
=
8
15
Reduce each improper fraction to a mixed numbers in lowest terms.
4.
24
!
5
5.
24
7
!
5 divides into 24
4 times with 4 left over
7 divides into 24
3 times with 3 left over
!
=4
6.
4
5
18
4
=3
!
7.
3
7
48
!
20
First reduce the fraction
First reduce the fraction
1/ 8/ 9
4/ 8/ 12 12
=
2/ 0/ 5 5
2 divides into 9
!
4 times with 1 left over
5 divides into 12
2times with 2 left over
9
=
2
2
4/
=4
1
2
Chapter 0
=2
!
HW WKD
!
2
5
© 2016 Eitel
Convert each mixed number into an improper fraction.
10.
13
13
1
!
2
11.
1
(13⋅ 2) + 1
=
2
2
9
2
3
9
2
(9 ⋅ 3) + 2
=
3
3
! !
=
27
2
Multiply and Divide Mixed Numbers
1
1
13.
3 •3 !
2
3
10
21 7
=
÷
10 4
3
!
÷
(1• 4) + 3
4
Infert (flip) the second fraction
21 4
= •
10 7
Cancel
7 1/ 0/ 5
= 1⋅
!
3
2/
35
=
3
Convert to a mixed number
2
= 11
3
Chapter 0
1
3
÷1 !
10
4
2
(2 •10) + 1
(3• 2) + 1 (3• 3) + 1
•
17.
Convert to improper fractions
Convert to improper fractions
2
7 10
= ⋅
2 3
Cancel
29
3
=
=
2/ 1/ 3
4/ 2
•
1/ 0/ 5 7/ 1
6
=
5
Convert to a mixed number
1
=1
5
HW WKD
!
© 2016 Eitel
Adding Mixed Numbers with a Common Denominator.
3
7
5
+1
7!
19.
5
5
9
7
+1
9!
20.
3
5
(add the fractions and)
7
5
+1
(add the whole numbers)
7
8
=6+
7
1
= 6 +1
7
1
=7
7
4
5
(add the fractions and)
9
7
+1
(add the whole numbers)
9
12
=5+
9
3
= 5 +1
9
3
=6
9
Reduce
1
=6
3
4
!
Subtracting Mixed Numbers with a Common Denominator.
5
6
1
− 2
6!
22.
8
24.
5
(subtract the fractions and)
6
1
−2
(subtract the whole numbers)
6
4
=6
6
reduce
2
=6
3
!
1
1
7
= 9/ 8 + 1 = 8
6
6
6
5
5
− 5 =
− 5
6
6
2
3
6
reduce
1
=3
3
9
8
Chapter 0
1
6
5
− 5
6
9
!
HW WKD
!
© 2016 Eitel
26.
9
3!
4
− 2
= 9/ 8 + 1 =
9
− 2
3
=
4
4
4
3
− 2
4
1
6
4
8
Adding Mixed Numbers without!
Subtracting Mixed Numbers without
a Common Denominator.!
a Common Denominator.
28.
5
6
!
1
+ 2
4
7
32.
The LCD is 12!
5
6
!
1
−2
4
5
The LCD is 12
5
5⋅2
10
=
= 7
6
6⋅2
12
1
1⋅ 3
3
+ 2
=
= +2
4
4⋅3
12
13
=9
12
5
5⋅2
10
=
= 5
6
6⋅2
12
1
1⋅ 3
3
− 2
=
= −2
4
4⋅3
12
7
=3
12
7
5
!
1
12
1
= 10
12
= 9 +1
Chapter 0
!
HW WKD
!
© 2016 Eitel
Converting Fractions to Decimals.
Change each fraction to an equivalent decimal.
3
!
8
37.
40.
.375
8) 3.000
24
60
56 !
40
40
28
!
5
!
!
5.6
5) 28.000
25
30
30
0
Change each decimal to an equivalent fraction or mixed number and reduce if possible.
43.
.24!
!
45.
.24 is read 124 hundredths and is
24
written as the fraction
100
now reduce
2/ 4/ 6
3.08 is read 3 and 8 hundredths and is
8
written as the mixed number 3
100
now reduce
!
1/ 0/ 0/ 25
.24 =
3.08!
3
6
25
Chapter 0
8/ 2
1/ 0/ 0/ 25
3.08 = 3
!
HW WKD
!
2
25
© 2016 Eitel
4
1
+ + .6
47. 5
!
2
Answer as a decimal
4
= .80
5
1
= .50
2
+.60
!
1.90
48.
3
2
+ + .75
!
2
5
Answer as a fraction
3
3•10 30
=
=
2
2 •10 20
2
2• 4 8
=
=
5
5 • 4 20
3
3• 5 15
=
=
4
4 • 5 20
!
=
53
13
=2
20
20
Be sure an include units with your answers.
49. Tom runs 7
2
3
miles and then walks 5 miles. What is his total distance he has traveled?
3
4
2
2⋅ 4
8
=
= 7
3
3⋅ 4
13
3
3⋅ 3
9
+ 5
=
= +5
4
4⋅3
12
17
= 12
12
5
= 12 + 1
12
5
= 13 miles
12
7
50. Mary fills a 20 ounce test tube with 13
20
− 13
6
= 2/ 0/ 19 + 1 =
5
=
9
5
ounces of water. How much empty space is left?
9
9
9
5
− 13
9
4
6
9
19
4
ounces
9
Chapter 0
!
HW WKD
!
© 2016 Eitel
3
1
pounds of clay to make a pot. She then uses 2 pounds of clay to make some
4
2
dishes. If she started with 10 pounds of clay, how much does she have left?
57. Janice uses 3
Step1. Find the total amount used!
3
4
2
4
5
=5
4
1
= 5+1
4
!
Step2 . Find the amount left.
3
3⋅1
=
= 3
4
4 ⋅1
1
1⋅ 2
+ 2
=
= +2
2
2⋅2
3
=6
There are 3
= 1/ 0/ 9 + 1 =
10
− 6
1
=
4
!
3
4
4
1
− 6
4
3
3
4
9
3
pounds left
4
1
pounds used
4
3
pounds left?
4
Add and Subtract, Multiply and Divide Decimals.
59.
4.2 + 3.05 + 5.08 !
60.
7.025 − 5.987 !
!
7/ 6. 1/ 0/ 9 1/ 2/ 11 15
− 5. 9
8
7
!
1 .0
3 8
4.20
3.05
!
+ 5.08
12.33
62. 6.02 × 3.1 !
63.
6.02
× 3.1
602
18060 !
18662
.147 ÷ .42
.35
42)14.7000
126
210
210
0
!
= 18.662
Chapter 0
!
HW WKD
!
© 2016 Eitel
65. Find the final selling price of a $ 28 item if it is to be marked down 25% and sales tax is 8%
Step 1. Find the discount!
28
× .25
140
560
700
Step 2. Find the selling price!
Step 3. Find the tax
21.00
× .08
16800
00000
16800
28.00 original price
− 7.00 discount
21.00 selling price
!
= 1.68 Tax
= 7.00 discount
off the selling price
Step 4. Find the final selling price.
21.00 selling price
+ 1.68 tax
22.68 final price
67.
16 is 20% of what number?!
68.
24 is what percent of 40!
16 = .20 • x
24 = x • 40
16 .20 • x
=
.20
.20
24 .x • 40
=
40
40
!
divide 16 by .20
divide 24 by 40
80
20) 1600
−160
00 !
–00
0
x = 80
!
.60
40) 24.00
−240
00
–00
0
x = 60%
!
Chapter 0
!
HW WKD
69. What is 8% of 22
x = .08 • 22
!
!
!
22
×.08
176
000
176
x = 1.76
© 2016 Eitel