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Unit 3: Linear Equations
Name _____________________________________
Adding and Subtracting Fractions 2
Directions: Solve.
72
Appendix B: Answer Keys
Transparency/Guided Practice Book Answers
54
Unit 2: Linear Equations
Name _____________________________________
Adding and Subtracting Fractions
Directions: Calculate.
30
Appendix B: Answer Keys
Transparency/Guided Practice Book Answers
67
2
How to
• • • • • • • • • • • • • • • • • Subtract Fractions
Facts to Know
Subtracting Fractions with the Same Denominators
When fractions have the same denominators, subtract the numerators only and place the total over the
denominator.
Sample: From a bag that contained 7– pound of birdseed, Margery poured 3– of a pound into the bird
8
8
feeder. How much birdseed is left?
Step 1
Subtract the numerators.
Step 2
Write the answer over the denominator.
Step 3
Reduce the final answer.
7–3=4
4–
8
4– pound = 1– pound
8
2
More on Finding Common Denominators
Sometimes you must change more than one denominator to add or subtract. For example, how would
you solve this problem:
Sample: 1– – 1– = ?
2 3
These fractions have different denominators. You cannot subtract them, nor can only one
denominator be changed because 2 won’t divide into 3 evenly, and 3 won’t divide into 2 evenly.
Therefore, you must find a common denominator, a number that both 2 and 3 will divide into evenly.
There are three methods for finding a common denominator.
Method 1— Check the largest denominator in the problem to find out whether it can be divided evenly
by the other denominator(s) in the problem.
– 1– = 2–
1
1
3 6
Sample: – – – = ?
3 6
– 1– = 1–
6 can be evenly divided by 3, so there’s no need to look for another number.
6 6
1–
Method 2—Multiply the denominators together to find a common denominator.
6
3
2
Sample: – – – = ?
4 3
Step 1
Multiply the denominators. The number 12
9
– 3– = —
4 12
is the common denominator.
8
– 2– = —
Step 2
Raise each fraction to 12ths.
3 12
1
—
Step 3
Subtract the new fractions.
12
Method 3—Go through the multiplication table of the largest denominator.
Sample: 5– – 1
–=?
9 6
5– = 10
Step 1
Go through the multiplication table of the largest
—
9 18
denominator, 9.
3
– 1– = —
Step 1
9 x 1 = 9 which cannot be divided evenly by 6.
6 18
25
7
Step 1
9 x 2 = 18 which can be divided evenly by 6 and 9.
— = 1—
18
18
Step 2
Raise each fraction to 18ths.
Step 3
Subtract the new fractions.
9
.
2
How to • • • • • • • • • • • • • • • • • Subtract Fractions
Facts to Know (cont.)
Subtracting Fractions with Different Denominators
When subtracting fractions with different denominators, find a common denominator.
Sample: Lupe walks 1– mile to the train. She stops for coffee at Tom’s restaurant, which is 3– mile to
2
8
the train. How much further does she have to walk after Tom’s?
You’ll have to subtract 3– from 1–, but they don’t have common denominators.
8
2
Step 1
Find the least common denominator. The numbers 2 and 8
1– = 4–
2 8
both evenly divisible by 8.
– 3– = 3–
Step 2
Raise 1– to eighths.
8 8
2
1– mile
Step 3
Subtract the fractions using the least common denominator.
8
Subtracting Fractions from a Whole Number
When subtracting fractions from the whole number 1, you must change the number 1 to a fraction with
the same numerator and denominator as the denominator in the fraction.
Sample: Ian took one cup of sugar from a bag. He only used 3– cup to make ice tea.
4
How much sugar is left?
Step 1
Change 1 to a fraction, using the same number for the
1 = 4–
4
numerator and denominator as the denominator of the
3
– – = 3–
4 4
original fraction (1 cup = 4– cup).
4
1– cup left
Step 2
Subtract the fractions.
4
When subtracting a fraction from a whole number larger than 1, you must regroup.
Sample: 3 – 3– = ?
8
3 = 2 8–
Step 1
Regroup by changing 3 to 2 8–.
8
8
3
(Remeber, 1 = 8–.)
– – = – 3–
8
8
8
Step 2
Subtract.
2 5–
8
Subtracting Mixed Numbers
You can subtract mixed numbers provided the fractions have the same denominators.
Sample : 4 1– – 1 3– = ?
3
4
4 = 3—
4 + 12
4 1– = 4 —
—
Step 1
Find the lowest common denominator.
3
12
12 12
9 = –1 —
9
9 from —
4 ;
– 1 3– = 1 —
Step 2
Since you can’t subtract —
4
12
12
12
12
4.
regroup 1 as 12
— from the 4. Add it to —
12
12
Step 3
Subtract the fractions. Then subtract the whole numbers.
10
=
=
3 16
—
12
9
–1 —
12
7
2 —
12
2
Practice
• • • • • • • • • • • • • • • Subtracting Fractions
Directions: Subtract the fractions. Remember, to reduce the fractions to lowest terms.
5 =
1. 4– – 2– =
5. 17
— – 11
—=
9. 1– – 1– =
13. 5– – —
5 5
23 23
6 18
2 6
9 –—
4 =
2. —
10 10
6. 20
— – 17
—=
21 21
10. 7– – 1– =
8 4
14. 19
— – 1– =
20 4
7 –—
6 =
3. —
12 12
7. 7– – 3– =
8 8
7 – 1– =
11. —
10 5
15. 3– – 1– =
4 2
4. 6– – 2– =
7 7
7 –—
6 =
8. —
15 15
12. 1– – 1– =
4 8
7 =
16. 13
—– —
15 30
Directions: Subtract the fraction from the whole number.
17.
5 3–
4
– 3–
4
19.
4 3–
4
– 3–
8
21.
12 3–
4
– 12
—
25
23.
5 3–
4
– 1–
4
25.
13 3–
4
– 11
—
22
18.
7 3–
4
1
– —
16
20.
10 3–
4
– 5–
7
22.
8 3–
4
9
– —
12
24.
25 3–
4
– 14
—
17
26.
5 3–
4
– 5–
7
11
.
2
Practice • • • • • • • • • • • • • • • Subtracting Fractions
Keys to Subtracting Fractions
• If the denominators in the fractions are not alike, find the lowest common
denominator.
• Regroup if a minuend (the number you subtract from) is a whole number or the
fraction in a minuend is smaller than the fraction in a subtrahend (the number being
subtracted).
• Subtract the fractions first and then subtract the whole numbers.
Directions: Subtract the mixed numbers. Remember, reduce to the lowest term.
9 7–
8
5
–6–
8
7.
9
15 —
10
7
– 7—
10
8.
9 3–
8
– 2 3–
8
3. 14 19
—
24
5
–8—
24
9.
4
7—
11
4
–3—
11
4.
11 5–
6
1
–5–
6
10.
4
8—
13
5
–6—
13
5.
6 7–
8
– 3 3–
8
11.
6 1–
4
– 3 1–
3
6.
5 3–
8
– 1 4–
7
12.
10 3–
5
– 8 3–
4
1.
2.
6
7
–5—
10
12
1– .50
50%
2
Page 8
1. 1 3/4
2. 1 4/5
3. 1 1/3
4. 1 3/5
5. 2 1/5
6. 1 3/4
7. 2 1/7
8. 2 1/5
9. 2 1/8
10. 5
11. 7/4
12. 8/5
13. 9/4
14. 23/8
15. 17/5
16. 13/3
17. 17/3
18. 23/2
19. 41/8
20. 53/12
21. 1/2
22. 2/3
23. 1/4
24. 2/3
25. 1/3
26. 6/13
27. 1/2
28. 1/3
29. 2/3
30. 1/2
31. 3/15
32. 9/12
33. 4/16
34. 6/40
35. 25/35
36. 6/36
37. 12/18
38. 10/45
39. 3/4
40. 5/7
41. 1
42 3 1/3
43. 1 1/7
44. 4
45. 2 1/2
46. 7 2/3
47. 1 3/8
48. 25/28
49. 31/36
50. 14 1/12
51. 2
52. 1 4/5
53. 11 11/24
54. 14 16/35
55. 1 7/10
Page 11
1. 2/5
2. 1/2
3. 1/12
4. 4/7
5. 6/23
6. 1/7
7. 1/2
8. 1/15
9. 1/3
10. 5/8
11. 1/2
12. 1/8
13. 5/9
14. 7/10
15. 1/4
16. 19/30
17. 4 1/4
18. 6 15/16
19. 3 5/8
20. 9 2/7
21. 11 13/25
22. 7 1/4
23. 4 3/4
24. 24 3/17
25. 12 1/2
26. 4 2/7
Page 12
1. 3 1/4
2. 8 1/5
3. 6 7/12
4. 6 2/3
5. 3 1/2
6. 3 3/7
7. 3/10
8. 6 5/8
9. 3 7/11
10. 1 12/13
11. 2 11/12
12. 1 17/20
13. 2 13/18
14. 8 5/12
15. 10 3/4
16. 7 13/15
17. 8 5/6
18. 7 27/40
Page 15
1. 3/8
2. 2/21
3. 9/40
• • • • • • • • • • • • • • • • • • • • • • Answer Key
4. 6/35
5. 1/6
6. 1/6
7. 2/7
8. 2/9
9. 1/4
10. 3/4
11. 1/4
12. 1/6
13. 3/20
14. 35/72
15. 1/8
16. 1/10
17. 1/5
18. 2/9
19. 3/5
20. 1/2
21. 1/5
22. 2/27
23. 3/7
24. 15/154
25. 11/16
26. 1/8
27. 4/39
28. 2/7
29. 11/30
30. 4/47
31. 17/611
32. 7/5,600
Page 16
1. 1 1/4
2. 2 2/3
3. 1 1/6
4. 3 3/5
5. 1 5/7
6. 3/10
7. 6 1/8
8. 2 2/5
9. 8/9
10. 1 1/8
11. 3 1/3
12. 3 1/3
13. 5 1/3
14. 4 2/3
15. 2 2/5
16. 7/16
17. 2 1/2
18. 1 1/35
19. 1 7/18
20. 5/6
21. 8
22. 2 4/33
23. 2 2/3
47
24. 5 3/5
25. 9
26. 3 1/8
27. 9 5/7
28. 4/21
Page 19
1. 11/14
2. 1 13/18
3. 14/19
4. 82/87
5. 18/29
6. 1 1/4
7. 2/3
8. 5
9. 3/4
10. 3/4
11. 2 1/6
12. 3/7
13. 5/12
14. 8/9
15. 1 5/27
16. 3/10
17. 3 1/9
18. 6 1/4
19. 9 3/4
20. 1/4
21. 25/133
22. 5/64
23. 2 31/32
24. 33 3/4
25. 18/175
26. 1/32
27. 150
28. 7 1/2
29. 4 2/27
30. 10
Page 20
1. 5/6
2. 4/9
3. 15/16
4. 2 4/7
5. 2/5
6. 4
7. 1/2
8. 1
9. 4
10. 2 1/3
11. 2/9
12. 4/15
13. 4
14. 1/12
15. 7/16
16. 6 2/3
17. 2/15
18. 6
19. 10
20. 18
21. 10 1/2
22. 9 1/3
23. 12
24. 13 1/2
25. 10 2/3
26. 7
27. 4 4/5
28. 3 1/3
29. 7 1/2
30. 7/20
31. 4 2/3
32. 9
33. 1 5/6
34. 1 1/4
35. 1
Page 24
1. nine tenths
2. three hundred six
thousandths
3. forty-two
thousandths
4. six and three
hundredths
5. eighty and seven
tenths
6. two hundred
thirty-four and six
hundred twelve
thousandths
7. sixty-eight and
thirty-five ten
thousandths
8. one thousand two
hundred thirtyfour ten
thousandths
9. one and two
hundred thirtyfour thousandths
10. twelve and thirtyfour hundredths
11. .43
12. 40.03
13. .017
14. 86.6
15. .0508
16. 5.04
17. 12.140; 12.404;
12.444; 12,400
18. 0.96; 0.9666;
10.96; 109.6
19. 0.055; 0.5; 0.505;
0.55
.