Math Skill Development Fraction Ratio Proportion Worksheets
Fractions, Ratios, and Proportions Work Sheets
The work sheets are grouped according to math skill. Each skill is then arranged in a sequence of work sheets that build from simple to complex. Choose the work sheets that best fit the student’s need and will bring him up to the desired level.
Work Sheet
Fractions
Title
Contents
Introduced
Page
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.
Reading and Writing Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Numerator and Denominator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Equal Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ordering Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mixed Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fractions that Equal 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Finding Half of a Larger Number . . . . . . . . . . . . . . . . . . . . . . . . . . . Finding a Fraction of a Number . . . . . . . . . . . . . . . . . . . . . . . . . . . . Proper and Improper Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Changing Mixed Numbers to Improper Fractions . . . . . . . . . . . . . . Making Equal Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Finding the Missing Numerator . . . . . . . . . . . . . . . . . . . . . . . . . . . . Finding the Fraction of a Number Mentally . . . . . . . . . . . . . . . . . . . Changing Fractions to Percents . . . . . . . . . . . . . . . . . . . . . . . . . . . . Rounding Mixed Numbers to the Nearest Whole Number . . . . . . .
Review from Level 200 Math 303, Lesson 9 Math 304, Lesson 3 Math 304, Lesson 11 Math 305, Lesson 6 Math 307, Lesson 1 Math 307, Lesson 3 Math 407, Lesson 7 Math 402, Lesson 14 Math 404, Lesson 1 Math 405, Lesson 7 Math 405, Lesson 12 Math 507, Lesson 8 Math 507, Lesson 14 Math 703, Lesson 12
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
16. 17. 18. 19. 20.
Adding and Subtracting Fractions Horizontally . . . . . . . . . . . . . . . . One Minus a Fraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Adding or Subtracting Mixed Numbers . . . . . . . . . . . . . . . . . . . . . . Subtracting a Mixed Number From a Whole Number . . . . . . . . . . . Borrowing to Subtract Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . .
Math 402, Lesson 4 Math 406, Lesson 14 Math 407, Lesson 8 Math 503, Lesson 1 Math 503, Lesson 12
16 17 18 19 20
21. 22. 23. 24. 25. 26. 27.
Lowest Common Multiple . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A Quicker Way to Find LCM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Using Common Denominators to Add or Subtract . . . . . . . . . . . . . . Finding the Lowest Common Denominator . . . . . . . . . . . . . . . . . . . Changing Fractions to Common Denominators . . . . . . . . . . . . . . . . Finding the LCD Before Adding/Subtracting Fractions . . . . . . . . . . Borrowing to Subtract Mixed Numbers With LCD . . . . . . . . . . . . .
Math 408, Lesson 3 Math 408, Lesson 8 Math 503, Lesson 2 Math 503, Lesson 12 Math 504, Lesson 1 Math 504, Lesson 8 Math 505, Lesson 12
21 22 23 24 25 26 27
28. 29. 30.
Multiplying Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Canceling Before Multiplying Fractions . . . . . . . . . . . . . . . . . . . . . Multiplying Fractions, Mixed Numbers, and Whole Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Multiplying Mixed Numbers, Whole Numbers, and Fractions With More Than Two Factors . . . . . . . . . . . . . . . . . . . Canceling Twice to Multiply Fractions . . . . . . . . . . . . . . . . . . . . . .
Math 505, Lesson 2 Math 505, Lesson 6
28 29
Adding/Subtracting (like denominators)
Adding/Subtracting (unlike denominators)
Multiplying
31. 32.
Math 506, Lesson 8
Math 603, Lesson 2 Math 603, Lesson 1
31
32 33
Dividing 33. 34.
Reciprocals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dividing Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Math 507, Lesson 6 Math 507, Lesson 12
34 35
35. 36. 37. 38.
Changing Improper Fractions to Whole or Mixed Numbers . . . . . . Simplifying Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Simplifying Mixed Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Simplifying Fractions to Simplest Form . . . . . . . . . . . . . . . . . . . . .
Math 405, Lesson 4 Math 405, Lesson 6 Math 407, Lesson 14 Math 406, Lesson 6
36 37 38 39
39. 40. 41. 42.
Converting Fractions and Mixed Numbers to Decimals . . . . . . . . . Converting Decimals to Fractions and Mixed Numbers . . . . . . . . . Changing Fractions to Decimals on a Calculator . . . . . . . . . . . . . . . Using Decimal Equivalents to Compare Fractions . . . . . . . . . . . . .
Math 602, Lesson 6 Math 603, Lesson 6 Math 605, Lesson 7 Math 607, Lesson 3
41 42 43 44
43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55.
Ratios Compare Amounts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ratios Compare Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . Three Ways to Write Ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Equivalent Ratios: Enlarging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Equivalent Ratios: Simplest Form . . . . . . . . . . . . . . . . . . . . . . . . . . Writing Ratios as Percents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Proportions: Finding the Missing Term . . . . . . . . . . . . . . . . . . . . . . Using Cross Products to Solve and Check Proportions . . . . . . . . . . Setting Up Proportions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Using Proportions to Convert U.S. Measures . . . . . . . . . . . . . . . . . Solving Percents Using Proportions . . . . . . . . . . . . . . . . . . . . . . . . . Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Using Proportions to Convert Measures Between U.S. and Metric Measure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Converting Between Kilograms and Pounds . . . . . . . . . . . . . . . . . . Converting Between Inches and Centimeters . . . . . . . . . . . . . . . . . . Converting Between Meters and Yards . . . . . . . . . . . . . . . . . . . . . .
Math 406, Lesson 3 Math 406, Lesson 7 Math 505, Lesson 9 Math 506, Lesson 6 Math 506, Lesson 9 Math 604, Lesson 2 Math 506, Lesson 12 Math 507, Lesson 1 Math 507, Lesson 11 Math 602, Lesson 8 Math 607, Lesson 12 Math 607, Lesson 18
45 46 47 48 49 50 51 52 54 55 56 58
Simplifying
Decimals
Ratio and Proportion
56. 57. 58.
Math 703, Lesson 15 Math 705, Lesson 15 Math 706, Lesson 15 Math 707, Lesson 15
59 61 62 63
Work Sheet 19
Math 503, Lesson 1
Subtracting a Mixed Number From a Whole Number
8 3 – 25
You can not subtract a fraction from nothing.
7
5
3 I cannot subtract 5 from nothing. I must borrow from 8.
85
Cross out 8 and write 7. You are subtracting fifths,
– 25 3
5
so change the 1 you borrowed to 5 and write it above the fraction.
7
5
85
– 25 3 2
55
Now you can subtract.
Borrow from the whole number before you subtract. 3
1. a. – 2
2. a.
3. a.
8
– 4
8
4 5
7 8
7
– 3 12
5
b. – 3
b.
b.
–
c. – 1
7 8
2
c.
5 1 12
6
6
c.
1
– 3 10
19
6
– 4
7
5 9
2 7
7
– 2 10
7
d. – 3
d.
d.
9
3 5
5
– 7 12
5
– 2
5 8
Work Sheet 20
Math 503, Lesson 12
Borrowing to Subtract Fractions
When the top fraction is smaller than the bottom fraction in a subtraction problem, you must borrow. 4
2
7 4 2
You cannot subtract 5 from 5 . Borrow 1 from 5. Change the 1 to
5 5
and add it to
The 5 becomes a 4 and the
2 5
2 5.
becomes
2 5
5
–2
7 5.
2
5
+
5 5
=
4 5
3 5
Subtract. Borrow as needed. Give answers in simplest form. 1
7 12 11
1. a. – 3 12
b.
1
75 3
2. a. – 2 5
b.
5
14 16 7
3. a. – 4 16
8
4. a. – 6
2 7 5 7
b.
12
3 8
17
1 8
7
–6
–8
–5
4
1 7
3 8
8
c. – 7
1 6
1 4
3
3 8
7 8
c.
3 4
c. –
3
b.
–3
2 7
5 6
7 8
1
d.
–
7 12
7
7
– 8 16
c. – 6 12
Note: If student doesn’t know how to simplify assign worksheets 36–38.
20
3 4
7
d.
d.
7 12 11
– 6 12
d.
4
1 9
4
1 9
–1
5
9 16
12 4
–
7 9
5 9
7 5
Work Sheet 31
Math 603, Lesson 2
Multiplying Mixed Numbers, Whole Numbers, and Fractions With More Than Two Factors
When multiplying mixed numbers, whole numbers, and fractions, the first step is to rewrite the problem, changing mixed and whole numbers to improper fractions. You can cancel any denominator with any numerator. Then multiply all the numerators together and all the denominators together. If the answer is an improper fraction, change it back to a mixed number.
1 37
There are no mixed numbers or whole numbers. Pairs that cancel are 5 and 15, 4 and 8, and 7 and 7. 1
5 8 2
1
1
7
4
3
1
1. a.
7 12
2
6 7
1
9 10
× 13 ×
2
2. a. 1 9 × 2 2 ×
3. a. 16 ×
4. a.
3 8
11
22 7
1
× 15 × 7 = 6
Solve. Cancel if possible.
1 21
2
1
=
=
× 12 =
× 13 × 3 =
×
2 3
×
1 32 1
2
7
Change all mixed numbers to improper fractions. Pairs that cancel are 22 and 2, and 7 and 7.
22
1
1
1
1
b. 2 × 2 2 × 2 4 =
1
b. 2 4 ×
7 20
b. 1 3 × 3
2
3 4
1
2
2
× 63 =
2
× 23 =
b. 3 3 × 1 5 × 12 =
Note: If student doesn’t know how to simplify assign worksheets 36–38.
32
1
× 3 × 2 = 3 = 73 c.
1 2
×
1 4
×
2 3
=
c.
2 9
×
1 5
×
5 8
=
c.
1 3
×
3 4
×
1 2
=
c.
2 3
×
1 8
×
1 4
=
Work Sheet 52
Math 602, Lesson 8
Using Proportions to Convert U.S. Measures
Proportions can be helpful in converting measures. They help us keep track of when we should multiply or divide.
60 feet is how many inches? First write the conversion ratio.
1 foot 12 inches
Then write the second ratio, keeping each unit (feet and inches) on the same level as the first ratio. The second ratio uses n for inches since we need to
1 foot 12 inches
=
60 feet n inches
find inches.
Solve. 12 x 60 ÷ 1 = 720. 60 feet is 720 inches.
336 hours is how many days? 1 x 336 ÷ 24 = 14.
1 day 24 hours
=
n days 336 hours
336 hours is 14 days. Often when you need to convert measures, you will know whether to divide or multiply. But if your answer does not seem sensible or if you get confused, setting up a proportion helps you stay on track. Proportions are especially helpful when you do more complicated conversions.
Set up a proportion to find each answer. 1. a. 180 in =
Set up a proportion.
yd
b. 4 yd =
lb
b. 12 gal =
ft
Solve cross products.
2. a. 112 oz =
Set up a proportion.
Solve cross products.
55
qt
The work sheets are grouped according to math skill. Each skill is then arranged in a sequence of work sheets that build from simple to complex. Choose the work sheets that best fit the student’s need and will bring him up to the desired level.
Work Sheet
Fractions
Title
Contents
Introduced
Page
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.
Reading and Writing Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Numerator and Denominator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Equal Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ordering Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mixed Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fractions that Equal 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Finding Half of a Larger Number . . . . . . . . . . . . . . . . . . . . . . . . . . . Finding a Fraction of a Number . . . . . . . . . . . . . . . . . . . . . . . . . . . . Proper and Improper Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Changing Mixed Numbers to Improper Fractions . . . . . . . . . . . . . . Making Equal Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Finding the Missing Numerator . . . . . . . . . . . . . . . . . . . . . . . . . . . . Finding the Fraction of a Number Mentally . . . . . . . . . . . . . . . . . . . Changing Fractions to Percents . . . . . . . . . . . . . . . . . . . . . . . . . . . . Rounding Mixed Numbers to the Nearest Whole Number . . . . . . .
Review from Level 200 Math 303, Lesson 9 Math 304, Lesson 3 Math 304, Lesson 11 Math 305, Lesson 6 Math 307, Lesson 1 Math 307, Lesson 3 Math 407, Lesson 7 Math 402, Lesson 14 Math 404, Lesson 1 Math 405, Lesson 7 Math 405, Lesson 12 Math 507, Lesson 8 Math 507, Lesson 14 Math 703, Lesson 12
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
16. 17. 18. 19. 20.
Adding and Subtracting Fractions Horizontally . . . . . . . . . . . . . . . . One Minus a Fraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Adding or Subtracting Mixed Numbers . . . . . . . . . . . . . . . . . . . . . . Subtracting a Mixed Number From a Whole Number . . . . . . . . . . . Borrowing to Subtract Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . .
Math 402, Lesson 4 Math 406, Lesson 14 Math 407, Lesson 8 Math 503, Lesson 1 Math 503, Lesson 12
16 17 18 19 20
21. 22. 23. 24. 25. 26. 27.
Lowest Common Multiple . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A Quicker Way to Find LCM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Using Common Denominators to Add or Subtract . . . . . . . . . . . . . . Finding the Lowest Common Denominator . . . . . . . . . . . . . . . . . . . Changing Fractions to Common Denominators . . . . . . . . . . . . . . . . Finding the LCD Before Adding/Subtracting Fractions . . . . . . . . . . Borrowing to Subtract Mixed Numbers With LCD . . . . . . . . . . . . .
Math 408, Lesson 3 Math 408, Lesson 8 Math 503, Lesson 2 Math 503, Lesson 12 Math 504, Lesson 1 Math 504, Lesson 8 Math 505, Lesson 12
21 22 23 24 25 26 27
28. 29. 30.
Multiplying Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Canceling Before Multiplying Fractions . . . . . . . . . . . . . . . . . . . . . Multiplying Fractions, Mixed Numbers, and Whole Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Multiplying Mixed Numbers, Whole Numbers, and Fractions With More Than Two Factors . . . . . . . . . . . . . . . . . . . Canceling Twice to Multiply Fractions . . . . . . . . . . . . . . . . . . . . . .
Math 505, Lesson 2 Math 505, Lesson 6
28 29
Adding/Subtracting (like denominators)
Adding/Subtracting (unlike denominators)
Multiplying
31. 32.
Math 506, Lesson 8
Math 603, Lesson 2 Math 603, Lesson 1
31
32 33
Dividing 33. 34.
Reciprocals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dividing Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Math 507, Lesson 6 Math 507, Lesson 12
34 35
35. 36. 37. 38.
Changing Improper Fractions to Whole or Mixed Numbers . . . . . . Simplifying Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Simplifying Mixed Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Simplifying Fractions to Simplest Form . . . . . . . . . . . . . . . . . . . . .
Math 405, Lesson 4 Math 405, Lesson 6 Math 407, Lesson 14 Math 406, Lesson 6
36 37 38 39
39. 40. 41. 42.
Converting Fractions and Mixed Numbers to Decimals . . . . . . . . . Converting Decimals to Fractions and Mixed Numbers . . . . . . . . . Changing Fractions to Decimals on a Calculator . . . . . . . . . . . . . . . Using Decimal Equivalents to Compare Fractions . . . . . . . . . . . . .
Math 602, Lesson 6 Math 603, Lesson 6 Math 605, Lesson 7 Math 607, Lesson 3
41 42 43 44
43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55.
Ratios Compare Amounts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ratios Compare Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . Three Ways to Write Ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Equivalent Ratios: Enlarging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Equivalent Ratios: Simplest Form . . . . . . . . . . . . . . . . . . . . . . . . . . Writing Ratios as Percents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Proportions: Finding the Missing Term . . . . . . . . . . . . . . . . . . . . . . Using Cross Products to Solve and Check Proportions . . . . . . . . . . Setting Up Proportions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Using Proportions to Convert U.S. Measures . . . . . . . . . . . . . . . . . Solving Percents Using Proportions . . . . . . . . . . . . . . . . . . . . . . . . . Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Using Proportions to Convert Measures Between U.S. and Metric Measure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Converting Between Kilograms and Pounds . . . . . . . . . . . . . . . . . . Converting Between Inches and Centimeters . . . . . . . . . . . . . . . . . . Converting Between Meters and Yards . . . . . . . . . . . . . . . . . . . . . .
Math 406, Lesson 3 Math 406, Lesson 7 Math 505, Lesson 9 Math 506, Lesson 6 Math 506, Lesson 9 Math 604, Lesson 2 Math 506, Lesson 12 Math 507, Lesson 1 Math 507, Lesson 11 Math 602, Lesson 8 Math 607, Lesson 12 Math 607, Lesson 18
45 46 47 48 49 50 51 52 54 55 56 58
Simplifying
Decimals
Ratio and Proportion
56. 57. 58.
Math 703, Lesson 15 Math 705, Lesson 15 Math 706, Lesson 15 Math 707, Lesson 15
59 61 62 63
Work Sheet 19
Math 503, Lesson 1
Subtracting a Mixed Number From a Whole Number
8 3 – 25
You can not subtract a fraction from nothing.
7
5
3 I cannot subtract 5 from nothing. I must borrow from 8.
85
Cross out 8 and write 7. You are subtracting fifths,
– 25 3
5
so change the 1 you borrowed to 5 and write it above the fraction.
7
5
85
– 25 3 2
55
Now you can subtract.
Borrow from the whole number before you subtract. 3
1. a. – 2
2. a.
3. a.
8
– 4
8
4 5
7 8
7
– 3 12
5
b. – 3
b.
b.
–
c. – 1
7 8
2
c.
5 1 12
6
6
c.
1
– 3 10
19
6
– 4
7
5 9
2 7
7
– 2 10
7
d. – 3
d.
d.
9
3 5
5
– 7 12
5
– 2
5 8
Work Sheet 20
Math 503, Lesson 12
Borrowing to Subtract Fractions
When the top fraction is smaller than the bottom fraction in a subtraction problem, you must borrow. 4
2
7 4 2
You cannot subtract 5 from 5 . Borrow 1 from 5. Change the 1 to
5 5
and add it to
The 5 becomes a 4 and the
2 5
2 5.
becomes
2 5
5
–2
7 5.
2
5
+
5 5
=
4 5
3 5
Subtract. Borrow as needed. Give answers in simplest form. 1
7 12 11
1. a. – 3 12
b.
1
75 3
2. a. – 2 5
b.
5
14 16 7
3. a. – 4 16
8
4. a. – 6
2 7 5 7
b.
12
3 8
17
1 8
7
–6
–8
–5
4
1 7
3 8
8
c. – 7
1 6
1 4
3
3 8
7 8
c.
3 4
c. –
3
b.
–3
2 7
5 6
7 8
1
d.
–
7 12
7
7
– 8 16
c. – 6 12
Note: If student doesn’t know how to simplify assign worksheets 36–38.
20
3 4
7
d.
d.
7 12 11
– 6 12
d.
4
1 9
4
1 9
–1
5
9 16
12 4
–
7 9
5 9
7 5
Work Sheet 31
Math 603, Lesson 2
Multiplying Mixed Numbers, Whole Numbers, and Fractions With More Than Two Factors
When multiplying mixed numbers, whole numbers, and fractions, the first step is to rewrite the problem, changing mixed and whole numbers to improper fractions. You can cancel any denominator with any numerator. Then multiply all the numerators together and all the denominators together. If the answer is an improper fraction, change it back to a mixed number.
1 37
There are no mixed numbers or whole numbers. Pairs that cancel are 5 and 15, 4 and 8, and 7 and 7. 1
5 8 2
1
1
7
4
3
1
1. a.
7 12
2
6 7
1
9 10
× 13 ×
2
2. a. 1 9 × 2 2 ×
3. a. 16 ×
4. a.
3 8
11
22 7
1
× 15 × 7 = 6
Solve. Cancel if possible.
1 21
2
1
=
=
× 12 =
× 13 × 3 =
×
2 3
×
1 32 1
2
7
Change all mixed numbers to improper fractions. Pairs that cancel are 22 and 2, and 7 and 7.
22
1
1
1
1
b. 2 × 2 2 × 2 4 =
1
b. 2 4 ×
7 20
b. 1 3 × 3
2
3 4
1
2
2
× 63 =
2
× 23 =
b. 3 3 × 1 5 × 12 =
Note: If student doesn’t know how to simplify assign worksheets 36–38.
32
1
× 3 × 2 = 3 = 73 c.
1 2
×
1 4
×
2 3
=
c.
2 9
×
1 5
×
5 8
=
c.
1 3
×
3 4
×
1 2
=
c.
2 3
×
1 8
×
1 4
=
Work Sheet 52
Math 602, Lesson 8
Using Proportions to Convert U.S. Measures
Proportions can be helpful in converting measures. They help us keep track of when we should multiply or divide.
60 feet is how many inches? First write the conversion ratio.
1 foot 12 inches
Then write the second ratio, keeping each unit (feet and inches) on the same level as the first ratio. The second ratio uses n for inches since we need to
1 foot 12 inches
=
60 feet n inches
find inches.
Solve. 12 x 60 ÷ 1 = 720. 60 feet is 720 inches.
336 hours is how many days? 1 x 336 ÷ 24 = 14.
1 day 24 hours
=
n days 336 hours
336 hours is 14 days. Often when you need to convert measures, you will know whether to divide or multiply. But if your answer does not seem sensible or if you get confused, setting up a proportion helps you stay on track. Proportions are especially helpful when you do more complicated conversions.
Set up a proportion to find each answer. 1. a. 180 in =
Set up a proportion.
yd
b. 4 yd =
lb
b. 12 gal =
ft
Solve cross products.
2. a. 112 oz =
Set up a proportion.
Solve cross products.
55
qt
