COMPARING FRACTIONS
PROBLEMS 2
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1. Same denominator. Each pair of fractions is in the same ratio as
1. which whole numbers? Express that ratio with the lowest terms.
| 1. a) |
3
8 |
is to |
5
8 |
as 3 is to 5. |
|
3. b) |
1
4 |
is to |
3
4 |
as 1 is to 3. |
| |
| 3. c) |
4
9 |
is to |
8
9 |
as 1 is to 2. |
|
3. d) |
6
11 |
is to |
8
11 |
as 3 is to 4. |
2. Cross-multiplying. Each pair of fractions is in the same ratio as
2. which whole numbers? Express that ratio with the lowest terms.
| 2. a) |
2
3 |
is to |
3
4 |
as 8 is to 9. |
|
2. b) |
5
8 |
is to |
7
9 |
as 45 is to 56. |
| |
| 2. c) |
1
6 |
is to |
1
2 |
as 1 is to 3. |
|
2. d) |
1
8 |
is to |
1
2 |
as 1 is to 4. |
| |
| 2. e) |
1
5 |
is to |
1
25 |
as 5 is to 1. |
|
2. f) |
1
3 |
is to |
1
12 |
as 4 is to 1. |
3. In the previous problem, why does cross-multiplying give the correct
5. answer?
Cross-multiplying gives the numerators of the common denominator.
4. What ratio has
| 4. a) |
2 to ½? |
2 is four times ½. |
| 4. b) |
3
4 |
to 2? |
|
3
4 |
is three eighths of 2. |
| 6. c) |
1¼ to 2? |
1¼ is five eighths of 2. |
| 4. d) |
3½ to 4? |
3½ is seven eighths of 4. |
| 6. e) 2 |
3
4 |
to 3? |
Eleven twelfths. |
|
f) |
2¼ to 3? |
Three quarters. |
| 5. a) Which is larger, |
5
6 |
or |
6
7 |
? |
|
6
7 |
6. b) Why does cross-multiplying give the right answer?
Cross-multiplying gives the numerators of the common denominator.
6. Which is larger,
| 6. a) |
3
4 |
or |
5
7 |
? |
3
4 |
|
6. b) |
3
8 |
or |
4
11 |
? |
3
8 |
|
6. c) |
7
10 |
or |
5
7 |
? |
5
7 |
| |
| 6. d) |
2
3 |
or |
7
11 |
? |
2
3 |
|
6. e) |
4
9 |
or |
3
7 |
? |
4
9 |
|
6. f) |
7
12 |
or |
3
5 |
? |
3
5 |
7. On a map, ½ inch represents 50 miles. How many miles does 2¼
10. inches represent? (Compare Example 5.)
225 miles.
8. More than or less than ½. Pick out those numbers which are less
10. than ½.
| |
5
8 |
|
5
12 |
|
7
16 |
|
9
16 |
|
9
20 |
|
13
24 |
|
14
30 |
|
2
5 |
|
3
5 |
|
4
9 |
|
5
9 |
|
7
15 |
|
8
15 |
|
13
25 |
5
12 |
|
7
16 |
|
9
20 |
|
14
30 |
|
2
5 |
|
4
9 |
|
7
15 |
9. Compare each number to ½, and decide which number is larger.
| 8. a) |
5
8 |
or |
7
14 |
? |
5
8 |
|
b) |
7
12 |
or |
9
20 |
? |
7
12 |
|
c) |
7
16 |
or |
6
11 |
? |
6
11 |
| 8. d) |
51
100 |
or |
99
200 |
? |
51
100 |
|
e) |
14
30 |
or |
26
50 |
? |
26
50 |
|
f) |
499
1000 |
or |
31
60 |
? |
31
60 |
10. Which is the largest number?
| b) |
3
8 |
|
8
15 |
|
9
15 |
|
10
21 |
|
9
15 |
| |
| c) |
7
11 |
|
7
12 |
|
8
17 |
|
9
20 |
|
7
11 |
| d) |
7
20 |
|
7
16 |
|
8
15 |
|
8
14 |
|
9
14 |
|
9
14 |
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