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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