COMPARING FRACTIONS

PROBLEMS 2

Do the problem yourself first!

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) 38 is to 58 as  3 is to 5. 3.  b) 14 is to 34 as  1 is to 3. 3.  c) 49 is to 89 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) 23 is to 34 as  8 is to 9. 2.  b) 58 is to 79 as  45 is to 56. 2.  c) 16 is to 12 as  1 is to 3. 2.  d) 18 is to 12 as  1 is to 4. 2.  e) 15 is to 1 25 as  5 is to 1. 2.  f) 13 is to 1 12 as  4 is to 1.

3.  In the previous problem, why does cross-multiplying give the correct

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) 34 to 2? 34 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 34 to 3? Eleven twelfths. f) 2¼ to 3? Three quarters.
 5.  a)  Which is larger, 56 or 67 ? 67

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) 34 or 57 ? 34 6.   b) 38 or 4 11 ? 3  8 6.   c) 7 10 or 57 ? 57 6.   d) 23 or 7 11 ? 23 6.   e) 49 or 37 ? 49 6.   f) 7 12 or 35 ? 35

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.

 58 5 12 7 16 9 16 9 20 1324 1430 25 35 49 59 7 15 8 15 1325
 5 12 7 16 9 20 1430 25 49 7 15

9.  Compare each number to ½, and decide which number is larger.

 8.   a) 58 or 7 14 ? 58 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) 1430 or 2650 ? 2650 f) 499 1000 or 3160 ? 3160

10.  Which is the largest number?

 9.   a) 12 45 5 11 7 10 45
 b) 38 8 15 9 15 1021 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
 e) 12 13 35 38 6 11 35

Continue on to the next Lesson.

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