COMPARING FRACTIONSLesson 23 Section 2 The ratio of two fractions We saw in Lesson 20 that when two fractions have equal denominators, then the larger the numerator, the larger the fraction.
In other words: Fractions with equal denominators are in the same ratio
We now ask: 



Why? Because 16 and 15 are the numerators we would get if we
as
The numerators 16 and 15 were obtained by "crossmultiplying."
For, 16 is larger than 15.
Answer. On crossmultiplying,
as 36 is to 35. Now, 36 is larger than 35. Therefore,
Note: We must begin multiplying with the numerator on the left: 4 × 9.
Answer. On crossmultiplying,
as 2 is to 4. That is,
Example 4. What ratio has 2½ to 3?
whole number 3 as a numerator, and crossmultiply:
2½ is five sixths of 6.
In general: To express the ratio of a fraction to a whole number,
For an application of this, see Lesson 26.
miles does 2 inches represent? Solution. Proportionally,
Therefore: 3 is to 8 as 60 miles is to ? miles. Since 20 × 3 = 60, then 20 × 8 = 160 miles. The theorem of the same multiple. Or, inversely,
8 is two and two thirds times 3. (Lesson 18, Example 5.) Therefore:
More than or less than ½ 



than half of 8.
of 20.
less than half of 25 (which is 12½). (Lesson 15, Question 7.) We could make these comparisons for any ratio of the terms. For example, we could know that
Because 5 is a third of 15, but 6 is less than a third of 21 (which is 7). Example 8 Which is the largest number?
Answer. First, let us examine the list to see if there are numbers less than ½ or greater than ½. We may eliminate any numbers less than (or equal to) ½.
Since the numerators are the same (Lesson 20, Question 11), we
Example 9. Which is the largest number?
are greater. Which is larger, then,
On crossmultiplying, we have 5 × 11 versus 9 × 6. And 55 is greater than 54. Therefore,
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