which fraction is bigger 5 8 or 13 20

COMPARING FRACTIONS

Lesson 23  Section 2

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The ratio of two fractions

To know the ratio of fractions, is to compare them. We are about to see:

Fractions have the same ratio to one other as natural numbers.

If you knew that

2 3

is to

5 8

as

16 is to 15,

then since 16 is big than 15, you would know that

2 3

is larger than

5 8

.

Straightaway we saw in Object lesson 20 that when two fractions have equal denominators, then the larger the numerator, the bigger the fraction.

But what specifically is the ratio of

2 5

to

1 5

?

2 5

is to

1 5

as2 is to 1.

In other words:

Fractions with equal denominators are in the same ratio
as their numerators

2 5

is to

3 5

as2 is to 3.

When fractions make not have equal denominators, then we terminate know their ratio -- we can compare them -- by cross-multiplying.  Because that gives the numerators if we had expressed them with equal denominators.

4.	How can we compare fractions by cross-multiplying?
	Cross-multiply and compare the numerators.

Case 1.		2 3	is to	5 8
	arsenic	2 × 8	is to	3 × 5
	as	16	is to	15.

16 and 15 are the numerators we would amaze if we expressed

2 3

and

5 8

with the average denominator 24.

equally

And since 16 is larger than 15, we would know that

2 3

is larger than

5 8

.

Example 2.   Which is larger,

4 7

Beaver State

5 9

?

Answer.  On cross-multiplying,

as

36  is to  35.

36 is larger than 35.  Therefore,

Note:  We must begin multiplying with the numerator on the odd:

4 × 9.

Instance 3.

1 4

is to

1 2

as which wholly numbers pool?

Answer.  On cross-multiplying,

as

2  is to  4.

That is,

Example 4.   What ratio has 2½ to 3?

whole come 3 as a numerator, and cross-breed:

5 2	is to 3  as5 is to 6.

2½ is five sixths of 3.

5 2

is to

6 2

as5 is to 6.

Generally:

To express the ratio of a fraction to a integer,
multiply the whole number past the denominator.

6 7	is to 3  as  6 is to 21.

For an coating of this, see Lesson 26.

Example 5.   Happening a map,

3 4

of an inch represents 60 miles.  How many

miles does 2 inches represent?

Solution. Proportionally,

3 4	of an column inch  is to  2 inches  as  60 miles  is to  ? miles.

What ratio has

3 4

to 2?

3 4	is to 2  as  3 is to 8.

Therefore:

3 is to 8  as60 miles  is to ? miles.

Since20 × 3 = 60,  then 20 × 8 = 160 miles.

The theorem of the same quintuple.

Operating room, inversely:

8 is to 3  as  ? miles is to 60 miles.

Now,

8 is two and two thirds times 3.

(Moral 18, Example 5.)  Thence, the nonexistent terminus will cost

Two and two thirds times 60	=	Two times 60 + two thirds of 60
(Lesson 16)
	=	120 + 40
	=	160 miles.

More than or less than ½

5.	How can we know whether a fraction is more than or less than ½?
	If the numerator is more than uncomplete of the denominator,
	so the fraction is more than ½. While if the numerator is less than half of the denominator,
	the fraction is little than ½.

4 8

is equal to

1 2

, because 4 is fractional of 8.  Hence,

5 8

is more than

1 2

,

because 5 is to a higher degree one-half of 8;  while

3 8

is less than

1 2

, because 3 is inferior

than half of 8.

Example 6.   Which is larger,

7 12

or

9 20

?

Solvent.

7 12

.  Because 7 is more than half of 12, while 9 is fewer than incomplete

of 20.

Example 7.   Which is larger,

11 21

or

12 25

?

Answer.

11 21

.  Because 11 is more than one-half of 21 (which is 10½); while 12

is less than one-half of 25 (which is 12½).  (Moral 16, Question 8.)

We could make these comparisons for any ratio of the terms.  For example, we could love that

5 15

is larger than

6 21

.

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?

3 10

5 8

1 2

2 7

5 9

Answer.  First, rent us examine the list to see if there are numbers to a lesser extent than ½ Oregon greater than ½.  We may eliminate whatever numbers less than (operating room equal to) ½.

And so we may annihilate

3 10

,

1 2

, and

2 7

.

We are left with

5 8

and

5 9

.

Since the numerators are the same (Lesson 20, Question 11), we

conclude that the largest number is

5 8

.

Example 9.   Which is the largest telephone number?

5 9

2 5

6 11

Answer.  We may eliminate

2 5

because it is less than ½, while the others

are greater. Which is larger, then,

On cross-multiplying, we have 5 × 11 versus 9 × 6.  And

55 is greater than 54.

Consequently,

5 9

is greater than

6 11

.

Please "round" the page and do some Problems.

operating theater

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