Question

arrange the following rational nu
numbers in ascending order:
(i) 3/4, 5/8, 11/16, 21/32
(ii) -2/5, 7/-10, -8/15, 17/-30
(iii) 5/-12, -2/3, -7/9, 11/-18
(iv) -4/7, 13/-28, 9/14, 23/42​

Answer 1

Answer:

안녕하세요

Step-by-step explanation:

Ans1)21/32,11/16,5/8,3/4

Ans2) 17/-30,-8/15,7/-10/-2/5

Ans3)11/-18,-7/9,5/-12,-2/3

Ans4)13/-28/-4/7,9/14,24/42

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Answer 2

Given:  

A set of fractions where each set has to be arranged in ascending order.

(i)3/4, 5/8, 11/16, 21/32

(ii) -2/5, 7/-10, -8/15, 17/-30

(iii) 5/-12, -2/3, -7/9, 11/-18

(iv) -4/7, 13/-28, 9/14, 23/42

To Find:

The ascending order of each set.

Solution:

The given problem can be solved by using mathematical operations on fractions.

(i) 3/4, 5/8, 11/16, 21/32

To compare the fractions, the denominators must be the same, Hence, make the denominators equal.

= >  3/4, 5/8, 11/16, 21/32,

=> $\frac{3*8}{4*8}$, $\frac{5*4}{8*4}$, $\frac{11*2}{16*2}$,$\frac{21}{32}$,

=> 24/32, 20/32, 22/32, 21/32.

• The fractions can now be compared, So the ascending order of the fractions is:

=> Ascending order = 20/32 < 21/32 < 22/32 < 24/32 (OR) 5/8 < 21/32 < 11/16 < 3/4.  

(ii) -2/5, -7/10, -8/15, -17/30  

• To compare the fractions, the denominators must be the same, Hence, make the denominators equal.

=>  -2/5, -7/10, -8/15, -17/30,

=>$\frac{-2*6}{5*6}$,$\frac{-7*3}{10*3}$, $\frac{-8*3}{15*2}$,$\frac{-17}{30}$,

=> -12/30, -21/30, -16/30, -17/32.

• The fractions can now be compared, So the ascending order of the fractions is:

=> Ascending order = -21/30 < -17/30 < -16/30 < -12/30 (OR) -7/10 < -17/30 < -8/15 < -2/5.

(iii) 5/-12, -2/3, -7/9, 11/-18

• To compare the fractions, the denominators must be the same, Hence, make the denominators equal.

= >  -5/12, -2/3, -7/9, -11/18,

= > $\frac{-5*3}{12*3}$, $\frac{-2*12}{3*12}$,$\frac{-7*4}{9*4}$,$\frac{-11*2}{18*2}$,

= > -30/36, -24/36, -28/36,-22/36.

• The fractions can now be compared, So the ascending order of the fractions is:

= > Ascending order = -30/36 < -28/36 < -24/32 < -22/36 (OR) -5/12 < -7/9 < -2/3 < -11/18.  

 

(iv) -4/7, 13/-28, 9/14, 23/42

• In order to compare the fractions, the denominators must be the same, Hence, make the denominators equal.

= >  -4/7, 13/-28, 9/14, 23/42,

= > -$\frac{-4*12}{7*12}$ ,$\frac{-13*3}{28*3}$, $\frac{9*6}{14*6}$,$\frac{23*2}{42*2}$,

= > -48/84, -39/84, 54/84, 46/84.

• The fractions can now be compared, So the ascending order of the fractions is:

= > Ascending order = -48/84 < -39/84 < 46/84 < 54/84 (OR) -4/7 < -13/28 < 9/14 < 23/42.