Question

Find answers to the following. Write and indicate how you solved them.
(a) Is 5/4 equal to 4/5 ?
(b) Is 9/16 equal to 5/9 ?
(c) Is 4/5 equal to 16/20?
(d) Is 1/15 equal to 4/30?

Answer 1

Answer:

4/5  = 16/20

Step-by-step explanation:

a/b = c/d

if a * d = b * c

5/4 = 4/5

if 5 * 5  = 4 * 4

if 25 = 16

but 25 ≠ 16

=>  5/4  ≠ 4/5

9/16 = 5/9

if 9 * 9  = 5 * 16

if 81 = 80

but 81 ≠ 80

=>  9/16  ≠ 5/9

4/5 = 16/20

if 4 * 20  = 5 * 16

if 80 = 80

=>  4/5  = 16/20

1/15 = 4/30

if 1 * 30  = 4 * 15

if 30 = 60

but 30 ≠ 60

=>  1/15  ≠ 4/30

Answer 2

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

TO CHECK

(a) Is 5/4 equal to 4/5

(b) Is 9/16 equal to 5/9

(c) Is 4/5 equal to 16/20

(d) Is 1/15 equal to 4/30

PROCESS TO SOLVE

All the given fractions are unlike fractions

Solve using LCM method

STEP : 1

First write the denominator of both fractions

STEP : 2

Take LCM of the denominators

STEP : 3

Convert the given fractions into like fractions

STEP : 4

Compare the reduced fraction as below :

1. If Numerator of 1st fraction > Numerator of 2nd fraction then 1st fraction is greater among the two

2. If Numerator of 1st fraction < Numerator of 2nd fraction then 2nd fraction is greater among the two

3. If Numerator of 1st fraction = Numerator of 1st fraction then two fractions are equal

CALCULATION

$\displaystyle \sf{ (a) \: Given \: fractions \: are \: \: \frac{5}{4} \: \: and \: \: \frac{4}{5} \: \: }$

Denominator of the two fractions are 4 & 5

LCM of the denominators = 20

$\displaystyle \sf{ \frac{5}{4} \: = \frac{25}{20} \: \: }$

$\displaystyle \sf{ \frac{4}{5} \: = \frac{16}{20} \: \: }$

Now Numerator of 1st fraction > Numerator of 2nd fraction then 1st fraction is greater among the two

$\displaystyle \sf{ \therefore \: \: \frac{5}{4} \: \: > \: \: \frac{4}{5} \: \: }$

$\displaystyle \sf{ (b) \: Given \: fractions \: are \: \: \frac{9}{16} \: \: and \: \: \frac{5}{9} \: \: }$

Denominator of the two fractions are 16 & 9

LCM of the denominators = 114

$\displaystyle \sf{ \frac{9}{16} \: = \frac{81}{114} \: \: }$

$\displaystyle \sf{ \frac{5}{9} \: = \frac{80}{114} \: \: }$

Now Numerator of 1st fraction > Numerator of 2nd fraction then 1st fraction is greater among the two

$\displaystyle \sf{ \therefore \: \: \frac{9}{16} \: \: > \: \: \frac{5}{9} \: \: }$

$\displaystyle \sf{ (c) \: Given \: fractions \: are \: \: \frac{4}{5} \: \: and \: \: \frac{16}{20} \: \: }$

Denominator of the two fractions are 5 & 20

LCM of the denominators = 20

$\displaystyle \sf{ \frac{4}{5} \: = \frac{16}{20} \: \: }$

$\displaystyle \sf{ \frac{16}{20} \: = \frac{16}{20} \: \: }$

Now Numerator of 1st fraction = Numerator of 2nd fraction then two fractions are equal

$\displaystyle \sf{ \therefore \: \: \frac{4}{5} \: \: = \: \: \frac{16}{20} \: \: }$

$\displaystyle \sf{ (d) \: Given \: fractions \: are \: \: \frac{1}{15} \: \: and \: \: \frac{4}{30} \: \: }$

Denominator of the two fractions are 15 & 30

LCM of the denominators = 30

$\displaystyle \sf{ \frac{1}{15} \: = \frac{2}{30} \: \: }$

$\displaystyle \sf{ \frac{4}{30} \: = \frac{4}{30} \: \: }$

Now Numerator of 1st fraction < Numerator of 2nd fraction then 2nd fraction is greater among the two

$\displaystyle \sf{ \therefore \: \: \frac{1}{15} \: \: < \: \: \frac{4}{30} \: \: }$

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