1

Problem

Identify the small fraction number given below:
\$(23)/(19), (17)/(21), (31)/(15)\$.

2

Step

The given fraction numbers are

\$(23)/(19), (17)/(21), (31)/(15)\$

3

Hint

First, we can convert fractions to have a common denominator.

4

Step

The least common multiple of 19, 21 and 15 is:

3995

5

Step

For \$ (23)/(19) \$ multiply both the numerator and denominator by 210

\$ (23 \times 210) / (19 \times 210) = (4830) / (3995) \$

6

Step

For \$ (17)/(21) \$ multiply both the numerator and denominator by 190

\$ (17 \times 190) / (21 \times 190) = (3230) / (3995) \$

7

Step

For \$ (31)/(15) \$ multiply both the numerator and denominator by 267

\$ (31 \times 267) / (15 \times 267) = (8277) / (3995) \$

8

Hint

The fractions have the same denominator, so you can compare the numerators. The fraction with the larger numerator is the smaller fraction.

9

Clue

Among the fractions \$(4830)/(3995), (3230)/(3995)\$, and \$(8277)/(3995)\$, \$(3230)/(3995)\$ has the smallest numerator, making it the smallest fraction.

10

Step

You can also convert them to decimals \$ (4830)/(3995)\$ is approximately

1.209

11

Step

And also \$(3230)/(3995)\$ is approximately

0.808

12

Step

And also \$(8277)/(3995) \$ is approximately

2.071

13

Step

So, the smallest fraction among \$ (23)/(19), (17)/(21)\$, and \$(31)/(15)\$ is

\$ (3230)/(3995)\$

14

Solution

Therefore, the smallest fraction number is \$(17)/(21)\$.

15

Sumup

Please summarize steps

Choices

16

Choice-A

This is not the smallest fraction; it has a value of approximately 1.21

Wrong \$(23)/(19)\$

17

Choice-B

This is not the smallest fraction; it has a value of approximately 2.07

Wrong \$(31)/(15)\$

18

Choice-C

This is the smallest fraction; it has a value of approximately 0.80

Correct \$(17)/(21)\$

19

Choice-D

This is incorrect because the smallest fraction is \$(17)/(21)\$

Wrong All the above

20

Step

Option

C

21

Sumup

Please summarize choices