1

Problem

Identify the small fraction number given below:
\$(47)/9, (17)/(33), (16)/5, (33)/(45)\$.

2

Step

The given fraction numbers are

\$(47)/9, (17)/(33), (16)/5, (33)/(45)\$

3

Clue

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

4

Step

The least common multiple of 9, 33, 5 and 45 is:

1485

5

Step

For \$(47)/9\$ multiply the numerator and denominator by 165:

\$ (47 \times 165)/(9 \times 165) = (7755)/(1485) \$

6

Step

For \$(17)/(33)\$ multiply both the numerator and denominator by 45:

\$ (17 \times 45)/(33 \times 45) = (765)/(1485) \$

7

Step

For \$(16)/5 \$ multiply both the numerator and denominator by 297:

\$ (16 \times 297)/(5 \times 297) = (4752)/(1485) \$

8

Step

For \$(33)/(45)\$ multiply both the numerator and denominator by 33:

\$ (33 \times 33)/(45 \times 33) = (1089)/(1485) \$

9

Hint

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

10

Clue

Among the fractions \$(7755)/(1485), (765)/(1485), (4752)/(1485)\$, and \$(1089)/(1485)\$, \$(765)/(1485)\$ has the smallest numerator, making it the smallest fraction.

11

Step

You can also convert them to decimals \$(7755)/(1485)\$ is approximately:

5.222222222

12

Step

And also \$ (765)/(1485) \$ is approximately:

0.51515151

13

Step

And also \$ (4752)/(1485) \$ is approximately:

3.2

14

Step

And also \$(1089)/(1485) \$ is approximately:

0.7333333333

15

Step

So, the smallest fraction among \$(47)/9, (17)/(33), (16)/5\$, and \$ (33)/(45)\$ is:

\$ (765)/(1485)\$

16

Solution

Therefore, the smallest fraction number is \$ (17)/(33)\$.

17

Sumup

Please summarize steps

Choices

18

Choice-A

This fraction is larger than \$(17)/(33)\$ because its decimal equivalent is 3.2, which is greater than 0.515

Wrong \$(16)/5\$

19

Choice-B

This is the correct answer because its decimal equivalent is the smallest at 0.515

Correct \$(17)/(33)\$

20

Choice-C

This fraction equals \$(11)/(15)\$, and its decimal equivalent is 0.733, which is larger than \$(17)/(33)\$

Wrong \$(33)/(45)\$

21

Choice-D

This is incorrect because only \$(17)/(33)\$ is the smallest

Wrong All the above

22

Step

Option

B

23

Sumup

Please summarize choices