Which is the smallest of the following?

a) #4/10#

b) #381/1000#

c) #39/100#

d) #37/10#

e) #379/1000#

2 Answers
SCooke
Nov 17, 2017

e) #379/1000#

Explanation:

There are two ways to compare different fractional values. The first is to put each of them into a form with the same denominator. You can then simply compare the numerators. That may not always be easy.

If the denominators do not have an easily determined common multiple, then you can simply do the indicated division of the denominator into the numerator and then compare the results.

In this case, they are all multiples of 10, so we will change all of the denominators to be the same by multiplying the fractions by the proper multiple of ten. In this case, making all of the denominators 1000.
a) #4/10 = 4/10 xx 100/100 = 400/1000#

b) #381/1000# OK as it is

c) #39/100 = 39/100 xx 10/10 = 390/1000#

d) #37/10 = 37/10 xx 100/100 = 3700/1000#

e) #379/1000# OK as it is

NOW we can compare the numerators equally and can see that
e) #379/1000#
is the smallest fraction (smallest numerator over the same denominator).

George C.
Nov 17, 2017

e) #379/1000#

Explanation:

SInce all of the denominators are powers of #10#, we can perform the divisions by shifting to get decimal results.

Each power of #10# that is divided by is equivalent to shifting the number one decimal place to the right.

So we can calculate the decimal forms:

a) #4/10 = 0.4#

b) #381/1000 = 0.381#

c) #39/100 = 0.39#

d) #37/10 = 3.7#

e) #379/1000 = 0.379#

We can pad these all out to three decimal places by adding trailing #0#'s as required to get:

a) #0.400#

b) #0.381#

c) #0.390#

d) #3.700#

e) #0.379#

The smallest of these is e) #0.379 = 379/1000#

Related questions
Impact of this question
516 views around the world
You can reuse this answer
Creative Commons License