Question

Which of the following ratios is not equal to $8:3$ in its simplest form?
A. $16:6$
B. $104:36$
C. $56:21$
D. $896:336$

Answer 1

Hint: For solving this question, we can simplify every option and check if their simplest form is equal to $8:3$ or not. Simplifying a ratio is very similar to simplification process of a fraction. We should write the factors of both the numbers and cancel out the common terms in them. When we reach a point where there is no common factor other than 1, that is the simplest form.

Complete answer:
Let’s start by listing out all four options and solve each one of them.
A. $16:6$
Now let’s simplify the ratio by cancelling out common factors.
$16 = 8 \times 2$
$6 = 3 \times 2$
2 is the common factor.
 $16:6 = 8:3$
Hence, $16:6$ is equal to $8:3$ in its simplest form.

B. $104:36$
Now let’s simplify the ratio by cancelling out common factors.
$104 = 26 \times 4$
$36 = 9 \times 4$
4 is the common factor.
 $104:36 = 26:9$
Hence, $104:36$ is not equal to $8:3$ in its simplest form.

C. $56:21$
Now let’s simplify the ratio by cancelling out common factors.
\[56 = 8 \times 7\]
$21 = 3 \times 7$
7 is the common factor.
$56:21 = 8:3$
Hence $56:21$ is equal to $8:3$ in its simplest form.

D. $896:336$
Now let’s simplify the ratio by cancelling out common factors.
$896 = 112 \times 8$
\[336 = 3 \times 112\]
112 is the common factor.
$896:336 = 8:3$
Hence $896:336$ is equal to $8:3$ in its simplest form.

Therefore, the correct option is B

Note: There are high chances that one can make a calculation mistake while writing down common factors in the ratio. Even if a minute mistake is committed, then the entire answer will be wrong. One should avoid any misconceptions while solving this question. A ratio is not a fraction, hence we shouldn’t convert them into decimals.