Write the given rates as fractions and simplify them as much as possible. Then, compare the simplified fractions.
B
Practice makes perfect
We want to find out which of the following ratios is not equivalent to 72:18.
&A.36:9 & &B.18:6
&C.4:1 & &D.288:72
One way to know if two ratios or rates are equivalent is by writing them as fractions. Let's do so!
Writing Rates as Fractions
To write 72:18 as a fraction, we can put the first number in the numerator and the second number in the denominator.
72: 18 ⇒ 72/18
Now, let's repeat these step for each of the other rates.
&A. 36: 9 & &B. 18: 6
&C. 4: 1 & &D. 288: 72
&&⇓ &
&A.36/9 & &B.18/6 [1em]
&C.4/1 & &D.288/72
To check if the ratios are equivalent, we can compare these fractions in their simplest form. Let's see if the given rates are equivalent!
We can repeat these steps for each of the remaining ratios.
Ratio
Simplification
Result
36/9
36Ă· 9/9Ă· 9
4/1
18/6
18Ă· 6/6Ă· 6
3/1
4/1
None needed
4/1
288/72
288Ă· 72/72Ă· 72
4/1
Let's now replace the fractions with their simplest forms.
&A.36/9 & &B.18/6 [1em]
&C.4/1 & &D.288/72
&&⇓ &
&A. 4/1 & &B. 3/1 [1em]
&C. 4/1 & &D. 4/1
Looking at these fractions, we see that there is only one that is different from the simplified first fraction, 41. It is fraction B. Therefore, B is the only rate that is not equivalent to 72:18.
