Solution: 46/66 as a percent is 69.697%
Methods
Method 1 – Converting 46/66 Into a Percentage:
First, let’s go over what a fraction represents. The number above the line is called the numerator, while the number below the line is called the denominator. The fraction shows how many portions of the number there are, in relation to how many would make up the whole. For instance, in the fraction 46/66, we could say that the value is 46 portions, out of a possible 66 portions to make up the whole.
For percentages, the difference is that we want to know how many portions there are if there are 100 portions possible. “Percent” means “per hundred”. For example, if we look at the percentage 25%, that means we have 25 portions of the possible 100 portions. Re-writing this in fraction form, we see 25/100.
The first step in converting a fraction to a percentage is to adjust the fraction so that the denominator is 100. To do this, you first divide 100 by the denominator:
100
66
=
1.515
\frac{100}{66} = 1.515
66 100 = 1.515
We can then adjust the whole fraction using this number, like so:
46
∗
1.515
66
∗
1.515
=
69.697
100
\frac{46*1.515}{66*1.515} = \frac{69.697}{100}
66 ∗ 1.515 46 ∗ 1.515 = 100 69.697
Reading this as a fraction, we can say that we have 69.697 portions of a possible 100 portions.
Re-writing this as a percentage, we can see that 46/66 as a percentage is 69.697%
Method 2 – Converting 46/66 Into a Percentage Using Decimals:
Another way we can convert 46/66 into a percentage is to first convert 46/66 into a decimal. We can do this by simply dividing the numerator by the denominator:
46
66
=
0.697
\frac{46}{66} = 0.697
66 46 = 0.697
Once we have the answer, we can multiply the new decimal by 100 to get the percentage:
0.697 × 100 = 69.697
As you can see, we get the same answer as the first method and find that 46/66 as a percentage is 69.697%.
Now you know of two different ways to convert 46/66 into a percentage! While converting using a decimal takes fewer steps, you first need to master converting fractions into decimals. Try out both methods and see which one works best for you!
Practice more percentage problems!
Practice makes perfect so why not check out some of other problems where you can convert a fraction to a percentage?
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