Question

Sam's class voted on whether or not to do science fair projects in groups. Out of 20 votes, 14 were in favor of working in groups. What percentage of the votes were in favor of working in groups

Answer 1

70% is the answer

Explanation:

The formula to calculate "Blank Is What Percent Of Blank?" is displayed below:

(1stBlank*100)/2ndBlank= (14 × 100) ÷ 20 = %70

Answer 2

70% of the class were in favor of working on groups.

Explanation:

The ratio/fraction:
`(14)/(20)` represents the total amount of students who voted for working in groups versus the total amount of votes. In order to find the percentage, we shall further convert this fraction into a percent.

There are 2 ways to approach this:

1) Common Denominator Method

Let's take an example:
`(87)/(100)`

This fraction is basically 87% because we know that percents are always out of 100. Since we have a denominator of 100, we know it is 87%.

But if the denominator was 50, how do we get it to 100?

`(87)/(50)` is the same as
`(87*2)/(50*2)` which gives us
`(142)/(100)`. So it is 147%.

But, this method ONLY works with a denominator which is a factor of 100.

Now, with your question:

`(14)/(20)` is the same as
`(14*5)/(20*5)` which gives us
`(70)/(100)`, which is 70%.

2) Fraction to Percent Conversion

For this method, we first convert the fraction into a decimal, then into a percent. Let us use the same example as before:

`(87)/(100)` is the same as 87÷100 since Fractions represent division. Using long division, we get 0.87. We have a hundredths place here, so it is 87%

Now, with your question:

`(14)/(20)` is the same as 14÷20 which gives us 0.70 when using long division. 0.70 is the same as 70%.

In summary, the answer as per the votes in favor of working in groups is 70%.