Video Transcript
Express 45 percent as a fraction. Calculate 45 percent plus three over 20 plus 0.35.
In the first part of this question, we are asked to convert a percentage into a fraction. To do this, we can recall that percentages are measured out of 100. So 45 percent will be equal to 45 out of 100. This is a fraction. However, we should always check if we can simplify our answer. We can cancel the shared factor of five in the numerator and denominator. This gives us nine over 20. We cannot simplify this fraction any further. So we have shown that 45 percent is equal to nine over 20 as a fraction in its simplest form.
In the second part of this question, we need to calculate the sum of three rational numbers: one given as a percentage, one given as a fraction, and another given as a decimal.
In general, to add rational numbers, we want them to be in the same form. For instance, we could add all of these rational numbers by writing them as decimals. However, it is usually easiest to convert the rational numbers into fractions. We can note that 0.35 times 100 is equal to 35. So 0.35 is 35 over 100. We can then cancel the shared factor of five in the numerator and denominator to obtain seven over 20. This then allows us to convert the terms of this sum into fractions. We have nine over 20 plus three over 20 plus seven over 20.
Now that we are adding fractions, we can recall that we can add two or more fractions together with the same denominator by adding their numerators. We have that 𝑎 over 𝑑 plus 𝑏 over 𝑑 plus 𝑐 over 𝑑 is equal to 𝑎 plus 𝑏 plus 𝑐 all over 𝑑, provided that 𝑑 is nonzero. All of our fractions have the same denominator. So we can add them together by adding their numerators. We get nine plus three plus seven all over 20. We can then evaluate the sum in the numerator to obtain 19 over 20.
We can give our answer in many different ways by converting the fraction into a decimal or a percentage. To do this, we want the denominator to be 100. So we multiply the fraction by five over five to get 95 over 100. This then gives us 95 percent or 0.95. Any of these answers are correct. The only difference is the form we choose to represent the value.
