Question Video: Evaluating Numerical Expressions Involving Percentages | Nagwa Question Video: Evaluating Numerical Expressions Involving Percentages | Nagwa

Question Video: Evaluating Numerical Expressions Involving Percentages Mathematics • First Year of Preparatory School

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Evaluate and simplify (−3/4) − 30%.

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Video Transcript

Evaluate and simplify negative three-quarters minus 30 percent.

In this question, we are asked to evaluate and simplify the difference between two given rational numbers. To do this, it is a good idea to write the numbers in the same form. Usually, it is easiest to rewrite the rational numbers as fractions. So, we will rewrite 30 percent as a fraction. We can do this by recalling that fractions are measured out of 100. So, 30 percent is equal to 30 over 100. We can simplify this by canceling the shared factor of 10 in the numerator and denominator. We get negative three-quarters minus three-tenths.

We can then recall that we can find the difference of two fractions with the same denominators by finding the difference in their numerators. We have that 𝑎 over 𝑐 minus 𝑏 over 𝑐 is equal to 𝑎 minus 𝑏 all over 𝑐. To apply this result, we need both fractions to have the same denominator. We can find that the lowest common multiple of the denominators is 20. So, we want to rewrite both of the fractions to have a denominator of 20. We do this by multiplying the first fraction by five over five and multiplying the second fraction by two over two. Evaluating these products gives us negative 15 over 20 minus six over 20.

Now that the denominators are the same, we can find the difference in the fractions by finding the difference of the numerators. We obtain negative 15 minus six all over 20, which is equal to negative 21 over 20. We can then convert this value into any form we want. For instance, we could write our answer as the mixed number negative one and one-twentieth.

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