Question Video: Finding the Difference between Rational Numbers Given in Different Forms | Nagwa Question Video: Finding the Difference between Rational Numbers Given in Different Forms | Nagwa

# Question Video: Finding the Difference between Rational Numbers Given in Different Forms Mathematics • 7th Grade

Express 5% as a fraction in its simplest form. Using the fraction form of 5%, find 5% − (3/20) − 0.35. Express your answer as a fraction in its simplest form.

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### Video Transcript

Express five percent as a fraction in its simplest form. Using the fraction form of five percent, find five percent minus three over 20 minus 0.35. Express your answer as a fraction in its simplest form.

In the first part of this question, we are asked to express five percent as a fraction in its simplest form. To do this, we can start by recalling that percentages are measured out of 100. So, 𝑎 percent is equal to 𝑎 divided by 100. This means that five percent must be equal to five divided by 100. We need to write this fraction in its simplest form. We can do this by canceling the shared factor of five in the numerator and denominator. This gives us one divided by 20.

In the second part of this question, we want to use our fractional form of five percent to evaluate an expression involving rational numbers, where we give our answer as a fraction in its simplest form. To do this, we first note that we are subtracting three rational numbers. We can recall that when subtracting rational numbers, we want them to be in the same form. So we will rewrite all of the rational numbers as fractions. Since we already know that five percent is equal to one over 20, we only need to convert 0.35 into a fraction.

There are many ways of doing this. We will note that 0.35 is equal to 35 over 100. And then, we can cancel the shared factor of five in the numerator and denominator to obtain seven over 20. We can then substitute these fractional representations of the numbers into the expression to see that it is equal to one over 20 minus three over 20 minus seven over 20.

We can then recall that we can subtract fractions with the same denominator by subtracting their numerators. In general, we have 𝑎 over 𝑑 minus 𝑏 over 𝑑 is equal to 𝑎 minus 𝑏 all over 𝑑. This result holds true for any number of fractions, provided that they have the same denominator. Applying this result gives us one minus three minus seven all over 20. We can then evaluate the subtraction in the numerator to obtain negative nine over 20. We cannot simplify this fraction any further, so our answer is negative nine over 20.

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