Question Video: Simplifying Numerical Expressions Involving Mixed Numbers | Nagwa Question Video: Simplifying Numerical Expressions Involving Mixed Numbers | Nagwa

Question Video: Simplifying Numerical Expressions Involving Mixed Numbers Mathematics • First Year of Preparatory School

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Simplify the following expression: −6 2/9 − (−6 4/9) + 12 8/9.

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Video Transcript

Simplify the following expression: negative six and two-ninths minus negative six and four-ninths plus 12 and eight-ninths.

In this question, we are asked to simplify an expression involving the sum and difference of rational numbers all given as mixed numbers. We can start by recalling that subtracting a negative is the same as adding the positive value. This allows us to rewrite the expression as negative six and two-ninths plus six and four-ninths plus 12 and eight-ninths.

We could now convert all of the numbers into fractions. However, it is easier to directly add the mixed numbers together. We do this by adding the integer and fractional parts separately.

First, we evaluate the integer parts. We have negative six plus six plus 12. Then, we want to evaluate the fractional parts. It’s very important to include the signs of each term in this calculation. We get negative two-ninths plus four-ninths plus eight ninths. We can now evaluate each part separately. We have that negative six plus six plus 12 is equal to 12. We can add the fractions together by recalling that we can add fractions together with the same denominator by adding their numerators.

In general, we have that 𝑎 over 𝑐 plus 𝑏 over 𝑐 is equal to 𝑎 plus 𝑏 all over 𝑐. This holds true for any number of fractions with the same denominator. So we get negative two plus four plus eight all over nine. If we evaluate the numerator, then we see that our expression is equal to 12 plus 10 over nine.

Since the original expression is given in terms of mixed numbers, we will give our answer as a mixed number. We can calculate that 10 over nine is equal to one and one-ninth. So our expression simplifies to give 13 and one-ninth.

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