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Video: Evaluating an Algebraic Expression Involving Fractions

Bethani Gasparine

Evaluate the expression 2/5 + (−4/9 + 4/9) − 7/10.


Video Transcript

Evaluate the expression two-fifths plus negative four-ninths plus four-ninths minus seven tenths.

Notice these parentheses. This means we have to evaluate what’s inside of these first. So we have negative four-ninths plus four-ninths, which means they cancel each other, or it’s zero. So all we have left is two-fifths minus seven tenths.

Now in order to subtract fractions, they must have a common denominator. So what number, the smallest number, does five and 10 both go into? They both go into 10. So how do I get two-fifths to now have a denominator of 10? Well, to make five be a 10, we must multiply by two. And whatever we multiply to the denominator we also have to multiply to the numerator.

So we need to multiply two times two and five times two. And we don’t need to do anything to the second fraction because it already has the denominator of 10. Two times two is four, and five times two is 10. And now we need to subtract seven tenths.

So when having a common denominator, that denominator will be in our answer. And we combine the numerators. So four minus seven is actually a negative number; it’s negative three, which means we will have a final answer of negative three tenths. So after evaluating our expression, we get a final answer of negative three tenths.