lesson
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Imagine a submarine dives 43 of a mile below sea level, then rises 41 of a mile back toward the surface. How deep is it now?
When we combine positive and negative fractions, we use the exact same integer rules we already know—we just apply them to the top numbers.
📊Interactive diagram
What should we do with that minus sign sitting in front of a fraction before we start adding?
Where Does the Negative Sign Go?
A negative fraction like −52 can be written as 5−2 or −52 because dividing numbers with different signs always gives a negative quotient.
To make adding easy, we always assign the negative sign to the numerator (the top number) while keeping the denominator (the bottom number) positive.
📊Interactive diagram
What happens when the fractions we want to combine already have matching denominators?
Adding with Common Denominators
When denominators match, our pieces are already the same size, so we add the numerators directly and keep the denominator.
Let's calculate −85+82.
Write the problem over a single denominator: 8−5+2. Since −5 and +2 have different signs, find their difference (5−2=3) and keep the sign of the larger absolute value, giving 8−3 or −83.