1.5 Operations with Integers and Fractions

Notes

Signs:

• Adding numbers with the same sign: add and keep the sign. Different signs: subtract and keep the sign of the larger absolute value. $-8 + 3 = -5$.
• Subtracting means adding the opposite: $4 - (-6) = 4 + 6 = 10$.
• Multiplying or dividing: same signs give a positive, different signs give a negative.

Fractions:

• Add or subtract with a common denominator: $\displaystyle \frac{1}{3} + \frac{1}{4} = \frac{4}{12} + \frac{3}{12} = \frac{7}{12}$.
• Multiply straight across: $\displaystyle \frac{2}{3} \cdot \frac{3}{5} = \frac{6}{15} = \frac{2}{5}$.
• Divide by multiplying by the reciprocal: $\displaystyle \frac{3}{4} \div \frac{1}{2} = \frac{3}{4} \cdot 2 = \frac{3}{2}$.