Beginning Algebra With Applications, Chapter 1, 1.3, Section 1.3, Problem 106

State whether each sum or difference is positive or negative.

a.) $\displaystyle \frac{1}{5} - \frac{1}{2}$

We know that $\displaystyle \frac{1}{5}$ is less than $\displaystyle \frac{1}{2}$ so the difference is negative.

b.) $-21.765 + 15.1$

The signs are different. So we subtract the absolute value of the number with the smaller absolute value from the absolute value of the number with the larger absolute value, then attach the sign of the number with larger absolute value. In this case, the sum is negative.

c.) $0.837 + (-0.24)$

The signs are different. So we subtract the absolute value of the number with the smaller absolute value from the absolute value of the number with the larger absolute value, then attach the sign of the number with larger absolute value. In this case, the sum is positive.

d.) $\displaystyle - \frac{3}{4} + \frac{9}{10}$

The signs are different. So we subtract the absolute value of the number with the smaller absolute value from the absolute value of the number with the larger absolute value, then attach the sign of the number with larger absolute value. In this case, the sum is positive.