# Chapter 1 - Section 1.5 - Addition of Real Numbers - Exercise Set - Page 63: 43

$-21$

#### Work Step by Step

Using the commutative and associative properties, - add all positive numbers - add all negatives - add the two sums Adding Two Numbers with the Same Sign 1. Add the absolute values. 2. Use the common sign as the sign of the sum. Adding Two Numbers with Different Signs 1. Subtract the smaller absolute value from the greater absolute value. 2. Use the sign of the number with the greater absolute value. --- $...=25+ [(-45)+(-\displaystyle \frac{3}{7})+(-\frac{4}{7})]=\quad$... same signs in brackets ... in the brackets, we choose to group the last two terms (assoc. property,)... $=25+ [(-45)+(-\displaystyle \frac{7}{7})]\qquad$...simplify the fraction (reduce by $7$) $=25+ [(-45)+(-1)]=\quad$... same signs in brackets $=25+(-46)\quad$...different signs, $-46$ has greater absolute value $= - (46-25)$ = $-21$

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