PARENTHESES.

16. $7-(7-3)$.

17. $(8-6)-1$.

18. $(3-2)-(1-1)$.

19. $(7-3)-(3-2)$.

20. $(8-2)-(5-3)$.

21. $15-(10-3-2)$.

39. Multiplying a Compound Expression.

The expression $4(5+3)$ means that we are to take the sum of the numbers $5$ and $3$ four times. The process can be represented by placing five dots in a line, and a little to the right three more dots in the same line, and then placing a second, third, and fourth line of dots underneath the first line and exactly similar to it. $$\begin{gathered} *9>r•\&•\&•\&•\&•\&\&•\&•\&• \\ •\&•\&•\&•\&•\&\&•\&•\&• \\ •\&•\&•\&•\&•\&\&•\&•\&• \\ •\&•\&•\&•\&•\&\&•\&•\&• \end{gathered}$$

There are $(5+3)$ dots in each line, and $4$ lines. The total number of dots, therefore, is $4\times (5+3)$.

We see that in the left-hand group there are $4\times 5$ dots, and in the right-hand group $4\times 3$ dots. The sum of these

two numbers $(4\times 5)+(4\times 3)$ must be equal to the total number; that is,

Again, the expression $4(8-3)$ means that we are to take the difference of the numbers $8$ and $3$ four times. The process can be represented by placing eight dots in a line and crossing the last three, and then placing a second, third, and fourth line of dots underneath the first line and exactly similar to it. $*9>r•\&•\&•\&•\&•\&\&•\text{{}$/$\}\&•\text{{}$/$\}\&•\text{{}$/$$\begin{gathered} \} \\ •\&•\&•\&•\&•\&\&•\text{{} \end{gathered}$$/$\}\&•\text{{}$/$\}\&•\text{{}$/$$\begin{gathered} \} \\ •\&•\&•\&•\&•\&\&•\text{{} \end{gathered}$$/$\}\&•\text{{}$/$\}\&•\text{{}$/$$\begin{gathered} \} \\ •\&•\&•\&•\&•\&\&•\text{{} \end{gathered}$$/$\}\&•\text{{}$/$\}\&•\text{{}$/$\}$

The whole number of dots not crossed in each line is evidently $(8-3)$, and the whole number of lines is $4$. Therefore the total number of dots not crossed is $4\times (8-3).$

The total number of dots (crossed and not crossed) is $(4\times 8)$, and the total number of dots crossed is $(4\times 3)$. Therefore the total number of dots not crossed is

(4 × 8) - (4 × 3); lintthat is, 4(8 - 3) = (4 × 8) - (4 × 3) = 32 - 12. [1] If $a$, $b$, and $c$ stand for any three numbers, we have a (b + c) = ab + ac, lintand a(b - c) = ab - ac. ,

multiply a compound expression by a simple one,

Multiply each term by the multiplier, and write the successive products with the same signs as those of the original terms.

Exercise 2.

Multiply and remove parentheses: