Question

4-16 draw a diagram that could be represented by each of the following number expressions. then circle the terms and calculate the value of each expression.
a. $4 + 2(5) + (- 3) = \underline{\quad\quad}$
b. $4 + 2(5 + (- 3)) = \underline{\quad\quad}$

Explanation:

Step1: Calculate \(2(5)\) in expression a

According to the order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction), we first calculate the multiplication. \(2(5)=10\). So the expression \(a\) becomes \(4 + 10+( - 3)\).

Step2: Calculate \(4 + 10+( - 3)\) in expression a

We add from left - to - right. \(4+10 = 14\), then \(14+( - 3)=14 - 3=11\). The terms in \(4 + 2(5)+(-3)\) are \(4\), \(2(5)\), and \((-3)\).

Step3: Calculate inside the parentheses in expression b

First, calculate \(5+( - 3)=5 - 3 = 2\). So the expression \(b\) becomes \(4+2\times2\).

Step4: Calculate \(2\times2\) in expression b

According to PEMDAS, we do the multiplication. \(2\times2 = 4\). Then the expression is \(4 + 4\).

Step5: Calculate \(4 + 4\) in expression b

\(4+4=8\). The terms in \(4 + 2(5+( - 3))\) are \(4\) and \(2(5+( - 3))\).

Answer:

a. \(11\)
b. \(8\)