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Chapter 1: Problem 31

Simplify. Show your steps. $$(19-16) 13+54 \div 9(7-5)$$

Short Answer

Expert verified
Question: Simplify the given expression using the order of operations: \((19-16) \cdot 13 + 54 \div 9 \cdot (7-5)\) Answer: 51

Step by step solution

01

Evaluate the parentheses

First, we need to evaluate the expressions inside the parentheses. In this case, we have two parenthetical expressions: \((19 - 16)\) and \((7 - 5)\). Evaluate both of them: \((19 - 16) = 3\) \((7 - 5) = 2\) Now the expression becomes: $$3 \cdot 13 + 54 \div 9 \cdot 2$$
02

Perform multiplication and division from left to right

Next, evaluate multiplication and division operations from left to right in the expression: $$3 \cdot 13 = 39$$ $$54 \div 9 = 6$$ The expression becomes: $$39 + 6 \cdot 2$$
03

Perform addition from left to right

Now we only have addition and multiplication left in the expression, so we can continue from left to right: $$6 \cdot 2 = 12$$ The expression becomes: $$39 + 12$$ Finally, perform the addition: $$39+12=51$$ The simplified expression is: $$51$$

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