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Chapter 5: Problem 97

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. \((24 \div 6) \div 2=24 \div(6 \div 2)\)

Short Answer

Expert verified
The statement is false. The corrected statement should be \((24 \div 6) \div 2= 24 \div 6 \div 2\).

Step by step solution

01

Analyze & Divide the expression into two parts

The statement can be divided into two parts: the left side is \((24 \div 6) \div 2\), and the right side is \(24 \div (6 \div 2)\). Now solve each side individually.
02

Solve the left side of the equation

First find the result of \(24 \div 6\) which gives 4. Now again divide this result by 2. Therefore, the left side value is \( 4 \div 2 = 2\)
03

Solve the right side of the equation

First calculate \(6 \div 2\) which equals 3. Now, divide 24 by this result. Therefore, for the right side of this equation we get \( 24 \div 3 = 8\)
04

Compare both the results

It is clear that \(2 \ne 8\), therefore, the statement in the exercise is false.
05

Correct the statement to make it true

A correct statement using the same numbers and divisors, but different branches would be \((24 \div 6) \div 2= 24 \div 6 \div 2\). This holds true as both sides simplify to 2.

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