Q59. - Algebra 1

Question

WHICH ONE DOESN'T BELONG? Identify the sentence that does not belong with the other three. Explain your reasoning.

Step-by-Step Solution

Answer

The fourth sentence $\left(2j\right)k=2\left(jk\right)$ doesn’t belong.

Step 1. Commutative and associative property.

The commutative property for any operation ‘*’ is defined as,

$a*b=b*a$

Associative property: $a+\left(b+c\right)=\left(a+b\right)+c$ or $a\left(bc\right)=\left(ab\right)c$

Where ‘a’, ‘b’, and ‘c’ are any numbers.

Step 2. Given information.

The four sentences given are as follows:

$\begin{array}{l}x+12=12+x\\ 7h=h\cdot 7\\ 1+a=a+1\\ \left(2j\right)k=2\left(jk\right)\end{array}$

Step 3. DESCRIPTION OF STEP.

Note that the first sentence follows the commutative property for addition since it follows:

$a+b=b+a$

Thus, $x+12=12+x$ follow the commutative property.

Similarly, the second sentence follows the commutative property for multiplication since it follows:

$a\cdot b=b\cdot a$

Similarly, the third sentence follows the commutative property for addition since it follows:

$a+b=b+a$

But the fourth sentence doesn’t follow the commutative rather it follows the associative property for multiplication as it follows:

$a\left(bc\right)=\left(ab\right)c$

As:

$\left(2j\right)k=2\left(jk\right)$

Thus, the fourth sentence $\left(2j\right)k=2\left(jk\right)$ is not similar to others, i.e. doesn’t belong.