Question

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Which description is paired with its correct expression?

two less than the quotient of a number cubed and four, increased by eight; 2 - n³/ 4 + 8

six times the difference of five and a number squared; 6 x (n³- 5)

three more than the quotient of nine and a number cubed, decreased by two;3 + 9/n³- 2

twice the difference of a number squared and three; 2 x ( n³- 3)

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Answer 1

Brackets

The order of the calculations is 'multiplication/division' then 'addition/subtraction.' However, we can change the order if we want, using brackets.

For example, if we want to add first then multiply, $3+2$ then $\times 5$, we can use brackets to show the changed order, $(3+2)\times 5$.

Solution

We can change the order by using brackets.

(1) $-2+\dfrac{n^3}{4}+8$ is the answer. (False)

(2) $6\times (n^2-5)$ is the answer. (False)

(3) $3+\dfrac{9}{n^3} -2$ is the answer. (True)

(4) $2\times (n^2-3)$ is the answer. (False)

More information

• $9+2+11+8=(9+11)+(2+8)=30$
• $2\div4\times4\div2=(2\div2)\times(4\div4)=1$

We can change the order in the group of 'multiplication/division' and 'addition/subtraction.' The result remains the same. Here, both commutative/associative property was used.

Answer 2

Answer

two less than the quotient of a number cubed and four, increased by eight;

2 - n³/ 4 + 8 =(False)

six times the difference of five and a number squared; 6 x (n³- 5) =(False)

three more than the quotient of nine and a number cubed, decreased by two

3 + 9/n³- 2 = (True)

twice the difference of a number squared and three; 2 x ( n³- 3) = (False)