Question

Which expressions have a value greater than 1? Choose all the correct answers. ​

Answer 1

A, C, E

Explanation:

To determine which expressions have a value greater than 1, evaluate the expressions following the order of operations (PEMDAS) and remembering the following:

• The quotient of two negative numbers is always positive.
• The product of two negative numbers is always positive.
• The product of a negative and positive number is always negative.

Expression A

`\;\;\;\:-(1)/(3) / (-2)+4\\\\= -(1)/(3) \cdot \left(-(1)/(2)\right)+4\\\\=((-1) \cdot (-1))/(3 \cdot 2)+4\\\\= (1)/(6)+4\\\\= 4(1)/(6)`

Expression B

`\;\;\;-(1)/(3) \cdot (-2)-4\\\\= (2)/(3) -4\\\\= (2)/(3) -(12)/(3)\\\\= (2-12)/(3)\\\\= -(10)/(3)\\\\=-3(1)/(3)`

Expression C

`\;\;\:\:-(1)/(3) \cdot (-2-4)\\\\= -(1)/(3) \cdot (-6)\\\\=\frac{(-1)\cdot (-6)}3{}\\\\= (6)/(3) \\\\= 2`

Expression D

`\;\;\:\:-(1)/(3) \cdot (-2)(-4)\\\\= -(1)/(3) \cdot (8)\\\\=((-1) \cdot 8)/(3)\\\\= -(8)/(3) \\\\= -2(2)/(3)`

Expression E

`\;\;\:\:-(1)/(3) + (-2)-(-4)\\\\= -(1)/(3) -2+ 4\\\\= -2(1)/(3) + 4\\\\=4 -2(1)/(3)\\\\= 1(2)/(3)`

Therefore, the expressions that have a value greater than 1 are:

• A, C and E.