Question

Which expression is NOT equivalent to −3/8⋅(−4+1/ 2)

1. -3/8 * -3 + -3/8 * -1/2
2. -3/8 * -4 + 3/8 * 1/2
3. -3/8 * -4 - 3/8 * 1/2
4. -3/8 * -31/2

Answer 1

2. -3/8 * -4 + 3/8 * 1/2

Answer 2

2. -3/8 * -4 + 3/8 * 1/2

Explanation:

The given expression is

`-(3)/(8)(-4+(1)/(2) )`

When we rewrite -4 as -3-1

We get
`-(3)/(8)(-3-1+((1)/(2) )`

Now add the -1 and the ½ to get:

`-(3)/(8)(-3+-(1)/(2) )`

Expand now to get:

`-(3)/(8)*-3+-(3)/(8)*-(1)/(2) )`...This gives the first option.

Again, we expand the parenthesis of the original directly using the distributive to obtain;

`-(3)/(8)*-4-(3)/(8)*(1)/(2)`......This gave us the third option.

We could also simplify the expression in the parenthesis first to get;

`-(3)/(8)*((-8+1)/(2))`

`-(3)/(8)*((-7)/(2))`

`-(3)/(8)*-3(1)/(2)`....This is the fourth option.

Hence the second options is NOT equivalent to the given expresion.