Question

Use the properties of operations and rules for multiplying and dividing to solve:
(−3)÷(3/4)×(2/7)×(−5/16)÷(5/7). Show your work.
Answer
The answer needs to be a whole number.
Answered by GPT 3.5
To solve this expression, we'll need to simplify the multiplication and division as we go along.

First, let's start with the multiplication: (-3) * (2/7) * (-5/16).

To simplify this, we multiply the numerators together (-3 * 2 * -5) and the denominators together (7 * 16):

(-3 * 2 * -5) / (7 * 16) = 30 / 1120.

Next, let's move on to the division: (30/1120) / (5/7).

To divide, we multiply the first fraction by the reciprocal of the second fraction:

(30/1120) * (7/5).

Next, we simplify this multiplication:

(30 * 7) / (1120 * 5) = 210 / 5600.

Finally, let's simplify the fraction 210/5600. Both the numerator and denominator can be divided by 10:

(21/560) / (56/560) = 21/56.

So the final result is 21/56.
Answered by GPT 3.5
Apologies for the mistake. Let's start over and solve the expression correctly.

(-3) ÷ (3/4) × (2/7) × (-5/16) ÷ (5/7)

First, let's simplify the division (-3) ÷ (3/4):

(-3) ÷ (3/4) = (-3) × (4/3) = -12/3 = -4

Now, let's simplify the remaining multiplication:

-4 × (2/7) × (-5/16) ÷ (5/7)

= -4 × 2/7 × -5/16 ÷ 5/7

= -4 × -5/7 × 2/16 ÷ 5/7

= 20/7 × 2/16 ÷ 5/7

Now, let's simplify the division:

20/7 × 2/16 ÷ 5/7 = 20/7 × 2/16 × 7/5

= 20/7 × 1/8 × 7/5

= (20 × 1 × 7) / (7 × 8 × 5)

= 20/8 = 10/4 = 5/2

So, the simplified expression is 5/2.