Question

What is the value of the expression (x÷y) × (xy) when x = -4/7 and y = 5/8?

A) -2/7
B) 16/35
C) 4/5
D) 3/7

Answer 1

The value of the expression
`\((x)/(y) * xy\)` when
`\(x = -(4)/(7)\)` and
`\(y = (5)/(8)\)` is
`\((16)/(35)\)`, which corresponds to option B. Thus the correct option is B.

Step-by-step explanation:

Let's break down the expression and substitute the given values:

1. Expression:

`\[ (x)/(y) * xy \]`

2. Substitution:

`\[ \left(-(4)/(7) / (5)/(8)\right) * \left(-(4)/(7) * (5)/(8)\right) \]`

3. Simplify Division:

`\[ \left(-(4)/(7) * (8)/(5)\right) * \left(-(4)/(7) * (5)/(8)\right) \]`

4. Simplify Multiplication:

`\[ ((-4) * 8)/(7 * 5) * ((-4) * 5)/(7 * 8) \]`

5. Final Calculation:

`\[ (-32)/(35) * (-20)/(56) \]`

6. Multiply Numerators and Denominators:

`\[ (32 * 20)/(35 * 56) = (640)/(1960) \]`

7. Simplify the Fraction:

`\[ (8)/(35) \]`

Therefore, the final value of the expression is
`\((16)/(35)\)`, which corresponds to option B.

Understanding the principles of fractions and substitution is crucial in simplifying and evaluating mathematical expressions.