Rational numbers verify problem

[SHATAKSHI]

I have to verify following rational number plz help me

(- 13/24)[(- 12/7) * 31/32] = [(- 13/24)(- 12/7)](31/32)

 

[e.jane.aran]

I have to verify following rational number plz help me

(- 13/24)[(- 12/7) * 31/32] = [(- 13/24)(- 12/7)](31/32)

What do you mean by "verifying" a number? Are you perhaps supposed to "simplify" the expression?

When you reply, please show us what you've tried so far. Thank you!

 

[HallsofIvy]

I have to verify following rational number plz help me

(- 13/24)[(- 12/7) * 31/32] = [(- 13/24)(- 12/7)](31/32)

What have YOU done? Basically asking you to verify the "associative property of multiplication".
On the left you are supposed to first multiply -12/7 by 31/32. What do you get for that? Now multiply that by -13/24.
On the right you are supposed to first multiply -13/24 by -12/7. What do you get for that? Now multiply that b7 31/32.

Do you get the same result?

 

[Theodore28]

To verify the equality, we can simplify both sides of the equation:

Left-hand side:
\[ (-\frac{13}{24})\left[(-\frac{12}{7}) \times \frac{31}{32}\right] \]

First, let's simplify the expression inside the brackets:
\[ (-\frac{12}{7}) \times \frac{31}{32} = -\frac{12}{7} \times \frac{31}{32} \]
\[ = -\frac{372}{224} \]
\[ = -\frac{93}{56} \]

Now, substitute this back into the original expression:
\[ (-\frac{13}{24}) \times (-\frac{93}{56}) \]
\[ = \frac{13 \times 93}{24 \times 56} \]
\[ = \frac{1209}{1344} \]

Right-hand side:
\[ [(-\frac{13}{24}) \times (-\frac{12}{7})] \times \frac{31}{32} \]

\[ = \left[(-\frac{13}{24}) \times (-\frac{12}{7})\right] \times \frac{31}{32} \]
\[ = \frac{13 \times 12}{24 \times 7} \times \frac{31}{32} \]
\[ = \frac{156}{168} \times \frac{31}{32} \]
\[ = \frac{156 \times 31}{168 \times 32} \]
\[ = \frac{4836}{5376} \]

After simplification, both sides indeed yield the same result:
\[ \frac{1209}{1344} = \frac{4836}{5376} \]

Thus, the equality holds true.