Question

Use the properties of operations and rules for multiplying and dividing to solve: (−2)×(15)÷(23)×(−56)÷(34) (1 point) Responses 16 Start Fraction 1 over 6 End Fraction −23 negative Start Fraction 2 over 3 End Fraction −16 negative Start Fraction 1 over 6 End Fraction 23 Start Fraction 2 over 3 End Fraction

Answer 1

To solve the expression \((-2) \times (15) \div (23) \times (-56) \div (34)\), we will follow the order of operations and simplify step-by-step.

1. Calculate the first part: \((-2) \times (15)\)
\[
-2 \times 15 = -30
\]

2. Now, divide by \(23\):
\[
-30 \div 23 = -\frac{30}{23}
\]

3. Next, multiply by \((-56)\):
\[
-\frac{30}{23} \times (-56) = \frac{30 \times 56}{23}
\]

4. Calculate \(30 \times 56\):
\[
30 \times 56 = 1680
\]
Thus, we have:
\[
\frac{1680}{23}
\]

5. Finally, divide by \(34\):
\[
\frac{1680}{23} \div 34 = \frac{1680}{23} \times \frac{1}{34} = \frac{1680}{23 \times 34}
\]

6. Calculate \(23 \times 34\):
\[
23 \times 34 = 782
\]
Therefore:
\[
\frac{1680}{782}
\]

7. Now we simplify \(\frac{1680}{782}\). We can find the GCD (Greatest Common Divisor) of 1680 and 782 to reduce it:
- The factors of 1680 are: \(2^4 \times 3 \times 5 \times 7\)
- The factors of 782 are: \(2 \times 391\) (where 391 is a prime number)

The GCD is \(2\). Dividing both the numerator and denominator by \(2\):
\[
\frac{1680 \div 2}{782 \div 2} = \frac{840}{391}
\]

This doesn't exactly match any of the provided options, but we can calculate the decimal or mixed number form to compare.

Calculating the decimal for \(\frac{840}{391}\):
\[
840 \div 391 \approx 2.148
\]

Expressed as a mixed number, \(2\) remainder \(58\) gives:
\[
2 + \frac{58}{391}
\]

Let’s check other options to find a close match:
- \(16\)
- \(-23\)
- \(-16\)
- \(\frac{2}{3}\)
- \(\frac{23}{3}\)

None of these are direct alternatives of our finding, but since all steps are correct; if amendments or different approaches lead to one of these causes, please clarify. However, based on exact calculations, we conclude with the right process yielding thus \( \frac{840}{391} \).