Use properties of rational numbers to multiply the following. -22 x (-56/209)

A. 56/19

B. 2299/28

C -17/209

D 112/19

5 answers

To multiply \(-22\) by \(-\frac{56}{209}\), we first note that the product of two negative numbers is positive. Thus, we can write:

\[ -22 \times -\frac{56}{209} = 22 \times \frac{56}{209} \]

Next, we can express \(22\) as a fraction:

\[ 22 = \frac{22}{1} \]

Now we can multiply the fractions:

\[ \frac{22}{1} \times \frac{56}{209} = \frac{22 \times 56}{1 \times 209} = \frac{1232}{209} \]

Next, we can simplify \(\frac{1232}{209}\) if possible. First, we find the GCD (greatest common divisor) of 1232 and 209.

After performing the calculation, we find that \(209\) divides evenly into \(1232\):

\[ 1232 \div 209 = 5.9 \quad \text{(this shows they don't share factors)} \]

So, the fraction \(\frac{1232}{209}\) is already in its simplest form.

To convert \(\frac{1232}{209}\) to a mixed number:

\[ 1232 \div 209 = 5 \quad \text{(with a remainder of 117)} \] Thus: \[ \frac{1232}{209} = 5 + \frac{117}{209} \]

However, the answer options appear to refer to simple fractions. Since \(1232\) is much greater than \(209\), let's check back if any of the provided options simplify correctly to facilitate the comparison.

Revisiting the provided options:

  • \(\frac{56}{19}\)
  • \(\frac{2299}{28}\)
  • \(-\frac{17}{209}\)
  • \(\frac{112}{19}\)

The integer associated with \(22 \times \frac{56}{209}\) computes to \(5.9 \text{ not equivalent to any provided answers}\).

Our only feasible conclusion is to express as:

  • Separated as \( \frac{1232}{209} = 5.9\) meaning none match the context.

Please check again if there is any mistake in options or assist in further calculations!

So, the answer simplifies to \( \frac{1232}{209} = \frac{1232}{209} \) thus none of the above options fit within the context of rational number properties satisfactory for the multiplication displayed.

just pick the most likely answer

Given the calculations we have done, the product \( -22 \times -\frac{56}{209} \) simplifies to \( \frac{1232}{209} \). Since this is not directly available in the options provided, we can evaluate which option is closest.

Let's convert the options to decimals or see if any fit with our calculated value.

  1. A. \( \frac{56}{19} \)

    • \( \frac{56}{19} \approx 2.947 \)
  2. B. \( \frac{2299}{28} \)

    • \( \frac{2299}{28} \approx 82.464 \)
  3. C. \( -\frac{17}{209} \)

    • This is negative and not close to a positive value.
  4. D. \( \frac{112}{19} \)

    • \( \frac{112}{19} \approx 5.895 \)

Comparing these to \( \frac{1232}{209} \approx 5.9 \), the closest answer is:

D. \( \frac{112}{19} \)

So, I would select D as the most likely answer.

good job you were right

Thank you! I’m glad the answer was correct. If you have any more questions or need further assistance, feel free to ask!