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Divide -3 1/7 divided 7 2/6. Explain each step you used to find the quotient.

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Answer:

-3/7

Step-by-step explanation:

[tex]-3\frac{1}{7} / 7 \frac{2}{6}[/tex]

[tex]-3 \frac{1}{7} = \frac{-22}{7}[/tex]

[tex]7\frac{2}{6} = 7\frac{1}{3} = \frac{22}{3}[/tex]

[tex]\frac{\frac{-22}{7} }{\frac{22}{3} }[/tex][tex]= \frac{-22}{7} * \frac{3}{22} = \frac{-3}{7}[/tex]

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Given the two dividends, we can solve accordingly through steps:

1. Convert to improper

3 • 7 = 21
21 + 1 = 22

Our improper fraction for -3 1/7 is -22/7.

7 • 6 = 42
42 + 2 = 44

Our improper fraction for 7 2/6 is 44/6.

2. Use Skip Flip Multiply method (SFM)

Our dividends are -22/7 and 44/6. We can solve by first using the skip principle, meaning we can leave -22/7 as it is.

Next, we can flip 44/6 so we have its reciprocal, which is 6/44.

Now, we multiply our new fractions:

-22/7 • 6/44 = -132/308

This converts to -66/154, which also converts to -3/7.

3. Finalize our answer

-3 1/7 divided by 7 2/6 gives us -3/7. This is our final answer.
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