Question

Find 1 1 10(-6 7 8) . Write your answer as a mixed number in simplest form.

Answer 1

1 1/10(-6 7/8) simplifies to -6 7/80.

Step-by-step explanation:

In order to simplify the expression 1 1/10(-6 7/8), we need to perform multiplication and addition operations. First, multiply the whole number part (1) by the fraction (1/10):

`\[1 * (1)/(10) = (1)/(10).\]`

Now, distribute this product across the parentheses:

`\[(1)/(10) * (-6) + (1)/(10) * (7)/(8).\]`

This simplifies to
`\(-(6)/(10) - (7)/(80).\)`

Next, convert
`\((6)/(10)\)` to its simplest form, which is
`\((3)/(5)\)` :

`\[-(3)/(5) - (7)/(80).\]`

To combine these two fractions, find a common denominator, which is 80:

`\[-(48)/(80) - (7)/(80).\]`

Combine the numerators:

`\[-(55)/(80).\]`

Reduce the fraction to its simplest form by dividing the numerator and denominator by their greatest common factor, which is 5:

`\[-(11)/(16).\]`

Finally, express the mixed number:

`\[-6 (7)/(80).\]`

So, 1 1/10(-6 7/8) simplifies to -6 7/80.