Question

How do you solve `17\frac { 7} { 9} - 10\frac { 7} { 8}`?

Answer 1

`\frac{497}{72}`

or

`6\frac{65}{72}`

or

`6.902\overline{7}`

Explanation:

First, convert both mixed numbers into improper fractions by multiplying the denominators of each fraction by the whole number, then adding the numerator. Then place the the sum of that over the denominator.

`17\frac{7}{9}-10\frac{7}{8}`

`\frac{160}{9}-\frac{87}{8}`

To subtract fractions, they use have a common denominator, aka the Least Common Multiple (LCM).

The LCM of `9` and `8` is `72`, since:

`9\cdot 8=72` and `8\cdot 9=72`

(If you're having trouble finding the LCM of two numbers, just multiply them and that will be okay. It may not always be the least common denominator, but you can always simplify the answer)

Now we have to multiply the numerators and denominators of both fractions by their LCM:

`(\frac{160}{9}\cdot\frac{8}{8})-(\frac{87}{8}\cdot\frac{9}{9})`

`=\frac{1280}{72}-\frac{783}{72}`

`=\frac{497}{72}`

or

`=6\frac{65}{72}`

or

`=6.902\overline{7}`

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The answers are equalivent; they're just expressed in different forms.

If you don't know what the line over the `7` is, it means the `7` repeats infinitely. The concept is called bar notation.