Here is your equation:
[tex]9 \frac{1}{6} - 5 \frac{5}{5}[/tex]
To subtract fractions, the denominator must be the same. The denominator is the bottom number in the fraction. The 2 denominators are 5 and 6. In order to make them the same, you have to find the LCM OF 5 and 6. To find it, list the multiples of both numbers and see which is common.
[tex]5- 5, 10, 15, 20, 25,\bf30[/tex]
[tex]6-6, 12, 18, 24,\bf 30[/tex]
The LCM of 5 and 6 is 30. Now change the mixed numbers so that they have common denominators.
[tex]9 \frac{1 \times 5}{6 \times 5} = 9 \frac{5}{30}[/tex]
[tex]5 \frac{5 \times 6}{5 \times 6} = 5 \frac{30}{30}[/tex]
Here is your new equation:
[tex]9 \frac{5}{30} - 5 \frac{30}{30}[/tex]
Now you have a problem. You're subtracting a smaller fraction from a bigger fraction. That means you need to remove 1 from the whole number and add it to the fraction. Here's how:
[tex]9 \frac{5}{30} \\ \\9-1 = 8\\ \\ 1 = \frac{30}{30} \\ \\ \frac{5}{30} + \frac{30}{30} = \frac{35}{30} \\ \\ 8 + \frac{35}{30} = 8 \frac{35}{30}[/tex]
Here is your new equation:
[tex]8 \frac{35}{30} - 5 \frac{30}{30}[/tex]
Subtract:
[tex]8 \frac{35}{30} - 5 \frac{30}{30} = 3 \frac{5}{30}[/tex]
Since the denominator(top number) is a multiple of the numerator(top number), divide both numbers by the numerator.
[tex]3 \frac{5 \div 5}{30 \div 5} = 3 \frac{1}{6}[/tex]
Your answer is [tex]3[/tex] [tex]\frac{1}{6}[/tex]
