The difference is:
[tex]\frac{-3}{4} - \frac{15}{16} = \frac{-27}{16}[/tex]
Solution:
Given expression is:
[tex]\frac{-3}{4} - \frac{15}{16}[/tex]
We have to find the difference
To find the difference, make the denominators same
Find the least common multiple of 4 and 16
List all prime factors for each number.
Prime Factorization of 4 is: 2 x 2
Prime Factorization of 16 is: 2 x 2 x 2 x 2
For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.
The new superset list is
2, 2, 2, 2
Multiply these factors together to find the LCM.
LCM = 2 x 2 x 2 x 2 = 16
Make the denominators as 16
[tex]\rightarrow \frac{-3}{4} - \frac{15}{16} = \frac{-3 \times 4}{4 \times 4} - \frac{15 \times 1}{16 \times 1}\\\\\rightarrow \frac{-3}{4} - \frac{15}{16} = \frac{-12}{16} - \frac{15}{16}\\\\\rightarrow \frac{-3}{4} - \frac{15}{16} = \frac{-12-15}{16}\\\\\rightarrow \frac{-3}{4} - \frac{15}{16} = \frac{-27}{16}[/tex]
Thus the difference is [tex]\frac{-27}{16}[/tex]
