# Fraction substraction arithmetic

$$3\frac38 - \frac56-1\frac23={}?$$

Can you solve this fraction substraction? I’m getting the wrong answer, on my book the answer is $$\frac78$$.

• What answer do you get, and how do you get there? Aug 5 at 23:14
• If you show us what you did then we may be able to help you spot where you went wrong Aug 5 at 23:16
• 3 3/8=2 3/8+8/8=2 11/8 . mmc =24 , 2 33/24-20/24-1 16/24??? Aug 5 at 23:17
• @GuilhermeWoolley your steps are correct so far Aug 5 at 23:32
• It’s mixed numbers, not multiplication Aug 5 at 23:36

First, expanding the fractions

$$\left(3+\frac{3}{8}\right)-\frac{5}{6}-\left(1+\frac{2}{3}\right) = \frac{24+3}{8}-\frac{5}{6}-\frac{3+2}{3}=\frac{27}{8}-\frac{5}{6}-\frac{5}{3}$$

Next, finding a common quotient and subtracting

$$\frac{27}{8}-\frac{5}{6}-\frac{5}{3} = \frac{(27\times 6 \times 3)-(5\times 8 \times 3)-(5\times 8 \times 6)}{8\times6\times3}=\frac{486-120-240}{144}=\frac{126}{144}=\frac{7\times(18)}{8\times(18)}=\frac{7}{8}$$

The answer is $$\boxed{\frac{7}{8}}$$

• I think $3\frac38$ means $3+\frac38$ not $3\times\frac38$. Aug 5 at 23:31
• It is common, at the level someone would ask this question, that $$3 \, \frac 3 8$$ is a mixed fraction, "3 and 3 eighths", not "$3 \cdot 3/8$" ($3$ times $3/8$), i.e. $$3 \, \frac 3 8 = 3 + \frac 3 8$$ Aug 5 at 23:31
• Makes sense! tks for observing Aug 5 at 23:32
• Ok! But on my books answer key is 7/8 Aug 5 at 23:32
• Did the corrections pointed on comments. Aug 5 at 23:38