In working with problems involving fractions that have more than one mathematical operation; i.e (Of, +, ×, ÷, – ). We use what we called BODMAS Rule in Mathematics to work it. BODMAS is an acronym that stands for (B-Bracket, O-Of, D-Division, M-Multiplication, A-Addition, and S-Subtraction).
There are steps to follow when working on a mathematical problem with more than one sign.
BODMAS Rule in Mathematics
The following rules in BODMAS should be followed accordingly when dealing with mathematical problems with more than one sign (of,+,-,÷,× ).
Step 1: Deal with anything involving brackets first (if there are any in a mathematical problem). i.e ( )
Step 2: Work with O = Of (if there is any). Note ‘Of’= Multiplication (×)
Step 3: Deal with Division ( if there is any) i.e ‘÷’
Step 4: Deal with Multiplication (if there is any) i.e ‘×’
Step 5: Deal with the Addition (if there is any ) i.e ‘+’
Step 6: Deal with Subtraction (if there is any ) i.e ‘-‘
Let’s look at the examples below using BODMAS
\text{Evaluate } (1\frac{1}{3} ×2\frac{1}{6})+(1\frac{1}{2}÷\frac{5}{6})\\
Answer: \text{Since there is bracket, deal}\\\text{with bracket first} \space(1\frac{1}{3}×2\frac{1}{6})+(1\frac{1}{2}÷\frac{5}{6})\\=(\frac{(1×3)+1}{3}×\frac{(2×6)+1}{6})\\+(\frac{(1×2)+1}{2}÷\frac{5}{6})= (\frac{4}{3}×\frac{13}{6})\\+(\frac{3}{2}÷\frac{5}{6})\\=(\frac{26}{6})+(\frac{3}{2}×\frac{6}{5})=\frac{26}{6}+\frac{18}{10}\\=\frac{13}{3}+\frac{9}{5}\\
\text{ the LCM of 3 and 5 is 15}\space =\frac{13}{3}+\frac{9}{5}\\=\frac{(5×13)+(3×9)}{15}=\frac{65+27}{15}=\frac{92}{15}\\=6\frac{2}{15}This is pretty good, right? All Mathematical problems with more than one sign is done the same way.
On how to divide fractions click here