Question

Evaluate the following
\[119-\left[ 48\div 6-75\times 12\div 3-\left( 15-\overline{3-8} \right) \right]\]

Answer 1

Hint: We are asked to simplify the given equation \[119-\left[ 48\div 6-75\times 12\div 3-\left( 15-\overline{3-8} \right) \right].\] We will use the BODMAS rule to solve it. First of all we will solve the Vinculum or the bar ( – ) given upon 3 – 8 or \[\overline{3-8}.\] To solve this, we will subtract 8 from 3 and then we will solve the round bracket. Once the round bracket is solved, we will simplify the square bracket by first dividing and then multiplying the terms. At the very last step, as BODMAS says, we add and then subtract the terms. Remember the product of 2 negatives is positive. So using this, we get our answer.

Complete step-by-step answer:
We are asked to simplify the term \[119-\left[ 48\div 6-75\times 12\div 3-\left( 15-\overline{3-8} \right) \right].\] To simplify this we use the VBODMAS rule which tells us about the sequence. We should follow this while solving mathematical operations. First of all, we will solve the bar. So, we get,
\[\Rightarrow 119-\left[ 48\div 6-75\times 12\div 3-\left( 15-\left( -5 \right) \right) \right]\left\{ \text{As }\overline{3-8}=-5 \right\}\]
Now, we will simplify the bracket. In brackets, we will first solve the round bracket. So,
\[\Rightarrow 119-\left[ 48\div 6-75\times 12\div 3-\left( 15+5 \right) \right]\]
\[\Rightarrow 119-\left[ 48\div 6-75\times 12\div 3-20 \right]\]
Now we solve the square bracket. Inside the bracket, first, we will solve division and then multiply.
As, \[48\div 6=8\] and \[12\div 3=4.\] So, we get,
\[\Rightarrow 119-\left[ 8-75\times 4-20 \right]\]
Now we will do multiplication. As, \[75\times 4=300,\] so we get,
\[\Rightarrow 119-\left[ 8-300-20 \right]\]
Now solving the terms inside the bracket, we get,
\[\Rightarrow 119-\left[ 8-320 \right]\]
\[\Rightarrow 119-\left[ -312 \right]\]
Now, opening the bracket, we get,
\[\Rightarrow 119+312\]
On addition, we get,
\[\Rightarrow 431\]

Note: Remember that ( – ) that is put on \[\overline{3-8}\] means that we have to solve it only and any sign outside, it will not affect it. That is, \[-\overline{3-8}\ne -3-8.\] For \[-\overline{3-8}\] we have to solve 3 – 8 = – 5 and then multiply it by a minus sign. So, \[-\overline{3-8}\] is the same as \[-\left( 3-8 \right).\] Also, the sequence is highly important. So, we always follow BODMAS while we have to multiply operations in one equation.