Question

Simplify: \[\left[ {42 \div \left( { - 7} \right)} \right] \div \left( { - 48} \right) \div 16\]

Answer 1

Hint:
Here, we will simplify the given arithmetic expression by using the BODMAS rule to find the simplified value. Arithmetic Expression is defined as an expression with numbers and arithmetic operators.

Complete step by step solution:
We are given with a arithmetic expression \[\left[ {42 \div \left( { - 7} \right)} \right] \div \left( { - 48} \right) \div 16\]
We will simplify it by using the BODMAS rule.
Here, we can see that the expression has only one operation that is the division operation. But, as the brackets are present, so by BODMAS rule we will operate the bracket first.
We will first divide the terms inside the bracket. Therefore, we get
\[\left[ {42 \div \left( { - 7} \right)} \right] \div \left( { - 48} \right) \div 16 = \left[ { - 6} \right] \div \left( { - 48} \right) \div 16\]
Now dividing \[ - 48\] by 16, we get
\[ \Rightarrow \left[ {42 \div \left( { - 7} \right)} \right] \div \left( { - 48} \right) \div 16 = \left[ { - 6} \right] \div \left( { - 3} \right)\]
Again, by dividing the numbers, we get
\[ \Rightarrow \left[ {42 \div \left( { - 7} \right)} \right] \div \left( { - 48} \right) \div 16 = 2\]
Therefore, the simplification of \[\left[ {42 \div \left( { - 7} \right)} \right] \div \left( { - 48} \right) \div 16\] is \[2\].
Note: We can also simplify the arithmetic expression.
\[\left[ {42 \div \left( { - 7} \right)} \right] \div \left( { - 48} \right) \div 16 = \dfrac{{\left[ {42 \div \left( { - 7} \right)} \right]}}{{\left( { - 48} \right) \div 16}}\]
By rewriting the equation, we get
\[ \Rightarrow \left[ {42 \div \left( { - 7} \right)} \right] \div \left( { - 48} \right) \div 16 = \dfrac{{42}}{{ - 7}} \times \dfrac{{ - 6}}{{48}}\]
Dividing 42 by \[ - 7\], we get
\[ \Rightarrow \left[ {42 \div \left( { - 7} \right)} \right] \div \left( { - 48} \right) \div 16 = - 6 \times \dfrac{{ - 16}}{{48}}\]
Dividing both numerator and denominator by \[ - 6\], we get
\[ \Rightarrow \left[ {42 \div \left( { - 7} \right)} \right] \div \left( { - 48} \right) \div 16 = \dfrac{{16}}{8}\]
Dividing 16 by 8, we get
\[ \Rightarrow \left[ {42 \div \left( { - 7} \right)} \right] \div \left( { - 48} \right) \div 16 = 2\]

Therefore, the simplified value of the Arithmetic expression \[\left[ {42 \div \left( { - 7} \right)} \right] \div \left( { - 48} \right) \div 16\] is 2.

Note:
We know that BODMAS rule states that the first operation has to be done which is in the brackets. Next, the operation applies on the indices or order, then it moves on to the division and multiplication and then using addition and subtraction we simplify the expression. If addition or subtraction and division or multiplication are in the same calculations, then it has to be done from left to right. An arithmetic expression is different from an algebraic expression. An algebraic expression is defined as an expression with both the numbers and the variables and the arithmetic operators like plus, minus, etc