Question

How do you simplify \[15\div 5\left( 8-6+3 \right)\times 5\]?

Answer 1

Hint: Use the BODMAS rule to simplify the given expression. First solve the terms present inside the bracket and multiply the obtained sum with the 5 present on the left side of (8 – 6 + 3). Now, divide 15 with this obtained product and finally multiply the obtained number with 5 which is present on the right side of (8 – 6 + 3) to get the answer.

Complete step-by-step answer:
Here, we have been provided with the expression \[15\div 5\left( 8-6+3 \right)\times 5\] and we are asked to solve it. So, let us assume the value of the given expression as ‘E’. Therefore, we have,
\[\Rightarrow E=15\div 5\left( 8-6+3 \right)\times 5\]
As we can see that here different mathematical operators like: - division, multiplication, subtraction and addition are present. Also, we can see there is a bracket. So, we are going to use the BODMAS rule to simplify the expression. Here, BODMAS stands for: -
B \[\to \] Bracket
O \[\to \] Of (usually multiplication)
D \[\to \] Division
M \[\to \] Multiplication
A \[\to \] Addition
S \[\to \] Subtraction
According to this rule first we need to solve the expression inside the bracket. So, we get,
\[\begin{align}
  & \Rightarrow E=15\div 5\left( 2+3 \right)\times 5 \\
 & \Rightarrow E=15\div 5\left( 5 \right)\times 5 \\
\end{align}\]
Now, here 5 (5) denotes ‘5 of 5’ that usually means 5 multiply 5. Therefore, we get,
\[\Rightarrow E=15\div 25\times 5\]
As you can see that now we are left with two operators, that is division and multiplication. So, according to BODMAS rule first we need to solve the division operator. So, we get,
\[\Rightarrow E=\left( \dfrac{15}{25} \right)\times 5\]
Cancelling the common factors, we get,
\[\Rightarrow E=3\]
Hence, the value of the given expression is 3.

Note: You may think that why we have taken the product of (8 – 6 + 3) with 5, which was present on the left side before division. Actually, if any number is present inside bracket and another number is present beside it without any sign given like a (b), then we have to consider it as ‘a’ of ‘b’, i.e., ‘a’ multiplied with ‘b’, and we consider ‘of’ before ‘division’ in BODMAS. Now, we cannot multiply 25 with 5 before dividing 15 with 25 because clearly there were ‘\[\div \]’ and ‘\[\times \]’ signs indicated in which we must consider ‘\[\div \]’ before ‘\[\times \]’ according to the BODMAS rule.