This question aims to find the right answer to the given expression using the correct order of operations.

The sequence in which an expression is simplified is referred to as the order of operations. The order of operations refers to how we add, subtract, multiply, or divide numbers to work out a problem. This implies that the operator at the top of the list must be solved first in a mathematical expression. In the case of commutative and associative laws of addition, the order of addition and multiplication is not followed. But it must be taken into account when mixed operations exist in an expression.

The rule for solving such expressions is known as BODMAS, BIDMAS, or PEMDAS. Bracket, Order, Division, Multiplication, Addition, and Subtraction are abbreviations for BODMAS. When solving an expression in BODMAS, we must first work out the brackets, then the exponents, division, multiplication, addition, and subtraction. This rule must be acknowledged when solving equations or expressions. The wrong answer will be obtained if this rule is not being followed.

## Expert Answer

The given expression is:

$5+1\times 10$

The above expression includes two operations that are addition and multiplication. According to the order of operations, we are intended to apply multiplication and then addition. Now, for simplification:

$5+(1\times 10)$

Next, solving the bracket will result in:

$5+10$

Finally, we are left with addition only, and so the answer will be:

$15$

## Example 1

Solve the following expression using the order of operations:

$4-[3-(3-4)]+(4-3)-10$

### Solution

In the given example, we have the square and round brackets. First, we will solve the round brackets and then follow the order of operations as:

$=4-[3-(-1)]+1-10$

$=4-[3+1]-9$

$=4-4-9$

$=-9$

## Example 2

Solve the following expression using the order of operations:

$5-\{9-[7-(13-16)-25]-29\}-33$

### Solution

In the given expression, we have the round bracket, the square bracket, and then the order of operations. First solve the round bracket as:

$=5-\{9-[7-(-3)-25]-29\}-33$

$=5-\{9-[7+3-25]-29\}-33$

Now solve the square bracket by first adding $7$ and $3$ and then subtracting the result from $25$:

$=5-\{9-[10-25]-29\}-33$

$=5-\{9-[-15]-29\}-33$

$=5-\{9+15-29\}-33$

In the curly bracket above, add $9$ and $15$ and then subtract the result from $29$:

$=5-\{24-29\}-33$

$=5-\{-5\}-33$

$=5+5-33$

Finally, add $5$ to $5$ and then subtract the result from $33$:

$=10-33$

$=-23$

## Example 3

Solve the following expression using the order of operations:

$16\div 4 \times 3\div 2$

### Solution

In the given example, first apply division as:

$=4 \times \dfrac{3}{2}$

Now apply multiplication as:

$=\cancel{4}\times \dfrac{3}{\cancel{2}}$

$=2\times 3$

$=6$