More than one type of operation means numbers that are in relation with each other through different types of operators.
When there is more than one type of operator involved in the problem then it must be solved in correct order of the operators.
Some rules for solving more than one type of operators:
1. In a mathematical problem calculation must be done from left to right.
2. While solving if you have parenthesis (brackets), solve the bracket first and then solve the problem. When you have a set of brackets or inner brackets, solve the inner brackets first.
3. In next step radical or exponent must be solved.
4. Then do divisions and after that multiplications to solve the problem.
5. At last do the additions and then to get the final answer.
From the above five steps we conclude that we should first solve the parenthesis then the radicals after that do the calculations like division then multiplication then subtraction and then addition. These operations together called PEDMAS rule. PEDMAS means Parentheses, Orders (Exponentiation), Multiplication Division, Addition and Subtraction.
PEDMAS is also known as BODMAS as parenthesis and brackets are same.
Sometimes we get an equation like:
In this case our mind gets confused and has many questions like:
From where to start the problem?? Left? Right? Or from center?
Or like when to solve the parenthesis(brackets)??
When to solve the exponents??
What we have to do divide or multiply??
Or what we have to do addition or subtraction first?
To give answer to all these questions and to solve the problem we use order of operator in more than one type of operator.
Rules for Order of Operation
To solve the problems let’s start to understand all these rules one by one:-
- Bracket rule/ parenthesis rule: - this rule states that whenever you come across parenthesis/ brackets in a problem, do solve brackets first.
Do things in Brackets First. Example:
6 × (3 + 6) | = | 6 × 9 | = | 54 | |||
6 × (3 + 6) | = | 18 + 3 | = | 21 | (wrong) |
- After the parenthesis exponents (Powers, Roots) must be solved and before Multiply, Divide, Add or Subtract. Example:
4 ×32 | = | 4 × 9 | = | 36 | |||
4 × 32 | = | 122 | = | 144 | (wrong) |
- Then after the exponents do the multiplications and then the divisions. Multiply or Divide before you Add or Subtract. At last do addition and subtraction in the problem. Example:
1 + 6 × 7 | = | 1 + 42 | = | 43 | |||
1 + 6 × 7 | = | 7 × 7 | = | 49 | (wrong) |
- Sometimes you will get the problem that do not have any parenthesis or exponents, in this you just simply go left to right. Example:
40 ÷ 5 × 2 | = | 8 × 2 | = | 16 | |||
40 ÷ 5 × 2 | = | 40 ÷ 10 | = | 4 | (wrong) |
this is how we solve the problem in the terms of broken steps.
Examples on Multiple Operation
Some examples based on the order of operation in more than a type of operators are:
Example 1: Evaluate 5+6-4
Solution: According to BODMAS rule first we will do the addition and then subtraction.
Step 1: add 5 and 6
5+6 = 11
Step 2: subtract 4 from the sum obtained
11-4 = 7
Hence the answer obtained is 5+6-4 =7
Example 2: Evaluate 1+3 x (4+6)
Solution: We do this question according to the BODMAS rule.
Step 1: solve the parenthesis or the braces
4+6 = 10
Step 2: do the multiplication of 3 with the answer obtained from step 1.
3 x 10 = 30
Step 3: then at last do the addition
1 + 30 = 31
Hence the answer to the problem is 31.
Example 3: Calculate -7+3
Solution: Whenever you get such type of problem in which you have one number with negative sign and another number with positive sign, we need to perform the subtraction operation. Subtract the smaller number from the greater number.
Therefore, 7-3= 4
Now we have to put the sign, since between these two numbers 7 is greater than 3 and it has negative sign hence, answer will also have negative sign.
So, -7 + 3 = -4
Example 4: Find -2 +5 -8
Solution: In such kind of problem, we have two operators, one of addition and another of subtraction.
Step 1: first solve the numbers with positive sign. Add the numbers that have positive sign.
So, we have only +5.
Step 2: now solve the numbers with negative sign. Add all the numbers that have negative sign. And at last put negative sign.
-2-8 = -8
Step 3: now add both the results
-8 + 5 = -3
Example 5: 6 – 4 + 7 -8 +1
Solution: In this problem
Step 1: first we will add the numbers with positive sign.
6+7+1 = 14
Step 2: now add the numbers with negative sign and then put the negative sign.
-4 -8 = -12
Step 3: now add the broth results
-12 + 14 = 2
Example 6: Simplify 6 + (4 x 3)
Solution: According to BODMAS rule we solve the braces/ parenthesis first
Hence, 4 x 3 =12
Now we will perform addition operation
6 + 12 = 18
Example 7: Simplify (2 x 4) – (3 + 4)
Solution: According to BODMAS rule we will solve the braces/ parenthesis first.
And since this problem has two braces we move from left to right. Hence we will first solve 2 x 4= 8 and then
3 + 4 = 7
Then put the value of its results in the problem
8 – 7 = 1
Hence the answer is 1
Example 8: Simplify 9÷3+4 x 5
Solution: According to BODMAS rule, will first do divide 9 ÷3 = 3
And then we will do multiplication 4 x 5 = 20
And then put the results in the question
3 + 20 = 23
Example 9: Simplify (8 ÷ 2) + 3 x (4 – 1)
Solution: In this case first we will solve the braces
Then 8 ÷ 2 = 4
And 4 -1 =3
And then substitute these values in the question
(8 ÷ 2) + 3 x (4 – 1) = 4 + 3 x 3
Then do the multiplication 3 x 3 =9
And then 4 + 9 = 13
Hence, the answer is 13.
Related Tags
additional One Type Of Operation , One more Type Of Operation