How to Solve Mixed Operation Questions Efficiently
Mixed operations are a set of operations in mathematics that can be defined as two or more operations, performed simultaneously on the same set of numbers. These are important to study in mathematics. Mixed operations are multiple operations involved like addition, subtraction, multiplication and division. Using PEMDAS or BODMAS rules, we demonstrate how to implement mixed operations. This article also helps you in attaining addition, subtraction, multiplication, and division worksheets pdf for free. So, let's begin.
What are Mixed Operations?
Mixed operations are those operations in which more than one operation is done. Suppose there is an expression, 5 + 2 -1. Here we can see that two operations are used. One is addition and the other one is subtraction. So such expressions will come under the mixed operations.
Mixed Operations
Order of Operation
The below-given image shows the order in which the operations are applied to a problem, having more than one operation.
Order of Operations
Mixed Operations Rules
Following are the mixed operation rules:
Operation rule 1: First thing to do while operating the expression is to solve the numbers inside the parenthesis or bracket. We solve the parenthesis inside to out, grouping the operations. Observe the pattern of brackets present in the expression. There is an order to solve brackets, that is $[\{()\}]$. First, we solve the round bracket (), then the curly bracket {} then the box(square) bracket []. The order of operations to be followed inside the brackets.
Operation rule 2: After operating on parenthesis, we look for exponents. If present, solve them.
Operation rule 3: Now, we operate on the four basic operations. In this step, we look for numbers with multiplication and division operations. If present, solve them from left to right.
Operation rule 4: Last operations to be carried out are addition or subtraction and solving them from left to right.
Solved Mixed Addition and Subtraction Word Problems for Grade 2
Below are some addition and subtraction worksheets for grade 2:
Q 1. $4 \times(5+2)$
Ans: $4 \times(7)=28$ (Correct $(\checkmark)$.) This is a correct way to solve the parentheses) Let us look at another approach for the same expression. $4 \times(5+2)=20+2=22$ (Incorrect $(X)$.) This is an incorrect way to solve.
Q 2. $4 \times(-5)^2$
Ans: $4 \times(25)=100$ (Correct $(\checkmark)$.) This is a correct way to solve the exponents)
Another approach for the same expression may be as follows
$4 \times(-5)^2=-20^2=-400$ ((Incorrect $(X)$.) This is an incorrect way to solve the exponent
Q 3. $3+5 \times 2$
Ans: $3+5 \times 2=3+10=13$ (Correct $(\checkmark)$. Correct order.)
Another approach for the same expression may be as follows
$3+5 \times 2=8 \times 2=16$ (Incorrect $(X)$. Incorrect order.)
Practice Problems
Here are some practice problems based on the addition and subtraction worksheets;
Q 1: Find the total of the difference of 230 and 101, with 452.
Ans. 581
Q 2. Find the sum of the difference of 435 and 281, with 412.
Ans. 566
Q 3. Subtract the sum of 79 and 53 from 123.
Ans. 9
Q 4. Multiply the quotient of 16 and 2 by 66.
Ans. 528
Q 5. Divide the multiplication of 6 and 3 by 9.
Ans. 2
Mixed Operations Worksheets
This article provides you with the addition, subtraction, multiplication, and division worksheets pdf to practice more and more to gain proficiency.
Mixed operations worksheets
Summary
Mixed operation is a mathematical concept that is used in many different fields of mathematics. It is used to describe situations where an operation produces more than one result, and can be viewed as a combination of two or more different operations. This concept can be applied to many fields such as combinatorics, probability and statistics. In this article, we tried to discuss some of these mixed operations in mathematics terms, along with some solved mixed addition and subtraction word problems for grade 2. If you understand the concept, you may find it interesting to solve the given addition and subtraction worksheets, even if you don't like studying mathematics.
FAQs on Mixed Operations Worksheets in Maths
1. What are mixed operations in Maths, and what is their importance?
Mixed operations in Maths refer to mathematical expressions or problems that involve more than one of the four basic arithmetic operations: addition (+), subtraction (-), multiplication (×), and division (÷). Their importance lies in building a strong foundation for more advanced mathematics, like algebra. Mastering mixed operations is crucial for developing logical thinking and accurately solving real-world problems that require multiple calculation steps.
2. What is the BODMAS rule and how is it used to solve mixed operations problems?
The BODMAS rule is an acronym that dictates the correct order of operations to solve a mathematical expression for a consistent and accurate answer. It stands for:
B - Brackets
O - Orders (powers and square roots)
D - Division
M - Multiplication
A - Addition
S - Subtraction
To solve a problem, you must first solve the operations inside brackets, then powers, then division and multiplication (from left to right), and finally addition and subtraction (from left to right).
3. Why is it important to follow a specific order like BODMAS when solving mixed operations? What happens if we don't?
Following a specific order of operations like BODMAS is essential because it ensures that everyone who solves the same problem arrives at the same, single correct answer. It provides a universal standard for calculation. If we don't follow this order, a single expression could yield multiple different results, leading to confusion and incorrect conclusions. For example, without BODMAS, 5 + 3 × 2 could be interpreted as (5+3) × 2 = 16 or 5 + (3×2) = 11. The BODMAS rule confirms that 11 is the only correct answer.
4. Can you provide an example of solving a mixed operation problem step-by-step?
Certainly. Let's solve the expression: 20 + (10 - 2) × 3 ÷ 4.
Step 1 (Brackets): Solve the operation inside the brackets first: (10 - 2) = 8. The expression becomes 20 + 8 × 3 ÷ 4.
Step 2 (Division/Multiplication): Perform multiplication and division from left to right. First, multiply 8 × 3 = 24. The expression is now 20 + 24 ÷ 4.
Step 3 (Division/Multiplication): Next, divide 24 ÷ 4 = 6. The expression simplifies to 20 + 6.
Step 4 (Addition/Subtraction): Finally, perform the addition: 20 + 6 = 26. The final answer is 26.
5. How are mixed operations used in real-life situations outside of school worksheets?
Mixed operations are used constantly in everyday life. For example:
Shopping: Calculating a total bill when you buy multiple items, some with a discount. You multiply item counts by prices, add them up, and then subtract the discount.
Budgeting: Planning monthly expenses involves adding up different sources of income and subtracting various costs like rent, groceries, and bills.
Cooking: Adjusting a recipe for more or fewer people requires multiplying or dividing ingredient quantities and then combining them.
6. What is the role of brackets in mixed operations, and how do we handle different types?
The primary role of brackets in mixed operations is to group parts of an expression that must be solved first, overriding the standard BODMAS sequence. If you have nested brackets, such as { [ ( ) ] }, you always solve the innermost bracket first and work your way outwards. For instance, in 10 × {5 + (4 - 2)}, you would first calculate (4 - 2) = 2, then {5 + 2} = 7, and finally 10 × 7 = 70.
7. How can students effectively tackle word problems involving mixed operations?
To effectively solve word problems with mixed operations, students should follow a structured approach:
Read and Understand: Carefully read the problem to identify what is being asked and what information is given.
Identify Keywords: Look for keywords that indicate operations (e.g., 'total' for addition, 'left' for subtraction, 'of' for multiplication, 'share' for division).
Formulate the Expression: Translate the words into a single mathematical expression with numbers and operators.
Solve using BODMAS: Apply the BODMAS rule to solve the expression accurately.
8. In the BODMAS rule, is addition always performed before subtraction?
This is a common misconception. In the BODMAS rule, Addition (A) and Subtraction (S) have equal priority. They are not performed in a fixed order but are solved as they appear from left to right in the expression. The same principle applies to Division (D) and Multiplication (M). For example, in the problem 15 - 5 + 3, you would solve it from left to right: first 15 - 5 = 10, then 10 + 3 = 13. Doing addition first would give an incorrect answer of 7.
