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More about Free 5th Grade Worksheets from eTutorWorld

These worksheets are suited for 5th graders in the age group of 9-11 years. The fun and challenging worksheets include problems from the 5th grade syllabus. They help children to reinforce their math concepts and have fun while doing it.

We have many 5th Grade Worksheets for Math, Science, and English. You can access them all at any time for free, and for as long as you wish. All you need to do is sign up to eTutorWorld using your email and phone number.

Once you sign up, verify your email, and go to your learning dashboard to access all worksheets.

Topics in arithmetic include multiplication, fractions, data analysis, number, and operations. Algebraic thinking and spatial understanding are also evaluated using these practice problems.

FREE 5TH GRADE WORKSHEET

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The standard order of operations is as follows:

  1. Perform any calculations inside parentheses or brackets first.
  2. Perform any calculations involving exponents or radicals.
  3. Perform any multiplications and divisions, working from left to right.
  4. Perform any additions and subtractions, working from left to right.

Using parentheses to specify the order in which calculations should be performed is a good idea, especially when working with more complex expressions.

The acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division, Addition and Subtraction, is often used to help remember the order of operations. The acronym PEMDAS is also used and is the same as PEMDAS, just with the M and D switched. It is essential to use the correct order of operations when evaluating mathematical expressions to ensure that the correct result is obtained.

Parentheses

In the order of operations, calculations inside parentheses or brackets are performed first. This is because parentheses and brackets are used to group calculations that should be done before any other functions in the expression. 

For example, consider the following expression:

Without any parentheses, it is not clear what should be calculated first. Should the multiplication be done before the addition or the other way around? To specify the order in which the calculations should be performed, we can use parentheses:

parenthesis

In this case, the expression inside the parentheses, 4 + 3, is calculated first, giving a result of 7. Then the multiplication is performed, showing a final result of 35 – 2, or 33.

Using parentheses correctly in an expression is essential to ensure that the intended order of operations is followed and the correct result is obtained.

Another example to show that groupings inside should be solved first.

parentheses

Step 1: In this case, the expression inside the parentheses (32 ÷ 4) should be calculated first. So it will be 8.

Step 2: Now the expression inside the square parentheses [8 + 3] should be solved. So, it will be 11.

Step 3: Then the multiplication is performed, showing a final result of 11 × 2 = 22.

Exponents

In the order of operations, calculations involving exponents, also known as powers or indices, are performed before any multiplications or divisions. This is because exponents indicate the number of times a number should be multiplied by itself, and these calculations should be done before any other operations (except parentheses)  in the expression.

An exponent is a small number written above and to the right of another number, called the base. The exponent tells you how many times to multiply the base by itself. For example, the base 4 and exponent 3 can be written like this: 4^3. This means to multiply 4 by itself 3 times, or 4*4*4. The result is 64.

exponents

For example, consider the following expression:

2 + 3 * 4^2

In this case, the exponent, 4^2, indicates that 4 should be multiplied by itself 2 times, or 4*4, which gives a result of 16. The exponent calculation is done before the multiplication, so the outcome of the expression is 2 + 3 * 16, or 2 + 48, or 50.

Multiplication and Division

In the order of operations, multiplication and division are performed before addition and subtraction. This is because multiplications and divisions are considered equal priorities and should be performed before any additions or subtractions.

For example, consider the following expression:

2 + 4 * 3 – 6 / 2

In this case, multiplication and division should be performed before the additions and subtractions. First, the multiplication is done: 4 * 3 = 12. Then the division is done: 6 / 2 = 3. Finally, the additions and subtractions are made: 2 + 12 – 3 = 11.

Here is another example:

5 – 4 / 2 + 8 * 3

In this case, the division and multiplication should be done first: 4 / 2 = 2 and 8 * 3 = 24. Then the additions and subtractions are done: 5 – 2 + 24 = 27.

Addition and Subtraction

In the order of operations, additions and subtractions are the final calculations that should be performed. This is because they are considered an equal priority and should be performed after all other calculations have been completed.

For example, consider the following expression:

2 + 4 * 3 – 6 / 2

In this case, multiplication and division should be performed before the additions and subtractions. First, the expansion is done: 4 * 3 = 12. Then the division is done: 6 / 2 = 3. Finally, the additions and subtractions are made: 2 + 12 – 3 = 11.

Here is another example:

5 – 4 / 2 + 8 * 3 

In this case, the division and multiplication should be done first: 4 / 2 = 2 and 8 * 3 = 24. Then the additions and subtractions are done: 5 – 2 + 24 = 27.

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Order of Operations Solved Examples:

Example 1: Solve: 2 + 6 × (4 + 5) ÷ 3 5 using PEMDAS.

Solution:

Step 1 – Parentheses : 2+6 × (4 + 5) ÷ 3 – 5 = 2 + 6 × 9 ÷ 3 – 5

Step 2 – Multiplication: 2 + 6 × 9 ÷ 3 – 5 = 2 + 54 ÷ 3 – 5

Step 3 – Division: 2 + 54 ÷ 3 – 5 = 2 + 18 – 5

Step 4 – Addition: 2 + 18 – 5 = 20 – 5

Step 5 – Subtraction: 20 5 = 15

Order of Operations Practice Problems:

  1. Solve 100 ÷ (6 + 7 × 2) 5 using PEMDAS.
  2. Solve 600 ÷ (44 + 14 × 4) 5 using PEMDAS.

 

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Order of Operations FAQS

What does PEMDAS stand for?

PEMDAS stands for Parentheses, Exponents, Multiplication, Division, and Addition and Subtraction. This acronym is used to help remember the order of operations in mathematics.

What is the order of operations in PEMDAS?

The order of operations in PEMDAS is as follows: Parentheses first, then Exponents, then Multiplication and Division (performed left to right), and finally Addition and Subtraction (performed left to right).

Why is the order of operations important?

The order of operations is important because it determines the order in which calculations are performed, which can affect the result. It is essential to use the correct order of operations to ensure that the correct result is obtained.

What is the meaning of the acronym PEMDAS?

The acronym PEMDAS stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction. These terms represent the order in which calculations should be performed in a mathematical expression.

Gloria Mathew writes on math topics for K-12. A trained writer and communicator, she makes math accessible and understandable to students at all levels. Her ability to explain complex math concepts with easy to understand examples helps students master math. LinkedIn

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