Year 7/8 Order of Operations BEDMAS Mathematics Worksheets - Free Printable

The image you provided appears to be a worksheet focused on the BEDMAS (Brackets, Exponents, Division/Multiplication, Addition/Subtraction) order of operations. Below, I will explain how to solve problems using BEDMAS and provide a general approach to tackling these types of questions.

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Understanding BEDMAS

BEDMAS is an acronym that helps us remember the correct order of operations when solving mathematical expressions:
1. Brackets: Solve anything inside brackets first.
2. Exponents: Solve any exponents (powers or roots).
3. Division and Multiplication: Perform these operations from left to right.
4. Addition and Subtraction: Perform these operations from left to right.

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General Steps to Solve Problems

1. Identify and solve expressions inside brackets first.
2. Handle exponents if present.
3. Perform division and multiplication from left to right.
4. Perform addition and subtraction from left to right.

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Example Problem Solving

Let’s take one example from the worksheet and solve it step by step:

#### Example Problem:
Evaluate the expression:
\[ 7 + 8 \times (9 - 5) \]

#### Step-by-Step Solution:
1. Brackets: Solve the expression inside the brackets first.
\[
9 - 5 = 4
\]
So the expression becomes:
\[
7 + 8 \times 4
\]

2. Multiplication: Next, perform the multiplication.
\[
8 \times 4 = 32
\]
So the expression now is:
\[
7 + 32
\]

3. Addition: Finally, perform the addition.
\[
7 + 32 = 39
\]

Thus, the final answer is:
\[
\boxed{39}
\]

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Explanation for Each Section in the Worksheet

The worksheet seems to have three main sections:
1. Completing Expressions: You are given incomplete expressions and need to fill in the missing parts to make the equation true.
2. Order of Operations: You are asked to evaluate expressions using the correct order of operations.
3. Inserting Brackets: You are tasked with inserting brackets to make the equations correct.

#### Section 1: Completing Expressions
For example:
\[ 7 + \_\_ = 10 \]
Here, you need to determine what number added to 7 equals 10. The answer is:
\[ 7 + 3 = 10 \]

#### Section 2: Order of Operations
For example:
\[ 2 \times (3 + 4) - 5 \]
1. Solve the brackets:
\[
3 + 4 = 7
\]
So the expression becomes:
\[
2 \times 7 - 5
\]
2. Perform multiplication:
\[
2 \times 7 = 14
\]
So the expression now is:
\[
14 - 5
\]
3. Perform subtraction:
\[
14 - 5 = 9
\]
The final answer is:
\[
\boxed{9}
\]

#### Section 3: Inserting Brackets
For example:
\[ 8 + 2 \times 3 = 30 \]
To make this equation true, you need to insert brackets so that the multiplication happens before the addition. The correct placement is:
\[ (8 + 2) \times 3 = 30 \]
1. Solve the brackets:
\[
8 + 2 = 10
\]
So the expression becomes:
\[
10 \times 3
\]
2. Perform multiplication:
\[
10 \times 3 = 30
\]
The equation is now correct.

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Final Answer

If you have a specific problem you'd like me to solve in detail, please let me know! Otherwise, the general approach outlined above should help you tackle all the problems in the worksheet.

If you need further clarification or assistance with any particular question, feel free to ask!