Using Brackets to Solve Expressions

Oct 13, 2025 by talynt.org 12 views

Introduction

In mathematics, brackets are used to group numbers and operations together, making it easier to solve expressions. When solving mathematical expressions, it's essential to follow the order of operations (PEMDAS) and use brackets to clarify the order of operations. In this article, we will explore how to use brackets to make each expression equal to 10.

Using Brackets to Solve Expressions

a) $14 - 12 \times 5$

To solve this expression, we need to follow the order of operations (PEMDAS). First, we need to multiply 12 and 5, then subtract the result from 14.

14 - (12 \times 5)

Using the order of operations, we can rewrite the expression as:

14 - 60

Now, we can simplify the expression by subtracting 60 from 14.

-46

However, we want the expression to equal 10. To achieve this, we can add 56 to both sides of the equation.

14 - 60 + 56 = 10

By adding 56 to both sides, we can rewrite the expression as:

14 + (-60 + 56) = 10

Using the distributive property, we can rewrite the expression as:

14 - (60 - 56) = 10

Now, we can simplify the expression by subtracting 4 from 14.

10 = 10

b) $11 - 6 - 5$

To solve this expression, we need to follow the order of operations (PEMDAS). First, we need to subtract 6 from 11, then subtract 5 from the result.

11 - 6 - 5

Using the order of operations, we can rewrite the expression as:

5 - 5

Now, we can simplify the expression by subtracting 5 from 5.

However, we want the expression to equal 10. To achieve this, we can add 10 to both sides of the equation.

5 - 5 + 10 = 10

By adding 10 to both sides, we can rewrite the expression as:

5 + (-5 + 10) = 10

Using the distributive property, we can rewrite the expression as:

5 - (5 - 10) = 10

Now, we can simplify the expression by subtracting 15 from 5.

-10 + 10 = 0

However, we want the expression to equal 10. To achieve this, we can add 20 to both sides of the equation.

-10 + 20 = 10

By adding 20 to both sides, we can rewrite the expression as:

-10 + 20 = 10

c) $20 - 15 - 5$

To solve this expression, we need to follow the order of operations (PEMDAS). First, we need to subtract 15 from 20, then subtract 5 from the result.

20 - 15 - 5

Using the order of operations, we can rewrite the expression as:

5 - 5

Now, we can simplify the expression by subtracting 5 from 5.

However, we want the expression to equal 10. To achieve this, we can add 10 to both sides of the equation.

5 - 5 + 10 = 10

By adding 10 to both sides, we can rewrite the expression as:

5 + (-5 + 10) = 10

Using the distributive property, we can rewrite the expression as:

5 - (5 - 10) = 10

Now, we can simplify the expression by subtracting 15 from 5.

-10 + 10 = 0

However, we want the expression to equal 10. To achieve this, we can add 20 to both sides of the equation.

-10 + 20 = 10

By adding 20 to both sides, we can rewrite the expression as:

-10 + 20 = 10

d) $20 \div 4 - 2$

To solve this expression, we need to follow the order of operations (PEMDAS). First, we need to divide 20 by 4, then subtract 2 from the result.

20 \div 4 - 2

Using the order of operations, we can rewrite the expression as:

5 - 2

Now, we can simplify the expression by subtracting 2 from 5.

However, we want the expression to equal 10. To achieve this, we can add 7 to both sides of the equation.

5 - 2 + 7 = 10

By adding 7 to both sides, we can rewrite the expression as:

5 + (-2 + 7) = 10

Using the distributive property, we can rewrite the expression as:

5 - (2 - 7) = 10

Now, we can simplify the expression by subtracting -5 from 5.

10 = 10

Conclusion

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. PEMDAS stands for:

Parentheses: Evaluate expressions inside parentheses first.
Exponents: Evaluate any exponential expressions next (e.g., 2^3).
Multiplication and Division: Evaluate any multiplication and division operations from left to right.
Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I use brackets to solve mathematical expressions?

A: To use brackets to solve mathematical expressions, follow these steps:

Identify the expression you want to solve.
Use parentheses to group numbers and operations together.
Follow the order of operations (PEMDAS) to evaluate the expression.
Simplify the expression by combining like terms.

Q: What is the distributive property?

A: The distributive property is a rule that allows us to distribute a single operation to multiple terms. For example:

a(b + c) = ab + ac

Q: How do I use the distributive property to solve mathematical expressions?

A: To use the distributive property to solve mathematical expressions, follow these steps:

Identify the expression you want to solve.
Look for opportunities to distribute a single operation to multiple terms.
Use the distributive property to rewrite the expression.
Simplify the expression by combining like terms.

Q: What are some common mistakes to avoid when using brackets to solve mathematical expressions?

A: Some common mistakes to avoid when using brackets to solve mathematical expressions include:

Not following the order of operations (PEMDAS)
Not using parentheses to group numbers and operations together
Not simplifying the expression by combining like terms
Not using the distributive property to rewrite the expression

Q: How do I know when to use brackets to solve mathematical expressions?

A: You should use brackets to solve mathematical expressions when:

You have multiple operations in an expression
You need to group numbers and operations together
You need to simplify the expression by combining like terms
You need to use the distributive property to rewrite the expression

Q: Can I use brackets to solve any type of mathematical expression?

A: Yes, you can use brackets to solve any type of mathematical expression, including:

Linear expressions
Quadratic expressions
Polynomial expressions
Rational expressions

Q: How do I evaluate expressions with multiple levels of parentheses?

A: To evaluate expressions with multiple levels of parentheses, follow these steps:

Evaluate the innermost parentheses first.
Work your way outwards, evaluating each set of parentheses in turn.
Simplify the expression by combining like terms.

Q: Can I use brackets to solve expressions with variables?

A: Yes, you can use brackets to solve expressions with variables. When working with variables, be sure to follow the order of operations (PEMDAS) and use parentheses to group numbers and operations together.

Conclusion

In this article, we answered some frequently asked questions about using brackets to solve mathematical expressions. We covered topics such as the order of operations (PEMDAS), the distributive property, and common mistakes to avoid. By following these tips and techniques, you can use brackets to solve mathematical expressions with confidence.