Evaluate numerical expressions involving rational numbers

Understanding Rational Numbers

Definition:

Examples:

Evaluating Numerical Expressions

Order of Operations (PEMDAS/BODMAS):

  • Parentheses/Brackets: Solve expressions inside parentheses/brackets first.
  • Exponents/Orders: Evaluate exponents or orders (powers and roots).
  • Multiplication and Division: From left to right.
  • Addition and Subtraction: From left to right.
Steps for Evaluating Expressions:
  • Simplify inside parentheses or brackets first.
  • Apply exponents or roots.
  • Perform multiplication and division from left to right.
  • Perform addition and subtraction from left to right.
Combining Rational Numbers:
  • Addition/Subtraction: Find a common denominator if needed.
  • Multiplication: Multiply the numerators and the denominators.
  • Division: Multiply by the reciprocal of the divisor.
Examples

Simple Addition:

Expression with Parentheses:
Expression with Exponents:
Complex Expression:
Practice Problems

Addition and Subtraction:

  • Multiplication and Division:
  • Expressions with Parentheses:
  • Expressions with Exponents:
Tips for Success

Follow Order of Operations:

  • Always follow the order of operations (PEMDAS/BODMAS) to evaluate expressions correctly.

Common Denominator:

  • When adding or subtracting fractions, always find a common denominator.

Simplify:

  • Simplify fractions whenever possible to make calculations easier.

Check Work:

  • Double-check calculations to ensure accuracy, especially when dealing with complex expressions.

Learn with an example

🎯 Evaluate the expression.

0.2÷2+0.6

Write your answer as an integer or a decimal. Do not round.

First, identify the operations in the expression.

0.2÷2+0.6

This expression has division and addition. The order of operations says to divide before adding.

0.2÷2+0.6=0.1+0.6

Now, add.0.1+0.6=0.7

The value of the expression is 0.7.

🎯 Evaluate the expression.

0.3÷3×0.2

Write your answer as an integer or a decimal. Do not round.

First, identify the operations in the expression.

0.3÷3×0.2

This expression has division and multiplication. The order of operations says to multiply and divide from left to right.

0.3÷3×0.2

=0.1×0.2

=0.1×0.2

=0.02

The value of the expression is 0.02.

🎯 Evaluate the expression.

0.6 + 0.4 ÷ 4

Write your answer as an integer or a decimal. Do not round.

First, identify the operations in the expression.

0.6 + 0.4 ÷ 4

This expression has addition and division. The order of operations says to divide before adding.

0.6 + 0.4 ÷ 4

0.6 + 0.1

Now, add.

0.6 + 0.1

0.7

The value of the expression is 0.7.

Let’s Practice!