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X.1 Addition, subtraction, multiplication, and division facts

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What are mixed operations?

Mixed operations mean solving problems that use more than one operation (addition, subtraction, multiplication, or division) in the same situation.

Examples:
  • 3 + 5 − 2 = 6
  • 4 × 3 + 2 = 14
  • 18 ÷ 3 − 4 = 2
Note

Mixed operations show how numbers can be combined in different ways. Always pay attention to what the problem is asking you to do.

Understanding each operation

Before solving mixed operation problems, review what each operation means and how it works.

Examples:
  • Addition: 7 + 2 = 9 (putting numbers together)
  • Subtraction: 10 − 4 = 6 (taking away)
  • Multiplication: 5 × 3 = 15 (equal groups)
  • Division: 12 ÷ 4 = 3 (sharing equally)
Note

Knowing your facts for all four operations helps you solve mixed operation problems more quickly and accurately.

Steps to solve mixed operation problems

When more than one operation appears in a problem, follow the correct order of operations to get the right answer.

Steps:
  • First, solve multiplication and division (left to right).
  • Next, solve addition and subtraction (left to right).
  • Check your answer by reading the problem again.
Note

A helpful way to remember the order is: multiplication and division before addition and subtraction. Parentheses come first if they are in the problem.

Using mixed operations in word problems

Word problems often ask you to use more than one operation to find the answer. Read carefully to decide which operations are needed.

Example:
  • Maria bought 3 packs of pencils with 4 pencils in each pack. Then she gave 5 pencils to her friend. How many pencils does Maria have now?
  • Step 1: 3 × 4 = 12 (total pencils)
  • Step 2: 12 − 5 = 7 (pencils left)
Note

Underline key words in the problem to decide which operations to use, and solve step by step.

Checking your work

After solving a mixed operation problem, it is important to check your answer to make sure it makes sense.

Ways to check:
  • Use the opposite operation (for example, check subtraction with addition).
  • Estimate to see if your answer is close to what you expected.
  • Read the problem again and see if your answer fits.
Note

Checking your work helps prevent mistakes and builds confidence in solving problems.