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L.4 Complete addition and subtraction sentences with fractions

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What are addition and subtraction sentences with fractions?

Addition and subtraction sentences with fractions are math equations that show how fractional parts are combined or taken away. Each sentence includes fractions, an operation sign (+ or −), and an equal sign (=) to show the result.

Examples:
  • 12 + 14 = 34
  • 3414 = 12
Note

A fraction sentence always shows a complete idea — it begins with fractions, includes an operation, and ends with an answer.

How to add fractions with like denominators

When fractions have the same denominator, add only the numerators and keep the denominator the same.

Steps:
  • Write the fractions: 14 + 24
  • Add the numerators: 1 + 2 = 3
  • Keep the denominator the same: 4
  • Result: 34
Note

Only the numerators change when adding fractions with the same denominator. The denominator stays the same.

How to add fractions with unlike denominators

When fractions have different denominators, find a common denominator before adding. A common denominator is a number both denominators can divide evenly into.

Steps:
  • Write the fractions: 12 + 13
  • Find the least common denominator (LCD): 6
  • Rename the fractions: 36 + 26
  • Add the numerators: 3 + 2 = 5
  • Result: 56
Note

Always make denominators the same before adding. Then simplify the fraction if needed.

How to subtract fractions

To subtract fractions, make sure the denominators are the same. Subtract the numerators and keep the denominator unchanged.

Example:
  • 3414 = 12
Note

If denominators are different, find a common denominator before subtracting. Simplify your answer when possible.

Completing fraction sentences

Sometimes a math sentence has a missing fraction or number. Use your knowledge of fractions to find the missing value that makes the sentence true.

Examples:
  • 14 + ___ = 34 → The missing part is 24
  • ___ − 13 = 23 → The missing part is 1
Note

Check your answer by doing the opposite operation. If both sides of the equation match, your sentence is correct.

Tips for working with fraction sentences

Using a number line or drawing fraction models can help you see how fractions are added or subtracted. Visuals make it easier to understand the size of each part.

Helpful Hints:
  • Find a common denominator before adding or subtracting unlike fractions.
  • Always simplify your answer to lowest terms.
  • Estimate to see if your answer makes sense.
Note

Fraction sentences show how parts relate to a whole. Knowing how to complete and solve them helps you understand addition and subtraction with fractions clearly.