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L.5 Compare fraction sums and differences

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What does it mean to compare sums and differences of fractions?

When you compare sums and differences of fractions, you find out which total or result is greater, less, or equal after adding or subtracting fractions. You must use equivalent denominators before comparing.

Example:
  • 14 + 14 = 24
  • 2313 = 13
  • Now compare: which is greater, 24 or 13?
Note

Always make sure fractions have the same denominator before adding, subtracting, or comparing them.

How to find sums and differences of fractions

To find a sum or difference, make the denominators the same, then add or subtract the numerators while keeping the denominator unchanged.

Steps:
  • Find a common denominator for both fractions.
  • Convert each fraction to an equivalent fraction with that denominator.
  • Add or subtract the numerators.
  • Simplify the answer if possible.
Note

Simplifying helps you write the fraction in its simplest form, but the value stays the same.

Comparing sums and differences

After finding the sums or differences, compare the results using comparison symbols: <, >, or =.

Example:
  • 12 + 14 = 34
  • 3414 = 12
  • Compare: 34 > 12
Note

When denominators are the same, the fraction with the larger numerator is greater.

Estimating to compare fractions

Estimation helps you check if your answers make sense. You can round fractions to benchmark numbers like 01, 12, or 11 to compare quickly.

Example:
  • 38 is close to 12
  • 56 is close to 11
  • Estimate: 56 + 38 ≈ about 1 and a half.
Note

Estimation does not give the exact answer but helps you see if your exact answer is reasonable.

Using sums and differences in real life

Adding and subtracting fractions is useful in everyday situations like measuring, cooking, or comparing time. Knowing how to compare results helps you make better decisions.

Example:
  • You used 34 cup of sugar and 12 cup of flour. Which is more?
  • 34 > 12, so you used more sugar than flour.
Note

Understanding fractions helps you compare quantities accurately in real-world situations.