Adding Fractions with Like Denominators

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Questions and Answers

What is the first step in adding mixed numbers with like denominators?

  • Simplify the resulting fraction.
  • Convert the mixed numbers to improper fractions. (correct)
  • Add the numerators of the whole numbers.
  • Add the numerators and keep the denominator the same.

What is the sum of 3 1/5 + 2 2/5?

  • 6 3/5
  • 6 1/5
  • 5 1/5
  • 5 3/5 (correct)

When adding fractions with like denominators, what happens to the denominator?

  • It is added to the other denominator.
  • It is divided by the other denominator.
  • It is multiplied by the other denominator.
  • It remains the same. (correct)

Why must mixed numbers be converted to improper fractions before adding?

<p>To accurately combine the whole number part and the fractional part. (D)</p> Signup and view all the answers

After adding 2/7 + 3/7, what is the resulting fraction?

<p>5/7 (C)</p> Signup and view all the answers

What is the sum of 4 3/8 + 1 5/8 expressed as a mixed number?

<p>6 1/8 (C)</p> Signup and view all the answers

What is the sum of 2/9 + 5/9 expressed in its simplest form?

<p>7/9 (C)</p> Signup and view all the answers

Which of these expressions represents the sum of 1 2/3 and 3 1/3?

<p>(1 x 3 + 2)/3 + (3 x 3 + 1)/3 (D)</p> Signup and view all the answers

If two fractions have different denominators, what should you do before adding them?

<p>Find a common denominator for both fractions. (C)</p> Signup and view all the answers

Flashcards

Adding Proper Fractions

To add fractions with like denominators, add the numerators and keep the denominator the same.

Proper Fraction

A fraction where the numerator is less than the denominator.

Converting Mixed Numbers

Change mixed numbers to improper fractions before adding.

Improper Fraction

A fraction where the numerator exceeds the denominator.

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Adding Improper Fractions

When adding improper fractions, add the numerators and keep the denominator the same.

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Converting Back to Mixed Numbers

Change an improper fraction back to a mixed number after adding.

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Example of Adding Mixed Numbers

1 1/3 + 2 2/3 = 4; add whole numbers then fractions.

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Like Denominators

Fractions that share the same denominator, allowing direct addition of numerators.

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Adding Numerators

When adding fractions, focus on adding the numerators to find the total.

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Simplifying Fractions

Reducing a fraction to its smallest form after addition, if possible.

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Study Notes

Adding Proper Fractions with Like Denominators

  • To add fractions with like denominators, add the numerators and keep the denominator the same.
  • Example: 1/4 + 2/4 = (1 + 2)/4 = 3/4
  • The sum will remain a proper fraction if the numerators do not exceed the denominator.

Adding Mixed Numbers with Like Denominators

  • Convert the mixed numbers to improper fractions.
  • Example: 2 1/4 + 1 2/4
  • First, convert the mixed numbers to improper fractions:
    • 2 1/4 becomes (2 x 4 + 1) / 4 = 9/4
    • 1 2/4 becomes (1 x 4 + 2) / 4 = 6/4
  • Add the improper fractions: 9/4 + 6/4 = (9 + 6) / 4 = 15/4
  • Convert the improper fraction back to a mixed number, if necessary. 15/4 = 3 3/4

Key Concepts and Steps for Adding Fractions with Like Denominators

  • Identifying Like Denominators: Ensure the fractions you are adding share the same number in the denominator.
  • Adding Numerators: Add the numbers in the numerator (top part) of the fractions.
  • Keeping the Denominator: The combined fraction will use the same denominator as the original fractions.
  • Simplifying (if possible): If the resulting fraction can be simplified to a smaller, equivalent fraction, it should be.

Important Considerations When Adding Mixed Numbers

  • Converting to Improper Fractions: Mixed numbers must be converted to improper fractions before they can be added. This rule applies to all fractional addition problems involving mixed numbers.
  • Adding the Improper Fractions: Apply the rule for adding proper fractions – add the numerators, retain the same denominator – to the improper fractions.
  • Converting Back to Mixed Numbers: The resulting improper fraction often needs to be converted back to a mixed number. This conversion helps maintain clarity and understandability.

Examples of Adding Mixed Numbers

  • Example 1: 1 1/3 + 2 2/3 = (1 x 3 + 1)/3 + (2 x 3 + 2)/3 = 4/3 + 8/3 = 12/3 = 4
  • Example 2: 5 2/7 + 3 4/7 = (5 x 7 + 2)/7 + (3 x 7 + 4)/7 = 37/7 + 25/7 = 62/7 = 8 6/7
  • Example 3: 3 1/5 + 2 3/5 = (16/5) + (13/5) = 29/5 = 5 4/5

Visual Representation of Addition (Optional)

  • A visual representation using fraction models (e.g., fraction bars, circles) can help students visualize the process of combining fractional parts with the same denominator. This aids in conceptual understanding.

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