Class Notes: Adding Fractions and Whole Numbers

Objective

Understand how to add a fraction to a whole number and vice versa by converting whole numbers to fractions and finding common denominators.

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Key Steps

1. Order Doesn't Matter
   • Addition is commutative: ( a + b = b + a ). So, fraction + whole number is same as whole number + fraction.
2. Convert Whole Number to Fraction
   • Place the whole number over 1.
     Example: ( 5 \rightarrow \frac{5}{1} ), ( 4 \rightarrow \frac{4}{1} )
3. Find Common Denominator
   • Multiply the numerator and denominator of the whole number by the denominator of the original fraction.
4. Add Numerators
   • With common denominators, add the numerators together and keep the denominator the same.
5. Write the Final Answer as an Improper Fraction

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Examples

Example 1: ( 5 + \frac{3}{4} )

• Convert 5 to a fraction: ( \frac{5}{1} )
• Get common denominator:
  ( \frac{5}{1} \times \frac{4}{4} = \frac{20}{4} )
• Now add:
  ( \frac{20}{4} + \frac{3}{4} = \frac{23}{4} )
• Final Answer: ( \frac{23}{4} )

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Example 2: ( \frac{2}{3} + 4 )

• Convert 4 to a fraction: ( \frac{4}{1} )
• Get common denominator:
  ( \frac{4}{1} \times \frac{3}{3} = \frac{12}{3} )
• Now add:
  ( \frac{2}{3} + \frac{12}{3} = \frac{14}{3} )
• Final Answer: ( \frac{14}{3} )

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Summary

To add a fraction to a whole number:

• Convert the whole number to a fraction.
• Find a common denominator.
• Add the numerators.
• Keep the denominator the same.
• Express the result as an improper fraction, if necessary.

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Quick Reference

1. Whole Number to Fraction: \( n \rightarrow \frac{n}{1} \)
2. Find common denominators.
3. Add the numerators.
4. The denominator stays the same.
5. Simplify if possible.