Operations with Fractions

1
Operations with Fractions

• Mrs. McBryar

2
Adding Fractions with Like Denominators

• Steps
• Add the numerators.
• Keep the denominator the same.
• 3. Simplify or make any improper fractions mixed
  numbers.
• Example 10 12 (10 12) 22 1 5
• 17 17 17 17 17

3
Subtracting Fractions with Like Denominators

• Steps
• 1. Subtract the numerator.
• Keep the denominator the same.
• Simplify or make any improper fractions mixed
  numbers.
• Example 15 - 4 (15 - 4) 11 1
• 22 22 22 22 2

4
Adding Mixed Numbers with Like Denominators

• Steps (Line them up vertically)
• Add the numerators.
• Keep the denominators the same.
• 3. Add the whole numbers.
• 4. Simplify or make any improper fractions mixed
  numbers.

5
Adding Mixed Numbers with Like Denominators

• Example 4 5
• 7
• 8 3
• 7
• 12 8 13 1
• 7 7

6
Subtracting Mixed Numbers with Like Denominators

• Steps (Line them up vertically)
• Subtract the numerators
• If you cannot subtract, you must borrow from
  the whole number. Borrow one whole then add the
  denominator to the numerator to get your new
  numerator).
• Keep the denominator the same.
• Subtract the whole numbers.
• 4. Simplify or make any improper fractions mixed
  numbers.

7
Subtracting Mixed Numbers with Like Denominators

• Example 9 3 8 11
• 8 8
• - 5 5 5 5
• 8 8
• 3 6 3
  3
• 8
  4

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Adding Fractions with Unlike Denominators

• Steps
• Find the LCD (least common denominator) Just
  find the LCM of the denominators.
• 2. Find equivalent fractions with the LCD.
• 3. Add the numerators.
• 4. Keep the denominators the same.
• 5. Simplify or make any improper fractions mixed
  numbers.

9
Adding Mixed Numbers with Unlike Denominators

• Steps (Line them up vertically)
• Find the LCD (least common denominator).
• Find equivalent fractions with the LCD.
• Add the numerators.
• Keep the denominators the same.
• Add the whole numbers.
• Simplify or make any improper fractions mixed
  numbers.

10
Subtracting Fractions with Unlike Denominators

• Steps
• Find the LCD (least common denominator).
• Find equivalent fractions with the LCD.
• Subtract the numerators.
• Keep the denominator the same.
• 5. Simplify.

11
Subtracting Mixed Numbers with Unlike Denominators

• Steps
• 1. Find the LCD (least common denominator).
• 2. Find equivalent fractions with the LCD.
• 3. Subtract the numerators (borrow from the
  whole number if needed)
• 4. Keep the denominator the same.
• 5. Subtract the whole numbers.
• 6. Simplify or make any improper fractions mixed
  numbers.

12
Multiplying with Fractions

• Steps
• Multiply the numerators.
• Multiply the denominators.
• Simplify or change any improper fractions to
  mixed numbers.

13
Multiplying with Mixed Numbers

• Steps
• Change mixed numbers to improper fractions.
• Multiply the numerators.
• Multiply the denominators.
• Simplify or change any improper fractions to
  mixed numbers.

14
Dividing with Fractions

• Steps (KCF)
• Keep the first fraction the same.
• Change the division sign to a multiplication
  sign.
• Flip the numerator and denominator of the last
  fraction. (Reciprocal)
• The numerator becomes the denominator and
  the denominator is now the numerator)
• 4. Multiply the numerators.
• 5. Multiply the denominators.
• 6. Simplify or change any improper fractions to
  mixed numbers.

15
Dividing Mixed Numbers

• Steps (KCF)
• Change any mixed numbers to improper fractions.
• Keep the first fraction.
• Change the division sign to a multiplication
  sign.
• Flip the second fraction.
• Multiply the numerators and denominators.
• Simplify or change any mixed numbers to improper
  fractions.