fraction worksheets adding and subtracting unlike denominators

Teaching Notes

Practice focus: fraction worksheets adding and subtracting unlike denominators. Focus: Mixed Fraction Addition and Subtraction. Use the worked example and teaching sequence below to explain the reasoning before independent practice.

Before You Begin

• Identify addition, subtraction, multiplication, and division.

Teaching Steps for Parents and Teachers

1. Fractions must refer to equal-sized parts before you combine them.
2. For like denominators, add the numerators and keep the denominator.
3. For unlike denominators, rewrite both fractions using a common denominator, then add.
4. Convert a mixed number to an equivalent improper fraction when that makes the calculation easier.
5. Finally, simplify the result.
6. Use a common denominator so both fractions name the same-sized parts.
7. Subtract the numerators in the stated order and keep that common denominator.
8. With mixed numbers, you can first convert to improper fractions.
9. Simplify the difference; if it is greater than one, read the equivalent improper and mixed forms together.

Worked Examples

Evaluate (1/2)+(1/3).

1. Use denominator 6: 1/2 = 3/6 and 1/3 = 2/6.
2. Keep denominator 6: (3 + 2)/6 = 5/6.
3. Simplify to 5/6.

Answer: 5/6

Evaluate (3/4)-(1/3).

1. Use denominator 12: 3/4 = 9/12 and 1/3 = 4/12.
2. Keep denominator 12: (9 − 4)/12 = 5/12.
3. Simplify to 5/12.

Answer: 5/12

Common Mistakes and How to Help

Do not add the denominators. Rewriting a fraction requires multiplying its numerator and denominator by the same number. Our answer key shows an improper fraction beside its equivalent mixed number when the result is greater than one.

Subtract one original fraction from the total. Use equivalent fractions if necessary to compare the result with the other addend.

Keep the subtraction order. Subtracting denominators or changing only a numerator does not preserve the original quantities.

Add the difference to the fraction subtracted. Simplify or find a common denominator to compare it with the starting amount.

Questions to Check Understanding

• Which operation must be completed first, and why?
• Which step explains your answer?
• Can you apply the same reasoning when the numbers change?

Practice Advice

Work through the example together. Ask the learner to explain the first two problems, then try three independently. Review the first incorrect step before assigning more practice.

Next Practice

• Use New Numbers to practice the same skill with different values.
• If the learner needs help, return to the example and model each step before trying again.