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Complete the Calculation Steps

Focus: Mixed Number + Mixed Number. Use the worked example and teaching sequence below to explain the reasoning before independent practice.

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Teaching Notes

Focus: Mixed Number + Mixed Number. Use the worked example and teaching sequence below to explain the reasoning before independent practice.

Before You Begin

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. For a blank, identify the missing quantity. Substitute the completed value back into the original statement to check it.

Worked Examples

Evaluate (1 1/3)+(2 1/4).

  1. Rewrite each mixed number as an improper fraction: 1 1/3 = 4/3; 2 1/4 = 9/4.
  2. Use denominator 12: 4/3 = 16/12 and 9/4 = 27/12.
  3. Keep denominator 12: (16 + 27)/12 = 43/12.
  4. Simplify to 43/12.
  5. 43/12 = 3 7/12.

Answer: 43/12 = 3 7/12

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.

Questions to Check Understanding

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.

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