Complete the Mixed-Number Decomposition

Teaching Notes

Focus: Separate the Whole and Fractional Parts. Use the worked example and teaching sequence below to explain the reasoning before independent practice.

Before You Begin

• Read the numbers and identify the operation.

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

1. Use denominator 3: 7/3 = 7/3 and 1/3 = 1/3.
2. Keep denominator 3: (7 − 1)/3 = 6/3.
3. Simplify to 2.

Answer: 2

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

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