Adding a Mixed Number and a Fraction
4A · Chapter 7 · Lesson 3 · MATH-4A-C07-L03
Learning goal. Add a fraction to a mixed number, including regrouping past a whole.
Before you begin
Recall: 4A Ch6: common units, equivalence and mixed number conversions; Adding and Subtracting Fractions — Part 2. Try these three warm-up problems. If they are difficult, revisit the prerequisite lesson before advancing.
Calculate 1/2 − 1/2. Simplify.
Show answer & reasoning
Use the common denominator 2, then subtract the equal-size parts. The simplified result is 0.
Calculate 1/3 + 1/3. Simplify.
Show answer & reasoning
Use the common denominator 3, then add the equal-size parts. The simplified result is 2/3.
Calculate 2/3 − 1/2. Simplify.
Show answer & reasoning
Use the common denominator 6, then subtract the equal-size parts. The simplified result is 1/6.
Key vocabulary
- common denominator
- shared unit-part size
- mixed number
- whole plus fractional part
- regroup
- exchange a whole for denominator-sized parts
- simplest form
- fraction with no common integer factor greater than one
Understand the concept
Adding a fraction to a mixed number combines its fractional parts while keeping the whole units. For 2 3/4+1/2, rename half as 2/4: five fourths is one and a fourth. The final result is 3 1/4. When fractional parts cross one whole, exchange that group into the whole-number part.
Model it: two-whole bars and fractional overflow. Explain what every part of the model represents, then write a matching equation.
Fully worked examples
Read the problem first and predict the answer. Then study how each quantity is represented and calculated.
Worked example 1
Calculate 5 3/4 + 1/2.
Add the fractional parts with a common denominator. Include the original 5 wholes; regroup if their sum reaches a whole.
Check your understanding 1
Calculate 2 9/10 + 4/5.
Show answer & reasoning
Add the fractional parts with a common denominator. Include the original 2 wholes; regroup if their sum reaches a whole.
Worked example 2
Calculate 4 9/10 + 2/5.
Add the fractional parts with a common denominator. Include the original 4 wholes; regroup if their sum reaches a whole.
Check your understanding 2
Calculate 1 1/6 + 1/3.
Show answer & reasoning
Add the fractional parts with a common denominator. Include the original 1 wholes; regroup if their sum reaches a whole.
Worked example 3
Calculate 2 1/4 + 1/2.
Add the fractional parts with a common denominator. Include the original 2 wholes; regroup if their sum reaches a whole.
Check your understanding 3
Calculate 2 1/4 + 3/4.
Show answer & reasoning
Add the fractional parts with a common denominator. Include the original 2 wholes; regroup if their sum reaches a whole.
Guided practice
Calculate 2 1/2 + 2/3.
Show answer & reasoning
Add the fractional parts with a common denominator. Include the original 2 wholes; regroup if their sum reaches a whole.
Calculate 1 3/4 + 1/6.
Show answer & reasoning
Add the fractional parts with a common denominator. Include the original 1 wholes; regroup if their sum reaches a whole.
Calculate 3 1/6 + 2/3.
Show answer & reasoning
Add the fractional parts with a common denominator. Include the original 3 wholes; regroup if their sum reaches a whole.
Calculate 3 1/2 + 1/2.
Show answer & reasoning
Add the fractional parts with a common denominator. Include the original 3 wholes; regroup if their sum reaches a whole.
Calculate 1 1/2 + 1/2.
Show answer & reasoning
Add the fractional parts with a common denominator. Include the original 1 wholes; regroup if their sum reaches a whole.
Independent practice
Calculate 3 4/5 + 3/5.
Show answer & reasoning
Add the fractional parts with a common denominator. Include the original 3 wholes; regroup if their sum reaches a whole.
Calculate 2 1/2 + 1/3.
Show answer & reasoning
Add the fractional parts with a common denominator. Include the original 2 wholes; regroup if their sum reaches a whole.
Calculate 4 7/10 + 4/5.
Show answer & reasoning
Add the fractional parts with a common denominator. Include the original 4 wholes; regroup if their sum reaches a whole.
Calculate 2 3/4 + 1/2.
Show answer & reasoning
Add the fractional parts with a common denominator. Include the original 2 wholes; regroup if their sum reaches a whole.
Calculate 2 1/2 + 1/2.
Show answer & reasoning
Add the fractional parts with a common denominator. Include the original 2 wholes; regroup if their sum reaches a whole.
Calculate 3 1/6 + 1/2.
Show answer & reasoning
Add the fractional parts with a common denominator. Include the original 3 wholes; regroup if their sum reaches a whole.
Calculate 5 1/2 + 1/2.
Show answer & reasoning
Add the fractional parts with a common denominator. Include the original 5 wholes; regroup if their sum reaches a whole.
Calculate 3 1/3 + 1/3.
Show answer & reasoning
Add the fractional parts with a common denominator. Include the original 3 wholes; regroup if their sum reaches a whole.
Challenge and transfer
Explain the relationships and justify your method. Multiple correct approaches may be accepted if the reasoning is valid.
A student calculates 2 1/4 + 1/2 and writes 2 2/6. Identify the mistake and give the correct simplified answer.
Show answer & reasoning
Convert 1/2 into 2/4 and combine with 1/4, keeping 2 whole units. The total is 2 3/4.
Calculate 5 4/5 + 1/5.
Show answer & reasoning
Add the fractional parts with a common denominator. Include the original 5 wholes; regroup if their sum reaches a whole.
Exit check
Calculate 4 1/3 + 1/6.
Show answer & reasoning
Add the fractional parts with a common denominator. Include the original 4 wholes; regroup if their sum reaches a whole.
Calculate 1 3/4 + 1/2.
Show answer & reasoning
Add the fractional parts with a common denominator. Include the original 1 wholes; regroup if their sum reaches a whole.
Calculate 2 1/4 + 1/6.
Show answer & reasoning
Add the fractional parts with a common denominator. Include the original 2 wholes; regroup if their sum reaches a whole.