Adding Mixed Numbers
4A · Chapter 7 · Lesson 4 · MATH-4A-C07-L04
Learning goal. Combine whole and fractional parts and rename improper fractional results.
Before you begin
Recall: 4A Ch6: common units, equivalence and mixed number conversions; Adding a Mixed Number and a Fraction. Try these three warm-up problems. If they are difficult, revisit the prerequisite lesson before advancing.
Calculate 5 5/8 + 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 2 2/5 + 1/5.
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 1/12 + 5/6.
Show answer & reasoning
Add the fractional parts with a common denominator. Include the original 2 wholes; regroup if their sum reaches a whole.
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
To add mixed numbers, combine whole portions and fractional portions separately. For 1 2/3 + 2 1/2, add three wholes and then 4/6+3/6 = 7/6, producing 4 1/6. Check whether the fractional sum contains another whole before giving the answer.
Model it: combined whole-unit bars and sixth strips. 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 1/2 + 3 1/2.
Combine wholes (5+3) and fractional parts (1/2+1/2); rename any extra whole.
Check your understanding 1
Calculate 4 1/12 + 4 1/2.
Show answer & reasoning
Combine wholes (4+4) and fractional parts (1/12+1/2); rename any extra whole.
Worked example 2
Calculate 4 3/4 + 1 1/4.
Combine wholes (4+1) and fractional parts (3/4+1/4); rename any extra whole.
Check your understanding 2
Calculate 2 1/6 + 2 1/3.
Show answer & reasoning
Combine wholes (2+2) and fractional parts (1/6+1/3); rename any extra whole.
Worked example 3
Calculate 3 7/8 + 2 1/2.
Combine wholes (3+2) and fractional parts (7/8+1/2); rename any extra whole.
Check your understanding 3
Calculate 1 1/2 + 2 1/2.
Show answer & reasoning
Combine wholes (1+2) and fractional parts (1/2+1/2); rename any extra whole.
Guided practice
Calculate 4 3/10 + 3 1/5.
Show answer & reasoning
Combine wholes (4+3) and fractional parts (3/10+1/5); rename any extra whole.
Calculate 2 5/12 + 3 2/3.
Show answer & reasoning
Combine wholes (2+3) and fractional parts (5/12+2/3); rename any extra whole.
Calculate 2 1/4 + 1 1/2.
Show answer & reasoning
Combine wholes (2+1) and fractional parts (1/4+1/2); rename any extra whole.
Calculate 5 1/2 + 2 1/2.
Show answer & reasoning
Combine wholes (5+2) and fractional parts (1/2+1/2); rename any extra whole.
Calculate 1 3/8 + 3 1/4.
Show answer & reasoning
Combine wholes (1+3) and fractional parts (3/8+1/4); rename any extra whole.
Independent practice
Calculate 5 9/10 + 4 2/5.
Show answer & reasoning
Combine wholes (5+4) and fractional parts (9/10+2/5); rename any extra whole.
Calculate 4 5/6 + 3 5/6.
Show answer & reasoning
Combine wholes (4+3) and fractional parts (5/6+5/6); rename any extra whole.
Calculate 1 1/8 + 1 1/2.
Show answer & reasoning
Combine wholes (1+1) and fractional parts (1/8+1/2); rename any extra whole.
Calculate 5 11/12 + 3 1/6.
Show answer & reasoning
Combine wholes (5+3) and fractional parts (11/12+1/6); rename any extra whole.
Calculate 2 2/3 + 4 1/2.
Show answer & reasoning
Combine wholes (2+4) and fractional parts (2/3+1/2); rename any extra whole.
Calculate 5 3/4 + 1 3/4.
Show answer & reasoning
Combine wholes (5+1) and fractional parts (3/4+3/4); rename any extra whole.
Calculate 2 9/10 + 2 2/5.
Show answer & reasoning
Combine wholes (2+2) and fractional parts (9/10+2/5); rename any extra whole.
Calculate 5 1/10 + 3 2/5.
Show answer & reasoning
Combine wholes (5+3) and fractional parts (1/10+2/5); rename any extra 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 4 1/2 + 2 2/3 and writes 6 3/5. Identify the mistake and give the correct simplified answer.
Show answer & reasoning
Combine 6 wholes and 3/6+4/6=7/6, regrouping one additional whole to reach 7 1/6.
Calculate 2 1/2 + 4 1/2.
Show answer & reasoning
Combine wholes (2+4) and fractional parts (1/2+1/2); rename any extra whole.
Exit check
Calculate 2 3/4 + 1 1/2.
Show answer & reasoning
Combine wholes (2+1) and fractional parts (3/4+1/2); rename any extra whole.
Calculate 1 3/8 + 4 3/4.
Show answer & reasoning
Combine wholes (1+4) and fractional parts (3/8+3/4); rename any extra whole.
Calculate 5 5/6 + 4 1/3.
Show answer & reasoning
Combine wholes (5+4) and fractional parts (5/6+1/3); rename any extra whole.