Adding and Subtracting Fractions — Part 2
4A · Chapter 7 · Lesson 2 · MATH-4A-C07-L02
Learning goal. Use equivalence to rename fractions with unlike but related denominators.
Before you begin
Recall: 4A Ch6: common units, equivalence and mixed number conversions; Adding and Subtracting Fractions — Part 1. Try these three warm-up problems. If they are difficult, revisit the prerequisite lesson before advancing.
Calculate 11/12 + 5/6. Simplify.
Show answer & reasoning
Use the common denominator 12, then add the equal-size parts. The simplified result is 1 3/4.
Calculate 3/8 − 1/4. Simplify.
Show answer & reasoning
Use the common denominator 8, then subtract the equal-size parts. The simplified result is 1/8.
Calculate 1/6 + 1/2. Simplify.
Show answer & reasoning
Use the common denominator 6, then add the equal-size parts. The simplified result is 2/3.
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
Unlike fractions must first be expressed using equal-size parts. For 1/2+1/4, rename the half as 2/4, then combine three fourths. Using a common denominator is a formal way of ensuring each counted part has the same area or length.
Model it: paired fraction strips with common partitions. 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 1/8 + 1/2. Simplify.
Use the common denominator 8, then add the equal-size parts. The simplified result is 5/8.
Check your understanding 1
Calculate 1/6 + 5/6. Simplify.
Show answer & reasoning
Use the common denominator 6, then add the equal-size parts. The simplified result is 1.
Worked example 2
Calculate 5/6 − 1/3. Simplify.
Use the common denominator 6, then subtract the equal-size parts. The simplified result is 1/2.
Check your understanding 2
Calculate 1/2 − 1/3. Simplify.
Show answer & reasoning
Use the common denominator 6, then subtract the equal-size parts. The simplified result is 1/6.
Worked example 3
Calculate 1/5 + 3/5. Simplify.
Use the common denominator 5, then add the equal-size parts. The simplified result is 4/5.
Check your understanding 3
Calculate 1/4 + 1/2. Simplify.
Show answer & reasoning
Use the common denominator 4, then add the equal-size parts. The simplified result is 3/4.
Guided practice
Calculate 3/4 − 1/2. Simplify.
Show answer & reasoning
Use the common denominator 4, then subtract the equal-size parts. The simplified result is 1/4.
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 2/5 − 2/5. Simplify.
Show answer & reasoning
Use the common denominator 5, then subtract the equal-size parts. The simplified result is 0.
Calculate 2/3 − 1/3. Simplify.
Show answer & reasoning
Use the common denominator 3, then subtract the equal-size parts. The simplified result is 1/3.
Calculate 5/6 + 2/3. Simplify.
Show answer & reasoning
Use the common denominator 6, then add the equal-size parts. The simplified result is 1 1/2.
Independent practice
Calculate 1/2 − 1/4. Simplify.
Show answer & reasoning
Use the common denominator 4, then subtract the equal-size parts. The simplified result is 1/4.
Calculate 1/4 + 3/4. Simplify.
Show answer & reasoning
Use the common denominator 4, then add the equal-size parts. The simplified result is 1.
Calculate 1/3 − 1/3. Simplify.
Show answer & reasoning
Use the common denominator 3, then subtract the equal-size parts. The simplified result is 0.
Calculate 2/3 − 5/12. Simplify.
Show answer & reasoning
Use the common denominator 12, then subtract the equal-size parts. The simplified result is 1/4.
Calculate 1/6 + 2/3. Simplify.
Show answer & reasoning
Use the common denominator 6, then add the equal-size parts. The simplified result is 5/6.
Calculate 3/10 + 1/5. Simplify.
Show answer & reasoning
Use the common denominator 10, then add the equal-size parts. The simplified result is 1/2.
Calculate 1/4 − 1/4. Simplify.
Show answer & reasoning
Use the common denominator 4, then subtract the equal-size parts. The simplified result is 0.
Calculate 4/5 + 1/5. Simplify.
Show answer & reasoning
Use the common denominator 5, then add the equal-size parts. The simplified result is 1.
Challenge and transfer
Explain the relationships and justify your method. Multiple correct approaches may be accepted if the reasoning is valid.
A student calculates 2/5 + 1/2 and writes 3/7. Identify the mistake and give the correct simplified answer.
Show answer & reasoning
Use equal-size fractional parts with denominator 10; the correct sum is 9/10.
Calculate 2/3 + 5/6. Simplify.
Show answer & reasoning
Use the common denominator 6, then add the equal-size parts. The simplified result is 1 1/2.
Exit check
Calculate 5/8 − 1/4. Simplify.
Show answer & reasoning
Use the common denominator 8, then subtract the equal-size parts. The simplified result is 3/8.
Calculate 3/4 + 1/2. Simplify.
Show answer & reasoning
Use the common denominator 4, then add the equal-size parts. The simplified result is 1 1/4.
Calculate 1/5 + 2/5. Simplify.
Show answer & reasoning
Use the common denominator 5, then add the equal-size parts. The simplified result is 3/5.