Adding and Subtracting Fractions — Part 1
4A · Chapter 7 · Lesson 1 · MATH-4A-C07-L01
Learning goal. Add and subtract like-denominator fractions with consistent unit-whole diagrams.
Before you begin
Recall: 4A Ch6: common units, equivalence and mixed number conversions. Try these three warm-up problems. If they are difficult, revisit the prerequisite lesson before advancing.
10 identical pies are shared equally among 2 children. What fraction of one pie does each child get?
Show answer & reasoning
Divide 10 equal wholes into 2 shares: each gets 10/2 of a pie, equivalent to 5.
4 identical pies are shared equally among 2 children. What fraction of one pie does each child get?
Show answer & reasoning
Divide 4 equal wholes into 2 shares: each gets 4/2 of a pie, equivalent to 2.
1 identical pies are shared equally among 6 children. What fraction of one pie does each child get?
Show answer & reasoning
Divide 1 equal wholes into 6 shares: each gets 1/6 of a pie, equivalent to 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
When fractions have the same denominator, they count parts of the same size. Add or subtract the numerators and keep the denominator. For 3/8+2/8, the result is 5/8; the eighths do not become sixteenths. Simplify the result when the numerator and denominator share a factor.
Model it: equal-eighth fraction strip. 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 1/5 + 2/5. Simplify.
Use the common denominator 5, then add the equal-size parts. The simplified result is 3/5.
Check your understanding 1
Calculate 2/3 + 1/2. Simplify.
Show answer & reasoning
Use the common denominator 6, then add the equal-size parts. The simplified result is 1 1/6.
Worked example 2
Calculate 2/3 − 1/2. Simplify.
Use the common denominator 6, then subtract the equal-size parts. The simplified result is 1/6.
Check your understanding 2
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.
Worked example 3
Calculate 1/3 + 2/3. Simplify.
Use the common denominator 3, then add the equal-size parts. The simplified result is 1.
Check your understanding 3
Calculate 1/2 + 1/4. Simplify.
Show answer & reasoning
Use the common denominator 4, then add the equal-size parts. The simplified result is 3/4.
Guided practice
Calculate 4/5 + 7/10. Simplify.
Show answer & reasoning
Use the common denominator 10, then add the equal-size parts. The simplified result is 1 1/2.
Calculate 9/10 − 2/5. Simplify.
Show answer & reasoning
Use the common denominator 10, then subtract the equal-size parts. The simplified result is 1/2.
Calculate 9/10 − 1/2. Simplify.
Show answer & reasoning
Use the common denominator 10, then subtract the equal-size parts. The simplified result is 2/5.
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 1/3 − 1/6. Simplify.
Show answer & reasoning
Use the common denominator 6, then subtract the equal-size parts. The simplified result is 1/6.
Independent practice
Calculate 3/4 − 3/8. Simplify.
Show answer & reasoning
Use the common denominator 8, then subtract the equal-size parts. The simplified result is 3/8.
Calculate 1/4 + 5/6. Simplify.
Show answer & reasoning
Use the common denominator 12, then add the equal-size parts. The simplified result is 1 1/12.
Calculate 5/6 − 1/2. Simplify.
Show answer & reasoning
Use the common denominator 6, then subtract the equal-size parts. The simplified result is 1/3.
Calculate 3/4 + 1/4. Simplify.
Show answer & reasoning
Use the common denominator 4, then add the equal-size parts. The simplified result is 1.
Calculate 7/10 − 7/10. Simplify.
Show answer & reasoning
Use the common denominator 10, then subtract the equal-size parts. The simplified result is 0.
Calculate 3/10 + 2/5. Simplify.
Show answer & reasoning
Use the common denominator 10, then add the equal-size parts. The simplified result is 7/10.
Calculate 1/3 + 5/6. Simplify.
Show answer & reasoning
Use the common denominator 6, then add the equal-size parts. The simplified result is 1 1/6.
Calculate 11/12 + 2/3. Simplify.
Show answer & reasoning
Use the common denominator 12, then add the equal-size parts. The simplified result is 1 7/12.
Challenge and transfer
Explain the relationships and justify your method. Multiple correct approaches may be accepted if the reasoning is valid.
A student calculates 3/6 + 2/6 and writes 5/12. Identify the mistake and give the correct simplified answer.
Show answer & reasoning
Both pieces are 6ths, so combine numerators and keep the denominator. The result is 5/6.
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 3/4 − 1/4. Simplify.
Show answer & reasoning
Use the common denominator 4, then subtract the equal-size parts. The simplified result is 1/2.
Calculate 1/4 + 1/6. Simplify.
Show answer & reasoning
Use the common denominator 12, then add the equal-size parts. The simplified result is 5/12.
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.