Subtracting a Fraction from a Mixed Number
4A · Chapter 7 · Lesson 5 · MATH-4A-C07-L05
Learning goal. Rename one whole into fractional units when the existing part is too small.
Before you begin
Recall: 4A Ch6: common units, equivalence and mixed number conversions; Adding Mixed Numbers. Try these three warm-up problems. If they are difficult, revisit the prerequisite lesson before advancing.
Calculate 2 1/6 + 4 2/3.
Show answer & reasoning
Combine wholes (2+4) and fractional parts (1/6+2/3); rename any extra whole.
Calculate 3 1/3 + 2 1/3.
Show answer & reasoning
Combine wholes (3+2) and fractional parts (1/3+1/3); rename any extra whole.
Calculate 2 1/2 + 2 3/5.
Show answer & reasoning
Combine wholes (2+2) and fractional parts (1/2+3/5); rename any extra 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
Subtraction sometimes requires exchanging a whole for fractional pieces. To find 3 1/4−3/4, rename the first amount as 2 5/4. Subtract 3/4 to leave 2 2/4 = 2 1/2. This is the fraction counterpart of regrouping tens into ones.
Model it: whole-to-four-quarters exchange bar. 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 2 1/6 − 2/3.
Rename one whole as denominator-sized parts if needed. The remaining quantity is 1 1/2.
Check your understanding 1
Calculate 2 1/12 − 5/6.
Show answer & reasoning
Rename one whole as denominator-sized parts if needed. The remaining quantity is 1 1/4.
Worked example 2
Calculate 2 1/4 − 1/2.
Rename one whole as denominator-sized parts if needed. The remaining quantity is 1 3/4.
Check your understanding 2
Calculate 4 1/4 − 1/2.
Show answer & reasoning
Rename one whole as denominator-sized parts if needed. The remaining quantity is 3 3/4.
Worked example 3
Calculate 4 1/3 − 2/3.
Rename one whole as denominator-sized parts if needed. The remaining quantity is 3 2/3.
Check your understanding 3
Calculate 3 1/2 − 1/2.
Show answer & reasoning
Rename one whole as denominator-sized parts if needed. The remaining quantity is 3.
Guided practice
Calculate 4 3/4 − 3/4.
Show answer & reasoning
Rename one whole as denominator-sized parts if needed. The remaining quantity is 4.
Calculate 5 1/3 − 1/3.
Show answer & reasoning
Rename one whole as denominator-sized parts if needed. The remaining quantity is 5.
Calculate 1 7/8 − 1/4.
Show answer & reasoning
Rename one whole as denominator-sized parts if needed. The remaining quantity is 1 5/8.
Calculate 5 1/2 − 2/3.
Show answer & reasoning
Rename one whole as denominator-sized parts if needed. The remaining quantity is 4 5/6.
Calculate 2 9/10 − 1/5.
Show answer & reasoning
Rename one whole as denominator-sized parts if needed. The remaining quantity is 2 7/10.
Independent practice
Calculate 4 3/4 − 1/2.
Show answer & reasoning
Rename one whole as denominator-sized parts if needed. The remaining quantity is 4 1/4.
Calculate 1 1/6 − 1/6.
Show answer & reasoning
Rename one whole as denominator-sized parts if needed. The remaining quantity is 1.
Calculate 5 2/3 − 1/3.
Show answer & reasoning
Rename one whole as denominator-sized parts if needed. The remaining quantity is 5 1/3.
Calculate 2 2/3 − 1/3.
Show answer & reasoning
Rename one whole as denominator-sized parts if needed. The remaining quantity is 2 1/3.
Calculate 4 1/4 − 1/3.
Show answer & reasoning
Rename one whole as denominator-sized parts if needed. The remaining quantity is 3 11/12.
Calculate 2 1/2 − 1/4.
Show answer & reasoning
Rename one whole as denominator-sized parts if needed. The remaining quantity is 2 1/4.
Calculate 1 1/6 − 1/3.
Show answer & reasoning
Rename one whole as denominator-sized parts if needed. The remaining quantity is 5/6.
Calculate 5 1/4 − 3/4.
Show answer & reasoning
Rename one whole as denominator-sized parts if needed. The remaining quantity is 4 1/2.
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 1/4 − 3/4 and writes 4 2/4. Identify the mistake and give the correct simplified answer.
Show answer & reasoning
Rename one whole as four fourths before subtracting; the correct difference is 3 1/2.
Calculate 2 11/12 − 5/6.
Show answer & reasoning
Rename one whole as denominator-sized parts if needed. The remaining quantity is 2 1/12.
Exit check
Calculate 1 2/3 − 1/3.
Show answer & reasoning
Rename one whole as denominator-sized parts if needed. The remaining quantity is 1 1/3.
Calculate 5 3/4 − 5/6.
Show answer & reasoning
Rename one whole as denominator-sized parts if needed. The remaining quantity is 4 11/12.
Calculate 1 3/4 − 1/2.
Show answer & reasoning
Rename one whole as denominator-sized parts if needed. The remaining quantity is 1 1/4.