Subtracting Mixed Numbers
4A · Chapter 7 · Lesson 6 · MATH-4A-C07-L06
Learning goal. Subtract mixed quantities using common denominators and whole-number exchanges.
Before you begin
Recall: 4A Ch6: common units, equivalence and mixed number conversions; Subtracting a Fraction from a Mixed Number. Try these three warm-up problems. If they are difficult, revisit the prerequisite lesson before advancing.
Calculate 1 4/5 − 3/5.
Show answer & reasoning
Rename one whole as denominator-sized parts if needed. The remaining quantity is 1 1/5.
Calculate 3 3/5 − 3/5.
Show answer & reasoning
Rename one whole as denominator-sized parts if needed. The remaining quantity is 3.
Calculate 2 3/4 − 1/2.
Show answer & reasoning
Rename one whole as denominator-sized parts if needed. The remaining quantity is 2 1/4.
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
Subtract mixed numbers by first choosing equal-size fraction parts. If the upper fractional portion is too small, exchange one whole for a complete denominator-sized group. Then subtract fractional parts and whole parts separately. Verify by adding the difference back to the amount subtracted.
Model it: two aligned mixed-number bars with exchange. 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 4 7/10 − 2 4/5.
Subtract whole quantities and equivalent fractional parts, borrowing one whole if the first fractional part is smaller.
Check your understanding 1
Calculate 5 5/8 − 1 1/2.
Show answer & reasoning
Subtract whole quantities and equivalent fractional parts, borrowing one whole if the first fractional part is smaller.
Worked example 2
Calculate 3 1/2 − 2 1/4.
Subtract whole quantities and equivalent fractional parts, borrowing one whole if the first fractional part is smaller.
Check your understanding 2
Calculate 4 1/6 − 2 2/3.
Show answer & reasoning
Subtract whole quantities and equivalent fractional parts, borrowing one whole if the first fractional part is smaller.
Worked example 3
Calculate 4 1/2 − 1 2/3.
Subtract whole quantities and equivalent fractional parts, borrowing one whole if the first fractional part is smaller.
Check your understanding 3
Calculate 7 1/4 − 5 1/2.
Show answer & reasoning
Subtract whole quantities and equivalent fractional parts, borrowing one whole if the first fractional part is smaller.
Guided practice
Calculate 5 1/2 − 4 1/2.
Show answer & reasoning
Subtract whole quantities and equivalent fractional parts, borrowing one whole if the first fractional part is smaller.
Calculate 5 2/3 − 1 1/3.
Show answer & reasoning
Subtract whole quantities and equivalent fractional parts, borrowing one whole if the first fractional part is smaller.
Calculate 4 7/10 − 2 1/5.
Show answer & reasoning
Subtract whole quantities and equivalent fractional parts, borrowing one whole if the first fractional part is smaller.
Calculate 3 1/2 − 3 2/5.
Show answer & reasoning
Subtract whole quantities and equivalent fractional parts, borrowing one whole if the first fractional part is smaller.
Calculate 2 1/6 − 1 1/6.
Show answer & reasoning
Subtract whole quantities and equivalent fractional parts, borrowing one whole if the first fractional part is smaller.
Independent practice
Calculate 1 1/2 − 1 1/2.
Show answer & reasoning
Subtract whole quantities and equivalent fractional parts, borrowing one whole if the first fractional part is smaller.
Calculate 4 3/4 − 2 1/2.
Show answer & reasoning
Subtract whole quantities and equivalent fractional parts, borrowing one whole if the first fractional part is smaller.
Calculate 2 3/5 − 2 2/5.
Show answer & reasoning
Subtract whole quantities and equivalent fractional parts, borrowing one whole if the first fractional part is smaller.
Calculate 7 1/4 − 5 3/4.
Show answer & reasoning
Subtract whole quantities and equivalent fractional parts, borrowing one whole if the first fractional part is smaller.
Calculate 4 1/4 − 2 2/3.
Show answer & reasoning
Subtract whole quantities and equivalent fractional parts, borrowing one whole if the first fractional part is smaller.
Calculate 5 1/2 − 2 1/3.
Show answer & reasoning
Subtract whole quantities and equivalent fractional parts, borrowing one whole if the first fractional part is smaller.
Calculate 3 1/10 − 1 2/5.
Show answer & reasoning
Subtract whole quantities and equivalent fractional parts, borrowing one whole if the first fractional part is smaller.
Calculate 2 3/4 − 1 3/4.
Show answer & reasoning
Subtract whole quantities and equivalent fractional parts, borrowing one whole if the first fractional part is smaller.
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 1/4 − 1 3/4 and writes 2 2/4. Identify the mistake and give the correct simplified answer.
Show answer & reasoning
Exchange one whole for four fourths, then subtract the whole and fractional parts. The difference is 1 1/2.
Calculate 3 1/8 − 1 1/2.
Show answer & reasoning
Subtract whole quantities and equivalent fractional parts, borrowing one whole if the first fractional part is smaller.
Exit check
Calculate 3 1/2 − 1 1/3.
Show answer & reasoning
Subtract whole quantities and equivalent fractional parts, borrowing one whole if the first fractional part is smaller.
Calculate 3 4/5 − 3 4/5.
Show answer & reasoning
Subtract whole quantities and equivalent fractional parts, borrowing one whole if the first fractional part is smaller.
Calculate 5 1/4 − 4 1/2.
Show answer & reasoning
Subtract whole quantities and equivalent fractional parts, borrowing one whole if the first fractional part is smaller.