Expressing an Improper Fraction as a Mixed Number
4A · Chapter 6 · Lesson 4 · MATH-4A-C06-L05
Learning goal. Use quotient and remainder to convert a nonnegative improper fraction into a mixed number.
Before you begin
Recall: Grade 3B: fractions of equal wholes, equivalence, number lines and simplifying; Improper Fractions and Mixed Numbers. Try these three warm-up problems. If they are difficult, revisit the prerequisite lesson before advancing.
Write 6/4 as a mixed number in simplest form.
Show answer & reasoning
6 ÷ 4 gives 1 full wholes and 2 remaining parts of size 1/4. Simplify the fractional part to obtain 1 1/2.
Write 71/12 as a mixed number in simplest form.
Show answer & reasoning
71 ÷ 12 gives 5 full wholes and 11 remaining parts of size 1/12. Simplify the fractional part to obtain 5 11/12.
Write 9/6 as a mixed number in simplest form.
Show answer & reasoning
9 ÷ 6 gives 1 full wholes and 3 remaining parts of size 1/6. Simplify the fractional part to obtain 1 1/2.
Key vocabulary
- equivalent fractions
- different numerators and denominators representing the same quantity
- mixed number
- whole number plus proper fraction
- improper fraction
- fraction with numerator at least its denominator
- denominator
- number of equal parts in one whole
Understand the concept
Convert an improper fraction to a mixed number by counting complete groups of denominator-sized parts. Eleven thirds contain three complete groups of three thirds, with two thirds left. Thus 11/3 = 3 2/3. When the division has no remainder, write a whole number instead of a mixed fraction with a zero numerator.
Model it: groups of denominator equal parts. 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
Write 16/3 as a mixed number in simplest form.
16 ÷ 3 gives 5 full wholes and 1 remaining parts of size 1/3. Simplify the fractional part to obtain 5 1/3.
Check your understanding 1
Write 49/12 as a mixed number in simplest form.
Show answer & reasoning
49 ÷ 12 gives 4 full wholes and 1 remaining parts of size 1/12. Simplify the fractional part to obtain 4 1/12.
Worked example 2
Write 32/6 as a mixed number in simplest form.
32 ÷ 6 gives 5 full wholes and 2 remaining parts of size 1/6. Simplify the fractional part to obtain 5 1/3.
Check your understanding 2
Write 41/12 as a mixed number in simplest form.
Show answer & reasoning
41 ÷ 12 gives 3 full wholes and 5 remaining parts of size 1/12. Simplify the fractional part to obtain 3 5/12.
Worked example 3
Write 25/6 as a mixed number in simplest form.
25 ÷ 6 gives 4 full wholes and 1 remaining parts of size 1/6. Simplify the fractional part to obtain 4 1/6.
Check your understanding 3
Write 17/3 as a mixed number in simplest form.
Show answer & reasoning
17 ÷ 3 gives 5 full wholes and 2 remaining parts of size 1/3. Simplify the fractional part to obtain 5 2/3.
Guided practice
Write 29/12 as a mixed number in simplest form.
Show answer & reasoning
29 ÷ 12 gives 2 full wholes and 5 remaining parts of size 1/12. Simplify the fractional part to obtain 2 5/12.
Write 45/10 as a mixed number in simplest form.
Show answer & reasoning
45 ÷ 10 gives 4 full wholes and 5 remaining parts of size 1/10. Simplify the fractional part to obtain 4 1/2.
Write 39/12 as a mixed number in simplest form.
Show answer & reasoning
39 ÷ 12 gives 3 full wholes and 3 remaining parts of size 1/12. Simplify the fractional part to obtain 3 1/4.
Write 27/5 as a mixed number in simplest form.
Show answer & reasoning
27 ÷ 5 gives 5 full wholes and 2 remaining parts of size 1/5. Simplify the fractional part to obtain 5 2/5.
Write 13/8 as a mixed number in simplest form.
Show answer & reasoning
13 ÷ 8 gives 1 full wholes and 5 remaining parts of size 1/8. Simplify the fractional part to obtain 1 5/8.
Independent practice
Write 5/2 as a mixed number in simplest form.
Show answer & reasoning
5 ÷ 2 gives 2 full wholes and 1 remaining parts of size 1/2. Simplify the fractional part to obtain 2 1/2.
Write 19/4 as a mixed number in simplest form.
Show answer & reasoning
19 ÷ 4 gives 4 full wholes and 3 remaining parts of size 1/4. Simplify the fractional part to obtain 4 3/4.
Write 13/4 as a mixed number in simplest form.
Show answer & reasoning
13 ÷ 4 gives 3 full wholes and 1 remaining parts of size 1/4. Simplify the fractional part to obtain 3 1/4.
Write 21/4 as a mixed number in simplest form.
Show answer & reasoning
21 ÷ 4 gives 5 full wholes and 1 remaining parts of size 1/4. Simplify the fractional part to obtain 5 1/4.
Write 20/12 as a mixed number in simplest form.
Show answer & reasoning
20 ÷ 12 gives 1 full wholes and 8 remaining parts of size 1/12. Simplify the fractional part to obtain 1 2/3.
Write 16/10 as a mixed number in simplest form.
Show answer & reasoning
16 ÷ 10 gives 1 full wholes and 6 remaining parts of size 1/10. Simplify the fractional part to obtain 1 3/5.
Write 9/4 as a mixed number in simplest form.
Show answer & reasoning
9 ÷ 4 gives 2 full wholes and 1 remaining parts of size 1/4. Simplify the fractional part to obtain 2 1/4.
Write 7/3 as a mixed number in simplest form.
Show answer & reasoning
7 ÷ 3 gives 2 full wholes and 1 remaining parts of size 1/3. Simplify the fractional part to obtain 2 1/3.
Challenge and transfer
Explain the relationships and justify your method. Multiple correct approaches may be accepted if the reasoning is valid.
A student says 11/3 = 3 1/3. Use groups of thirds to correct the mixed number.
Show answer & reasoning
Eleven thirds contain three groups of three thirds with two thirds left.
Write 5/4 as a mixed number in simplest form.
Show answer & reasoning
5 ÷ 4 gives 1 full wholes and 1 remaining parts of size 1/4. Simplify the fractional part to obtain 1 1/4.
Exit check
Write 57/10 as a mixed number in simplest form.
Show answer & reasoning
57 ÷ 10 gives 5 full wholes and 7 remaining parts of size 1/10. Simplify the fractional part to obtain 5 7/10.
Write 41/8 as a mixed number in simplest form.
Show answer & reasoning
41 ÷ 8 gives 5 full wholes and 1 remaining parts of size 1/8. Simplify the fractional part to obtain 5 1/8.
Write 8/6 as a mixed number in simplest form.
Show answer & reasoning
8 ÷ 6 gives 1 full wholes and 2 remaining parts of size 1/6. Simplify the fractional part to obtain 1 1/3.