Expressing a Mixed Number as an Improper Fraction
4A · Chapter 6 · Lesson 5 · MATH-4A-C06-L06
Learning goal. Use equal-size parts to convert whole-plus-fraction to one improper fraction.
Before you begin
Recall: Grade 3B: fractions of equal wholes, equivalence, number lines and simplifying; Expressing an Improper Fraction as a Mixed Number. Try these three warm-up problems. If they are difficult, revisit the prerequisite lesson before advancing.
Write 7/6 as a mixed number in simplest form.
Show answer & reasoning
7 ÷ 6 gives 1 full wholes and 1 remaining parts of size 1/6. Simplify the fractional part to obtain 1 1/6.
Write 9/2 as a mixed number in simplest form.
Show answer & reasoning
9 ÷ 2 gives 4 full wholes and 1 remaining parts of size 1/2. Simplify the fractional part to obtain 4 1/2.
Write 9/8 as a mixed number in simplest form.
Show answer & reasoning
9 ÷ 8 gives 1 full wholes and 1 remaining parts of size 1/8. Simplify the fractional part to obtain 1 1/8.
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
Converting a mixed number works in reverse. Two and three fifths contains two sets of five fifths plus three extra fifths: 10/5 + 3/5 = 13/5. The whole number multiplies the denominator; then add the numerator. Leave the denominator unchanged because part size does not change.
Model it: whole bars partitioned into fifths. 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 3 6/12 as an improper fraction.
Each whole has 12 parts. 3 wholes and 6 more parts make 42 parts.
Check your understanding 1
Write 2 2/3 as an improper fraction.
Show answer & reasoning
Each whole has 3 parts. 2 wholes and 2 more parts make 8 parts.
Worked example 2
Write 4 1/2 as an improper fraction.
Each whole has 2 parts. 4 wholes and 1 more parts make 9 parts.
Check your understanding 2
Write 1 6/8 as an improper fraction.
Show answer & reasoning
Each whole has 8 parts. 1 wholes and 6 more parts make 14 parts.
Worked example 3
Write 5 1/4 as an improper fraction.
Each whole has 4 parts. 5 wholes and 1 more parts make 21 parts.
Check your understanding 3
Write 4 7/10 as an improper fraction.
Show answer & reasoning
Each whole has 10 parts. 4 wholes and 7 more parts make 47 parts.
Guided practice
Write 4 5/6 as an improper fraction.
Show answer & reasoning
Each whole has 6 parts. 4 wholes and 5 more parts make 29 parts.
Write 4 3/4 as an improper fraction.
Show answer & reasoning
Each whole has 4 parts. 4 wholes and 3 more parts make 19 parts.
Write 4 3/5 as an improper fraction.
Show answer & reasoning
Each whole has 5 parts. 4 wholes and 3 more parts make 23 parts.
Write 2 1/2 as an improper fraction.
Show answer & reasoning
Each whole has 2 parts. 2 wholes and 1 more parts make 5 parts.
Write 3 2/3 as an improper fraction.
Show answer & reasoning
Each whole has 3 parts. 3 wholes and 2 more parts make 11 parts.
Independent practice
Write 4 4/8 as an improper fraction.
Show answer & reasoning
Each whole has 8 parts. 4 wholes and 4 more parts make 36 parts.
Write 2 8/10 as an improper fraction.
Show answer & reasoning
Each whole has 10 parts. 2 wholes and 8 more parts make 28 parts.
Write 3 6/10 as an improper fraction.
Show answer & reasoning
Each whole has 10 parts. 3 wholes and 6 more parts make 36 parts.
Write 1 3/5 as an improper fraction.
Show answer & reasoning
Each whole has 5 parts. 1 wholes and 3 more parts make 8 parts.
Write 3 5/6 as an improper fraction.
Show answer & reasoning
Each whole has 6 parts. 3 wholes and 5 more parts make 23 parts.
Write 2 3/8 as an improper fraction.
Show answer & reasoning
Each whole has 8 parts. 2 wholes and 3 more parts make 19 parts.
Write 1 2/4 as an improper fraction.
Show answer & reasoning
Each whole has 4 parts. 1 wholes and 2 more parts make 6 parts.
Write 3 2/4 as an improper fraction.
Show answer & reasoning
Each whole has 4 parts. 3 wholes and 2 more parts make 14 parts.
Challenge and transfer
Explain the relationships and justify your method. Multiple correct approaches may be accepted if the reasoning is valid.
A student converts 2 3/5 to 5/13. Explain the mistake and provide the correct improper fraction.
Show answer & reasoning
Two wholes contain ten fifths, plus three fifths gives thirteen fifths.
Write 5 1/3 as an improper fraction.
Show answer & reasoning
Each whole has 3 parts. 5 wholes and 1 more parts make 16 parts.
Exit check
Write 5 1/2 as an improper fraction.
Show answer & reasoning
Each whole has 2 parts. 5 wholes and 1 more parts make 11 parts.
Write 1 2/3 as an improper fraction.
Show answer & reasoning
Each whole has 3 parts. 1 wholes and 2 more parts make 5 parts.
Write 3 3/4 as an improper fraction.
Show answer & reasoning
Each whole has 4 parts. 3 wholes and 3 more parts make 15 parts.