Convert improper fractions to mixed numbers using the division method
Convert mixed numbers to improper fractions using the multiply-and-add method
Compare and order mixed numbers using common denominators
Apply these skills to real-life contexts such as measurements and cooking
Real-World Applications
Cooking: A recipe calls for \(2\frac{3}{4}\) cups of flour — understanding mixed numbers means you can measure accurately.
Construction: A plank is \(\frac{13}{8}\) m long — converting to \(1\frac{5}{8}\) m makes it easier to measure on a ruler.
Comparing quantities: Which is more — \(2\frac{1}{3}\) litres or \(2\frac{1}{4}\) litres? Converting to a common denominator gives the answer instantly.
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An improper fraction has a numerator (top number) that is greater than or equal to its denominator (bottom number). It can be converted to a mixed number by dividing the numerator by the denominator.
Example 1 — Convert \(\frac{11}{4}\) to a mixed number
Step 1
Divide: \(11 \div 4 = 2\) remainder \(3\)
Step 2
Whole number \(= 2\), new numerator \(= 3\), denominator stays \(= 4\)
Step 3
Answer: \(\mathbf{2\frac{3}{4}}\)
Example 2 — Convert \(\frac{17}{5}\) to a mixed number
Step 1
Divide: \(17 \div 5 = 3\) remainder \(2\)
Step 2
Answer: \(\mathbf{3\frac{2}{5}}\)
Key tip: The denominator NEVER changes when converting — it stays the same throughout. Only the whole number and the new numerator change.
This is the reverse process. To convert a mixed number to an improper fraction: multiply the whole number by the denominator, then add the numerator. The denominator stays the same.
Example 3 — Convert \(3\frac{3}{4}\) to an improper fraction
To compare mixed numbers, first compare the whole-number parts. If they are equal, compare the fraction parts using a common denominator. This skill is essential for real-life tasks like cooking quantities and taking measurements.
Example 5 — Order \(2\frac{1}{3}\), \(1\frac{3}{4}\), \(2\frac{1}{4}\) from smallest to largest
Step 1
\(1\frac{3}{4}\) is smallest — whole number 1 < 2, so it comes first regardless of fraction part
Step 2
Compare \(2\frac{1}{3}\) and \(2\frac{1}{4}\): common denominator 12. \(\frac{1}{3} = \frac{4}{12}\), \(\frac{1}{4} = \frac{3}{12}\). Since \(\frac{3}{12} < \frac{4}{12}\), we have \(2\frac{1}{4} < 2\frac{1}{3}\)
Example 6 — Order planks: \(1\frac{5}{8}\) m, \(1\frac{1}{2}\) m, \(1\frac{3}{4}\) m from shortest to longest
Step 1
All have whole number 1 — compare fractions using denominator 8: \(\frac{1}{2} = \frac{4}{8}\), \(\frac{5}{8} = \frac{5}{8}\), \(\frac{3}{4} = \frac{6}{8}\)
Step 2
Order of fractions: \(\frac{4}{8} < \frac{5}{8} < \frac{6}{8}\)
Exam tip: In exams, always convert to a common denominator before comparing fractions. Never compare by looking at numerators alone without checking the denominator.
✓ Quick Check 3 — Comparing and Ordering Mixed Numbers
Question 1 of 10
Practice: Convert Between Mixed Numbers and Improper Fractions
Type your answers, then click Check Answers. For mixed numbers write e.g. 2 1/3. For improper fractions write e.g. 7/3.
Part A — Improper Fraction to Mixed Number
#
Question
Answer
Result
1
\(\frac{7}{3}\)
2
\(\frac{11}{4}\)
3
\(\frac{13}{5}\)
4
\(\frac{9}{2}\)
5
\(\frac{17}{6}\)
Part B — Mixed Number to Improper Fraction
#
Convert this mixed number
Your answer
Result
6
\(2\frac{1}{3}\)
7
\(3\frac{1}{4}\)
8
\(4\frac{2}{5}\)
9
\(1\frac{5}{8}\)
10
\(5\frac{1}{2}\)
⚠ Things to Watch Out For
Converting mixed → improper: forgetting to add the numerator: 2⅗ = (2×5)+3 / 5 = 13/5. Students often just multiply: 2×5=10/5, forgetting to add the 3.
Converting improper → mixed: using the wrong operation: Divide the numerator by the denominator. 13÷5 = 2 remainder 3 → 2 and 3/5. Do NOT divide denominator by numerator.
Leaving an improper fraction in the answer: In most contexts, especially worded problems, give your answer as a mixed number. Check what the question asks for.
Negative mixed numbers: the minus sign applies to the whole mixed number, not just the whole-number part. Convert as if it were positive first, then negate: \(2\frac{1}{3} = \frac{7}{3}\) (multiply 2×3, add 1), so \(-2\frac{1}{3} = -\frac{7}{3}\) — it is not \(-2 + \frac{1}{3}\), which would be a different (larger) value.
Adding mixed numbers by converting incorrectly: When adding mixed numbers, either convert both to improper fractions OR add the whole number parts and fraction parts separately. Don't mix the two approaches.