Finding a common multiple quickly: List multiples of the larger denominator (6, 12, 18…) and stop at the first one the smaller denominator also divides into.
✓ Quick Check 2 — Different Denominators
Question 1 of 10
Mixed Numbers and Real-Life Problems
A mixed number has a whole part and a fraction part (e.g. \(2\frac{3}{4}\)). You can add/subtract mixed numbers by either:
Method A: Deal with whole numbers and fractions separately, then combine.
Method B: Convert to improper fractions first, then add/subtract.
Example 5 — \(2\frac{3}{4} - 1\frac{1}{3}\) (Method A: separate parts)
Step 1
Subtract whole numbers: \(2 - 1 = 1\)
Step 2
Subtract fractions — LCM of 4 and 3 is 12: \(\frac{3}{4} - \frac{1}{3} = \frac{9}{12} - \frac{4}{12} = \frac{5}{12}\)
Example 6 — A plank is \(3\frac{1}{2}\) m long. You cut off \(1\frac{3}{4}\) m. How much is left?
Step 1
Convert to improper fractions: \(3\frac{1}{2} = \frac{7}{2}\) \(1\frac{3}{4} = \frac{7}{4}\)
Step 2
LCM of 2 and 4 is 4. Convert: \(\frac{7}{2} = \frac{14}{4}\)
Step 3
\(\frac{14}{4} - \frac{7}{4} = \frac{7}{4} = \mathbf{1\frac{3}{4}}\) m remaining
Example 6b — \(4\frac{1}{3} - 1\frac{3}{4}\) (Method A, with borrowing)
Step 1
Subtract the fraction parts first — LCM of 3 and 4 is 12: \(\frac{1}{3} - \frac{3}{4} = \frac{4}{12} - \frac{9}{12}\). But \(4 < 9\), so this would go negative.
Step 2 — borrow
Take 1 whole from the 4, leaving 3, and turn that whole into twelfths to add to the \(\frac{4}{12}\): \(\frac{4}{12} + \frac{12}{12} = \frac{16}{12}\)
Step 3
Now subtract: \(\frac{16}{12} - \frac{9}{12} = \frac{7}{12}\)
Step 4
Combine with the reduced whole number: \(3 - 1 = 2\), so the answer is \(\mathbf{2\frac{7}{12}}\)
Borrowing check: Before subtracting mixed numbers, always compare the fraction parts first. If the fraction you're subtracting is bigger than the fraction you're subtracting from (like \(\frac{1}{3}\) vs \(\frac{3}{4}\) above), you must borrow 1 from the whole number — exactly like borrowing in column subtraction. Skipping this step is one of the most common mistakes with mixed-number subtraction.
✓ Quick Check 3 — Mixed Numbers and Real-Life
Question 1 of 10
Practice: Mixed Number Calculations
Work out each answer. Write as a mixed number or simplified fraction, then click Check All.
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Question
Answer
Result
1
1½ + 2¼
2
3⅓ + 1½
3
2¾ − 1¼
4
2⅔ + 1⅓
5
3½ − 1¾
6
1⅕ + 2⅖
7
4⅓ − 2⅙
8
2½ + 3⅔
9
5¼ − 2½
10
1¾ + 2¼
⚠ Things to Watch Out For
Adding denominators together: ½ + ⅓ ≠ 2/5. You must find a common denominator first. The denominator tells you the size of each piece — you can only add pieces of the same size.
Finding the common denominator incorrectly: The common denominator must be a multiple of BOTH denominators. For ½ + ⅓, use 6 (not 5). Convert: 3/6 + 2/6 = 5/6.
Changing the value when converting: To convert ½ to sixths: multiply top AND bottom by 3 → 3/6. If you only change the bottom, the fraction's value changes.
Not simplifying the answer: 4/8 should be simplified to ½. Always check if the answer simplifies.
Mixed numbers — not converting first: For 1½ + 2⅓, it's safest to convert to improper fractions first (3/2 + 7/3), find a common denominator, then convert back.