Subtracting Mixed Numbers Worksheets with Detailed Solutions for Grade 4

Master subtracting mixed numbers: converting to improper fractions, borrowing, simplifying, through these 5 detailed exercises designed for worksheets.

Worksheet Problems 1 to 3 with Solutions
1 Basic subtraction without borrowing
Problem 1
Subtract:
\(3\frac{3}{4} - 1\frac{1}{4}\)
Definition:

Mixed number: A whole number combined with a fraction (e.g., \(3\frac{3}{4}\))

Improper fraction: A fraction where the numerator is greater than or equal to the denominator (e.g., \(\frac{15}{4}\))

Subtraction method:
  1. Subtract the whole numbers
  2. Subtract the fractions
  3. Combine the results
  4. Simplify the fraction if needed
Original Expression
\(3\frac{3}{4} - 1\frac{1}{4}\)
Subtract Wholes
\(2 + \frac{2}{4}\)
Simplify
\(2\frac{1}{2}\)
Step 1: Subtract the whole numbers

\(3 - 1 = 2\)

Step 2: Subtract the fractions

\(\frac{3}{4} - \frac{1}{4} = \frac{2}{4}\)

Step 3: Combine the results

\(2 + \frac{2}{4} = 2\frac{2}{4}\)

Step 4: Simplify the fraction

\(\frac{2}{4} = \frac{1}{2}\), so the answer is \(2\frac{1}{2}\)

\(3\frac{3}{4} - 1\frac{1}{4} = 2\frac{1}{2}\)
Final answer:

\(3\frac{3}{4} - 1\frac{1}{4} = 2\frac{1}{2}\)

Applied rules:

• Fraction subtraction: \(\frac{a}{c} - \frac{b}{c} = \frac{a-b}{c}\)

• Same denominators: Subtract numerators, keep denominator

• Simplification: Reduce fraction to lowest terms by dividing by GCD

33/4
-
11/4
=
22/4
→
21/2
2 Subtraction requiring borrowing
Problem 2
Subtract:
\(4\frac{1}{3} - 2\frac{2}{3}\)
Definition:

Borrowing: When the fraction part of the subtrahend is larger than the fraction part of the minuend, borrow 1 from the whole number part.

Original Expression
\(4\frac{1}{3} - 2\frac{2}{3}\)
Borrow 1
\(3\frac{4}{3} - 2\frac{2}{3}\)
Subtract
\(1\frac{2}{3}\)
Step 1: Identify the need to borrow

Since \(\frac{1}{3} < \frac{2}{3}\), we need to borrow from the whole number part.

Step 2: Borrow 1 from the whole number

Take 1 from 4, which equals \(\frac{3}{3}\)

Add to the fraction: \(\frac{1}{3} + \frac{3}{3} = \frac{4}{3}\)

New mixed number: \(3\frac{4}{3}\)

Step 3: Subtract the whole numbers

\(3 - 2 = 1\)

Step 4: Subtract the fractions

\(\frac{4}{3} - \frac{2}{3} = \frac{2}{3}\)

Step 5: Combine results

\(1 + \frac{2}{3} = 1\frac{2}{3}\)

\(4\frac{1}{3} - 2\frac{2}{3} = 1\frac{2}{3}\)
Final answer:

\(4\frac{1}{3} - 2\frac{2}{3} = 1\frac{2}{3}\)

Applied rules:

• Borrowing: When fraction part is smaller, borrow 1 from whole part

• Conversion: 1 whole = denominator over denominator

• Subtraction: Subtract whole numbers separately from fractions

41/3
→
34/3
-
22/3
=
12/3
3 Different denominators
Problem 3
Subtract:
\(5\frac{1}{2} - 2\frac{1}{3}\)
Definition:

Least Common Denominator (LCD): The smallest number that both denominators divide evenly into.

Original Expression
\(5\frac{1}{2} - 2\frac{1}{3}\)
Find LCD
\(5\frac{3}{6} - 2\frac{2}{6}\)
Result
\(3\frac{1}{6}\)
Step 1: Find the LCD

The denominators are 2 and 3. The LCD is 6.

Step 2: Convert fractions to equivalent forms

\(\frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6}\)

\(\frac{1}{3} = \frac{1 \times 2}{3 \times 2} = \frac{2}{6}\)

Step 3: Rewrite the expression

\(5\frac{3}{6} - 2\frac{2}{6}\)

Step 4: Subtract the whole numbers

\(5 - 2 = 3\)

Step 5: Subtract the fractions

\(\frac{3}{6} - \frac{2}{6} = \frac{1}{6}\)

Step 6: Combine results

\(3 + \frac{1}{6} = 3\frac{1}{6}\)

\(5\frac{1}{2} - 2\frac{1}{3} = 3\frac{1}{6}\)
Final answer:

\(5\frac{1}{2} - 2\frac{1}{3} = 3\frac{1}{6}\)

Applied rules:

• LCD: Find the least common multiple of denominators

• Equivalent fractions: Multiply numerator and denominator by same number

• Subtraction: Only possible when denominators are the same

51/2
→
53/6
-
21/3
→
22/6
=
31/6
Rules and Methods for Subtracting Mixed Numbers
\(a\frac{b}{c} = \frac{(a \times c) + b}{c}\)
Mixed Number to Improper Fraction
Rule 1
\(\frac{a}{c} - \frac{b}{c} = \frac{a-b}{c}\)
Same Denominator Subtraction
Rule 2
\(1 = \frac{n}{n}\)
Borrowing Identity
Rule 3
\(\frac{a}{b} = \frac{a \times n}{b \times n}\)
Equivalent Fractions
Key Steps: 1) Find LCD, 2) Convert fractions, 3) Borrow if needed, 4) Subtract, 5) Simplify
Visual Model: Use fraction bars or circles to represent mixed numbers
Worksheet Problems 4 to 5 with Solutions
4 Complex borrowing scenario
Problem 4
Subtract:
\(7\frac{1}{5} - 3\frac{4}{5}\)
Definition:

Regrouping: Converting a whole number to an equivalent fraction to facilitate subtraction.

Original Expression
\(7\frac{1}{5} - 3\frac{4}{5}\)
Borrow 1
\(6\frac{6}{5} - 3\frac{4}{5}\)
Subtract
\(3\frac{2}{5}\)
Step 1: Identify the need to borrow

Since \(\frac{1}{5} < \frac{4}{5}\), we need to borrow from the whole number part.

Step 2: Borrow 1 from the whole number

Take 1 from 7, which equals \(\frac{5}{5}\)

Add to the fraction: \(\frac{1}{5} + \frac{5}{5} = \frac{6}{5}\)

New mixed number: \(6\frac{6}{5}\)

Step 3: Subtract the whole numbers

\(6 - 3 = 3\)

Step 4: Subtract the fractions

\(\frac{6}{5} - \frac{4}{5} = \frac{2}{5}\)

Step 5: Combine results

\(3 + \frac{2}{5} = 3\frac{2}{5}\)

\(7\frac{1}{5} - 3\frac{4}{5} = 3\frac{2}{5}\)
Final answer:

\(7\frac{1}{5} - 3\frac{4}{5} = 3\frac{2}{5}\)

Applied rules:

• Regrouping: When fraction part is too small, convert 1 whole to fraction form

• Subtraction: Only subtract numerators when denominators match

• Combining: Add whole number result to fraction result

71/5
→
66/5
-
34/5
=
32/5
5 Multiple steps with simplification
Problem 5
Subtract:
\(6\frac{3}{8} - 2\frac{5}{12}\)
Definition:

Greatest Common Divisor (GCD): The largest number that divides both numerator and denominator.

Original Expression
\(6\frac{3}{8} - 2\frac{5}{12}\)
Find LCD
\(6\frac{9}{24} - 2\frac{10}{24}\)
Borrow
\(5\frac{33}{24} - 2\frac{10}{24}\)
Result
\(3\frac{23}{24}\)
Step 1: Find the LCD of 8 and 12

Factors of 8: 1, 2, 4, 8
Factors of 12: 1, 2, 3, 4, 6, 12
LCD = 24

Step 2: Convert fractions to equivalent forms

\(\frac{3}{8} = \frac{3 \times 3}{8 \times 3} = \frac{9}{24}\)

\(\frac{5}{12} = \frac{5 \times 2}{12 \times 2} = \frac{10}{24}\)

Step 3: Rewrite the expression

\(6\frac{9}{24} - 2\frac{10}{24}\)

Step 4: Identify need to borrow

Since \(\frac{9}{24} < \frac{10}{24}\), we need to borrow from the whole number.

Step 5: Borrow 1 from the whole number

Take 1 from 6, which equals \(\frac{24}{24}\)

Add to the fraction: \(\frac{9}{24} + \frac{24}{24} = \frac{33}{24}\)

New mixed number: \(5\frac{33}{24}\)

Step 6: Subtract the whole numbers

\(5 - 2 = 3\)

Step 7: Subtract the fractions

\(\frac{33}{24} - \frac{10}{24} = \frac{23}{24}\)

Step 8: Combine results

\(3 + \frac{23}{24} = 3\frac{23}{24}\)

\(6\frac{3}{8} - 2\frac{5}{12} = 3\frac{23}{24}\)
Final answer:

\(6\frac{3}{8} - 2\frac{5}{12} = 3\frac{23}{24}\)

Applied rules:

• LCD calculation: Find LCM of denominators using prime factorization

• Equivalent fractions: Multiply numerator and denominator by LCD factors

• Borrowing: Convert 1 whole to fraction form when needed

63/8
→
69/24
→
533/24
-
25/12
→
210/24
=
323/24
Complete Guide to Subtracting Mixed Numbers
\(a\frac{b}{c} = \frac{(a \times c) + b}{c}\)
Mixed Number Conversion
Key definitions:

Mixed Number: A combination of a whole number and a proper fraction (e.g., \(3\frac{1}{2}\))

Improper Fraction: A fraction where the numerator is greater than or equal to the denominator (e.g., \(\frac{7}{2}\))

Least Common Denominator (LCD): The smallest number that both denominators divide evenly into

Borrowing: Taking 1 whole unit and converting it to fractional form to allow subtraction

Complete methodology:
  1. Identify denominators: Check if they are the same or different
  2. Find LCD: If denominators differ, find the least common denominator
  3. Convert fractions: Change fractions to equivalent forms with the LCD
  4. Check for borrowing: If the fractional part of subtrahend > minuend, borrow 1 from whole number
  5. Subtract: Subtract whole numbers and fractions separately
  6. Simplify: Reduce fraction to lowest terms if possible
Tip 1: Always check if borrowing is needed BEFORE subtracting fractions.
Tip 2: When borrowing, 1 whole = denominator over denominator.
Tip 3: To find LCD, multiply denominators together (or find LCM for efficiency).
Tip 4: Always simplify your final answer by reducing fractions.
Common errors: Forgetting to borrow when needed, subtracting denominators instead of just numerators, not finding LCD for different denominators.
Memory aid: "Before you subtract fractions, make sure they have the same bottom number!"
Formulas to know by heart:

• Mixed to improper: \(a\frac{b}{c} = \frac{(a \times c) + b}{c}\)

• Equivalent fractions: \(\frac{a}{b} = \frac{a \times n}{b \times n}\)

• Fraction subtraction: \(\frac{a}{c} - \frac{b}{c} = \frac{a-b}{c}\)

• Borrowing: \(1 = \frac{n}{n}\) where n is the denominator

Worksheet Practice: Visualizing Mixed Number Subtraction
Visual Method: Fraction Bars
Using fraction bars to visualize:
\(4\frac{1}{3} - 1\frac{2}{3}\)
Visualization: Need to borrow since 1/3 < 2/3

Analysis: The visual representation helps understand why borrowing is necessary when subtracting mixed numbers.

  • Blue bars represent the minuend (what we're subtracting from)
  • Red bars represent the subtrahend (what we're subtracting)
  • When the fractional part of the subtrahend is larger, we must regroup

Questions & Answers

Question: I don't understand when I need to borrow when subtracting mixed numbers. Can you explain the rule?

Answer: Great question! You need to borrow when the fractional part of the number you're subtracting (the subtrahend) is larger than the fractional part of the number you're subtracting from (the minuend).

Example: In \(4\frac{1}{4} - 2\frac{3}{4}\), since \(\frac{1}{4} < \frac{3}{4}\), you need to borrow.

How to borrow:

  • Take 1 from the whole number part (4 becomes 3)
  • Convert that 1 to the same denominator: \(1 = \frac{4}{4}\)
  • Add it to the fractional part: \(\frac{1}{4} + \frac{4}{4} = \frac{5}{4}\)
  • Your new mixed number is \(3\frac{5}{4}\)

Now you can subtract: \(3\frac{5}{4} - 2\frac{3}{4} = 1\frac{2}{4} = 1\frac{1}{2}\)

Question: When I have different denominators like in \(3\frac{1}{2} - 1\frac{1}{3}\), how do I find the LCD quickly?

Answer: Here are quick methods to find the LCD:

  • If one denominator is a multiple of the other: Use the larger number. Example: denominators 2 and 4 → LCD = 4
  • For small numbers: List multiples of the larger denominator until you find one divisible by the smaller. For 2 and 3: multiples of 3 are 3, 6, 9... Since 6 ÷ 2 = 3, LCD = 6
  • As a last resort: Multiply the denominators together (not always the LCD but always works). For 2 and 3: 2 × 3 = 6

For your example \(3\frac{1}{2} - 1\frac{1}{3}\):

LCD of 2 and 3 is 6, so: \(\frac{1}{2} = \frac{3}{6}\) and \(\frac{1}{3} = \frac{2}{6}\)

Then: \(3\frac{3}{6} - 1\frac{2}{6} = 2\frac{1}{6}\)

Question: My child gets confused about converting mixed numbers to improper fractions. Is there an easy way to remember this?

Answer: Yes! Here's a memorable phrase: "Multiply the whole number by the denominator, then add the numerator."

Formula: \(a\frac{b}{c} = \frac{(a \times c) + b}{c}\)

Example: For \(4\frac{3}{5}\):

  • Multiply: \(4 \times 5 = 20\)
  • Add: \(20 + 3 = 23\)
  • Keep denominator: \(\frac{23}{5}\)

Memory trick: Think "MAD" - Multiply, Add, Denominator stays the same!

This conversion is especially helpful when dealing with complex borrowing situations, as it eliminates the need to consider whole numbers and fractions separately.