Worksheet: Subtracting Mixed Numbers with Same Denominator in Grade 4

Master subtracting mixed numbers with same denominator: borrowing, regrouping, step-by-step solutions through this comprehensive worksheet.

Worksheet Summary & Key Concepts
Key Definitions:

Mixed Number: A number combining a whole number and a fraction (e.g., \(3\frac{2}{5}\))

Same Denominator: Both mixed numbers have identical denominators in their fractional parts

Borrowing/Regrouping: Taking 1 whole unit and converting it to fractional form when the top fraction is smaller than the bottom fraction

Improper Fraction: A fraction where numerator ≥ denominator (e.g., \(\frac{7}{5}\))

Subtraction Method Steps:
  1. Check denominators: Ensure both mixed numbers have the same denominator
  2. Compare fractional parts: If top fraction ≥ bottom fraction, proceed normally
  3. Borrow if needed: If top fraction < bottom fraction, borrow 1 from the whole number
  4. Convert borrowed amount: 1 whole = denominator/denominator (e.g., 1 = 5/5)
  5. Add to top fraction: Combine borrowed fraction with original top fraction
  6. Subtract components: Subtract whole numbers and fractional parts separately
  7. Simplify: Reduce the resulting fraction to lowest terms if possible
Important Rules & Laws:

Rule 1: When denominators are the same, subtract numerators and keep denominator: \(\frac{a}{c} - \frac{b}{c} = \frac{a-b}{c}\)

Rule 2: Borrowing rule: Take 1 from whole number, convert to fractional form using denominator

Rule 3: Always check if the resulting fraction can be simplified

Common Mistakes & Tips:

Mistake 1: Forgetting to borrow when top fraction is smaller than bottom fraction

Mistake 2: Subtracting denominators instead of keeping them the same

Mistake 3: Not simplifying the final fraction

Tip 1: Always check if you need to borrow BEFORE starting subtraction

Tip 2: Remember: 1 whole = denominator/denominator (e.g., 1 = 4/4 when denominator is 4)

Problem Set 1-3: Basic Subtraction
Problem 1: No borrowing needed
1. Subtract: \(4\frac{3}{5} - 2\frac{1}{5}\)
Analysis:

Since \(\frac{3}{5} > \frac{1}{5}\), we don't need to borrow.

Expression
\(4\frac{3}{5} - 2\frac{1}{5}\)
Separate
\((4 - 2) + (\frac{3}{5} - \frac{1}{5})\)
Result
\(2\frac{2}{5}\)
Step 1: Subtract whole numbers

\(4 - 2 = 2\)

Step 2: Subtract fractional parts

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

Step 3: Combine results

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

\(4\frac{3}{5} - 2\frac{1}{5} = 2\frac{2}{5}\)
Final answer: \(2\frac{2}{5}\)
Problem 2: No borrowing needed
2. Subtract: \(7\frac{5}{8} - 3\frac{2}{8}\)
Analysis:

Since \(\frac{5}{8} > \frac{2}{8}\), we don't need to borrow.

Expression
\(7\frac{5}{8} - 3\frac{2}{8}\)
Subtract
\(4\frac{3}{8}\)
Step 1: Subtract whole numbers

\(7 - 3 = 4\)

Step 2: Subtract fractional parts

\(\frac{5}{8} - \frac{2}{8} = \frac{3}{8}\)

Step 3: Combine results

\(4\frac{3}{8}\)

\(7\frac{5}{8} - 3\frac{2}{8} = 4\frac{3}{8}\)
Final answer: \(4\frac{3}{8}\)
Problem 3: With borrowing
3. Subtract: \(5\frac{2}{7} - 2\frac{5}{7}\)
Analysis:

Since \(\frac{2}{7} < \frac{5}{7}\), we need to borrow 1 from the whole number.

Original
\(5\frac{2}{7}\)
After Borrowing
\(4\frac{9}{7}\)
Result
\(2\frac{4}{7}\)
Step 1: Recognize need to borrow

\(\frac{2}{7} < \frac{5}{7}\), so we must borrow 1 from 5

Step 2: Borrow 1 from whole number

\(5\frac{2}{7} = 4 + 1 + \frac{2}{7} = 4 + \frac{7}{7} + \frac{2}{7} = 4\frac{9}{7}\)

Step 3: Subtract whole numbers

\(4 - 2 = 2\)

Step 4: Subtract fractional parts

\(\frac{9}{7} - \frac{5}{7} = \frac{4}{7}\)

Step 5: Combine results

\(2\frac{4}{7}\)

\(5\frac{2}{7} - 2\frac{5}{7} = 2\frac{4}{7}\)
Final answer: \(2\frac{4}{7}\)
Problem Set 4-5: Advanced Subtraction
Problem 4: With borrowing
4. Subtract: \(6\frac{1}{4} - 3\frac{3}{4}\)
Analysis:

Since \(\frac{1}{4} < \frac{3}{4}\), we need to borrow 1 from the whole number.

Original
\(6\frac{1}{4}\)
After Borrowing
\(5\frac{5}{4}\)
Result
\(2\frac{2}{4} = 2\frac{1}{2}\)
Step 1: Recognize need to borrow

\(\frac{1}{4} < \frac{3}{4}\), so we must borrow 1 from 6

Step 2: Borrow 1 from whole number

\(6\frac{1}{4} = 5 + 1 + \frac{1}{4} = 5 + \frac{4}{4} + \frac{1}{4} = 5\frac{5}{4}\)

Step 3: Subtract whole numbers

\(5 - 3 = 2\)

Step 4: Subtract fractional parts

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

Step 5: Combine results

\(2\frac{1}{2}\)

\(6\frac{1}{4} - 3\frac{3}{4} = 2\frac{1}{2}\)
Final answer: \(2\frac{1}{2}\)
Applied rules:

• Borrowing: When top fraction < bottom fraction

• Conversion: 1 whole = denominator/denominator

• Simplification: \(\frac{2}{4} = \frac{1}{2}\)

Problem 5: With borrowing and simplification
5. Subtract: \(8\frac{2}{6} - 4\frac{5}{6}\)
Analysis:

Since \(\frac{2}{6} < \frac{5}{6}\), we need to borrow 1 from the whole number.

Original
\(8\frac{2}{6}\)
After Borrowing
\(7\frac{8}{6}\)
Result
\(3\frac{3}{6} = 3\frac{1}{2}\)
Step 1: Recognize need to borrow

\(\frac{2}{6} < \frac{5}{6}\), so we must borrow 1 from 8

Step 2: Borrow 1 from whole number

\(8\frac{2}{6} = 7 + 1 + \frac{2}{6} = 7 + \frac{6}{6} + \frac{2}{6} = 7\frac{8}{6}\)

Step 3: Subtract whole numbers

\(7 - 4 = 3\)

Step 4: Subtract fractional parts

\(\frac{8}{6} - \frac{5}{6} = \frac{3}{6} = \frac{1}{2}\)

Step 5: Combine results

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

\(8\frac{2}{6} - 4\frac{5}{6} = 3\frac{1}{2}\)
Final answer: \(3\frac{1}{2}\)
Applied rules:

• Borrowing: When top fraction < bottom fraction

• Conversion: 1 whole = denominator/denominator

• Simplification: \(\frac{3}{6} = \frac{1}{2}\)

Additional Practice Problems
\(a\frac{b}{c} - d\frac{e}{c} = (a-d)\frac{b-e}{c}\) (if \(b \geq e\))
Direct Subtraction Rule
Key definitions:

Mixed Number: A number combining a whole number and a proper fraction

Same Denominator: Both fractions have identical denominators

Borrowing: Taking 1 from the whole number and converting to fractional form

Complete methodology:
  1. Compare denominators: Ensure they are the same
  2. Check fractional parts: If top ≥ bottom, subtract directly
  3. Borrow if necessary: If top < bottom, borrow 1 from whole number
  4. Convert borrowed amount: 1 whole = denominator/denominator
  5. Perform subtraction: Subtract whole numbers and fractional parts separately
  6. Simplify: Reduce final fraction to lowest terms
Tip 1: Always check if you need to borrow BEFORE starting subtraction.
Tip 2: Remember: 1 whole = denominator/denominator (e.g., 1 = 5/5 when denominator is 5).
Tip 3: Always simplify your final answer if possible.
Tip 4: Draw fraction models to visualize the subtraction.
Common errors: Forgetting to borrow, subtracting denominators, not simplifying final answers.
Practice focus: Master the borrowing technique and fraction simplification.
Formulas to know by heart:

• Same Denominator: \(a\frac{b}{c} - d\frac{e}{c} = (a-d)\frac{b-e}{c}\) (if \(b \geq e\))

• Borrowing: \(a\frac{b}{c} = (a-1)\frac{b+c}{c}\) (when borrowing 1)

• Simplification: Reduce fractions by dividing numerator and denominator by GCD

More Practice Problems
Try These Problems:
  1. Subtract: \(7\frac{3}{8} - 4\frac{1}{8}\)
  2. Subtract: \(9\frac{2}{5} - 3\frac{4}{5}\)
  3. Subtract: \(6\frac{1}{3} - 2\frac{2}{3}\)
  4. Subtract: \(10\frac{5}{6} - 7\frac{1}{6}\)
  5. Subtract: \(5\frac{3}{4} - 2\frac{3}{4}\)

Answers:

  1. \(3\frac{2}{8} = 3\frac{1}{4}\)
  2. \(5\frac{3}{5}\)
  3. \(3\frac{2}{3}\)
  4. \(3\frac{4}{6} = 3\frac{2}{3}\)
  5. \(3\frac{0}{4} = 3\)

Questions & Answers

Question: In problem \(5\frac{2}{7} - 2\frac{5}{7}\), why do I need to borrow? It seems like I could just subtract \(\frac{2}{7} - \frac{5}{7}\).

Answer: Great question! You're right that \(\frac{2}{7} - \frac{5}{7}\) would give a negative result, which is impossible when working with positive mixed numbers. When the top fraction is smaller than the bottom fraction, you need to borrow from the whole number.

  • Before borrowing: \(5\frac{2}{7}\) has \(\frac{2}{7}\) which is smaller than \(\frac{5}{7}\)
  • After borrowing: We take 1 from 5 (making it 4) and convert it to sevenths: \(1 = \frac{7}{7}\)
  • So: \(5\frac{2}{7} = 4 + \frac{7}{7} + \frac{2}{7} = 4\frac{9}{7}\)
  • Now: \(\frac{9}{7} > \frac{5}{7}\), so we can subtract: \(\frac{9}{7} - \frac{5}{7} = \frac{4}{7}\)

The borrowing allows us to have enough fractional parts to perform the subtraction!

Question: How can I help my child remember when to borrow in mixed number subtraction?

Answer: Here are some memory aids to help your child remember when to borrow:

  • "Top vs Bottom" Rule: Look at the fractions only. If the top numerator is smaller than the bottom numerator, you need to borrow.
  • Think Money: If you have $5.20 and want to spend $2.50, you can't because 20¢ < 50¢. You'd need to break a dollar bill into smaller pieces.
  • Visual Cue: Circle the fractional parts first. If the left circle is smaller than the right circle, borrowing is needed.

Practice with simple examples like \(2\frac{1}{4} - 1\frac{3}{4}\) where it's clearly necessary to borrow.

Question: Should students always convert the final fraction to simplest form?

Answer: Yes, students should always simplify their final answers when possible. This is a fundamental principle in mathematics:

  • Standard Practice: Answers should be in their simplest form unless specified otherwise
  • Mathematical Convention: Simplified fractions are easier to work with and understand
  • Checking Work: Simplifying helps catch computational errors

For example, if a student gets \(\frac{4}{8}\) as their fractional part, they should simplify it to \(\frac{1}{2}\), making the final answer \(3\frac{1}{2}\) instead of \(3\frac{4}{8}\).