Solved Exercises on Subtracting Mixed Numbers in Grade 4

Master subtracting mixed numbers: borrowing, common denominators, and simplification through these 3 detailed exercises.

Solution: Exercises 1 to 3
1 Basic subtraction
Exercise 1
Subtract:
\(3\frac{1}{4} - 1\frac{3}{4}\)
Definition:

Mixed number: A whole number combined with a fraction, like \(3\frac{1}{4}\)

Subtraction method:
  1. Convert mixed numbers to improper fractions if needed
  2. Find a common denominator
  3. Subtract the numerators
  4. Simplify and convert back to mixed number if possible
Expression
\(3\frac{1}{4} - 1\frac{3}{4}\)
Borrowing
\(2\frac{5}{4} - 1\frac{3}{4}\)
Result
\(1\frac{2}{4} = 1\frac{1}{2}\)
Step 1: Check if borrowing is needed

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

Borrowing process:

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

Step 2: Subtract the whole numbers and fractions separately

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

Step 3: Simplify the fraction

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

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

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

Applied rules:

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

• Subtraction: Subtract whole numbers and fractions separately

• Simplification: Reduce fractions to lowest terms

2 Different denominators
Exercise 2
Subtract:
\(4\frac{2}{3} - 2\frac{1}{6}\)
Definition:

Common denominator: Same bottom number in fractions, needed for addition/subtraction

Expression
\(4\frac{2}{3} - 2\frac{1}{6}\)
Common Denominator
\(4\frac{4}{6} - 2\frac{1}{6}\)
Result
\(2\frac{3}{6} = 2\frac{1}{2}\)
Step 1: Find the least common denominator (LCD)

The LCD of 3 and 6 is 6

Step 2: Convert fractions to equivalent fractions

\(\frac{2}{3} = \frac{4}{6}\) because \(2 \times 2 = 4\) and \(3 \times 2 = 6\)

Step 3: Rewrite the expression with common denominator

\(4\frac{2}{3} - 2\frac{1}{6} = 4\frac{4}{6} - 2\frac{1}{6}\)

Step 4: Subtract the whole numbers and fractions

\(4\frac{4}{6} - 2\frac{1}{6} = (4-2) + (\frac{4}{6}-\frac{1}{6}) = 2 + \frac{3}{6}\)

Step 5: Simplify the fraction

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

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

\(4\frac{2}{3} - 2\frac{1}{6} = 2\frac{1}{2}\)

Applied rules:

• Common denominator: Find LCD before adding/subtracting fractions

• Equivalent fractions: Multiply numerator and denominator by same number

• Simplification: Reduce fractions to lowest terms

3 Borrowing with different denominators
Exercise 3
Subtract:
\(5\frac{1}{3} - 2\frac{2}{3}\)
Definition:

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

Expression
\(5\frac{1}{3} - 2\frac{2}{3}\)
Borrowing
\(4\frac{4}{3} - 2\frac{2}{3}\)
Result
\(2\frac{2}{3}\)
Step 1: Check if borrowing is needed

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

Step 2: Convert the borrowed 1 to fraction form

\(1 = \frac{3}{3}\) (same denominator as the existing fraction)

Borrowing process:

\(5\frac{1}{3} = 4 + 1 + \frac{1}{3} = 4 + \frac{3}{3} + \frac{1}{3} = 4\frac{4}{3}\)

Step 3: Subtract the whole numbers and fractions separately

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

Step 4: Write the final answer

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

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

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

Applied rules:

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

• Conversion: Convert borrowed 1 to fraction with same denominator

• Subtraction: Subtract whole numbers and fractions separately

Key Concepts and Methods
\(a\frac{b}{c} - d\frac{e}{c} = (a-d) + \frac{b-e}{c}\)
Subtracting Mixed Numbers
Key definitions:

Mixed Number: A combination of a whole number and a fraction (e.g., \(3\frac{1}{4}\))

Improper Fraction: A fraction where the numerator is greater than or equal to the denominator (e.g., \(\frac{13}{4}\))

Common Denominator: Same bottom number in fractions, required for addition/subtraction

Complete methodology:
  1. Check denominators: If different, find the least common denominator (LCD)
  2. Compare fractions: If the top fraction is smaller, borrow from the whole number
  3. Convert if needed: Change the borrowed whole number to fraction form
  4. Subtract: Subtract whole numbers and fractions separately
  5. Simplify: Reduce the fraction to lowest terms
Tip 1: Always check if the fractional part of the first number is smaller than the second. If so, you'll need to borrow.
Tip 2: When borrowing, convert the whole number to the same denominator as the existing fraction.
Tip 3: Remember to simplify fractions to lowest terms in your final answer.
Tip 4: You can verify your answer by adding the result to the subtracted number to get back the original.
Common errors: Forgetting to borrow when needed, not finding common denominators, incorrect fraction simplification.
Practice tips: Work with visual models like fraction bars, practice converting between mixed numbers and improper fractions, check answers by addition.
Key formulas and rules:

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

• Subtraction with same denominator: \(a\frac{b}{c} - d\frac{e}{c} = (a-d) + \frac{b-e}{c}\)

• Common denominator: Multiply numerator and denominator by the same number to create equivalent fractions

• Simplification: Divide numerator and denominator by their greatest common factor

Visual Examples and Properties
\(3\frac{1}{4} = \frac{13}{4}\)
Mixed to Improper
Borrowing Example
\(5\frac{1}{3} = 4\frac{4}{3}\)
After borrowing 1
Common Denominator
\(\frac{1}{3} = \frac{2}{6}\)
Multiply by 2/2
Simplification
\(\frac{2}{4} = \frac{1}{2}\)
Divide by 2/2
Subtraction Process
📊
Step 1: Check denominators

If denominators are different, find the LCD and convert fractions

\(\frac{1}{3} \to \frac{2}{6}\) (multiply by 2/2)
Step 2: Compare fractions

If top fraction is smaller, borrow 1 from the whole number

\(3\frac{1}{4} \to 2\frac{5}{4}\) (borrow 1 = 4/4)
Step 3: Subtract parts

Subtract whole numbers and fractions separately

\((a-d) + \frac{b-e}{c}\)
Step 4: Simplify

Reduce fraction to lowest terms if possible

\(\frac{2}{4} = \frac{1}{2}\)
Visual Process
1
Check Denominators
2
Borrow if Needed
3
Subtract Parts
4
Simplify
Fraction Bar Model
Visual representation showing how mixed numbers represent parts of wholes
Practice Makes Perfect!
Frequently Asked Questions

Question: Why do I need to borrow when subtracting mixed numbers? Can't I just subtract the fractions directly?

Answer: You need to borrow when the fractional part of the first number is smaller than the fractional part of the second number. For example, in \(3\frac{1}{4} - 1\frac{3}{4}\), you can't subtract \(\frac{3}{4}\) from \(\frac{1}{4}\) because \(\frac{1}{4}\) is smaller.

Borrowing converts one whole unit into fraction form to make the top fraction larger. In our example: \(3\frac{1}{4}\) becomes \(2\frac{5}{4}\) (since \(1 = \frac{4}{4}\), so \(\frac{1}{4} + \frac{4}{4} = \frac{5}{4}\)). Now you can subtract: \(2\frac{5}{4} - 1\frac{3}{4} = 1\frac{2}{4} = 1\frac{1}{2}\).

Question: How do I know when to find a common denominator when subtracting mixed numbers?

Answer: You must find a common denominator whenever the fractions in your mixed numbers have different denominators. You can only add or subtract fractions when they have the same denominator.

For example, in \(4\frac{2}{3} - 2\frac{1}{6}\), the denominators are 3 and 6. The least common denominator (LCD) is 6. Convert \(\frac{2}{3}\) to \(\frac{4}{6}\) by multiplying both numerator and denominator by 2. Then you can subtract: \(4\frac{4}{6} - 2\frac{1}{6} = 2\frac{3}{6} = 2\frac{1}{2}\).

Question: I sometimes get confused about simplifying fractions. How do I know if I've simplified correctly?

Answer: A fraction is in its simplest form when the numerator and denominator have no common factors other than 1. To simplify:

  • Find the greatest common factor (GCF) of the numerator and denominator
  • Divide both the numerator and denominator by the GCF
  • Repeat until no common factors remain

For example, to simplify \(\frac{6}{8}\): The GCF of 6 and 8 is 2. Divide both by 2: \(\frac{6÷2}{8÷2} = \frac{3}{4}\). Since 3 and 4 have no common factors other than 1, \(\frac{3}{4}\) is fully simplified.