What is 3/4 minus 2/3? (Answer: 1/12)

Exact Answer

==================================================
Problem: What is 3/4 minus 2/3?
Formula / Expression: 3/4 − 2/3
Final Answer: 1/12
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 4 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 4 × 3 = 12.
Working: LCD(4, 3) = 12

Step 2: Convert to Equivalent Fractions with Common Denominator 12
Multiply the numerator and denominator of 3/4 by 3, and multiply the numerator and denominator of 2/3 by 4 so both fractions share the common base 12.
Working: 3 × 3/4 × 3 = 9/12 and 2 × 4/3 × 4 = 8/12

Step 3: Subtract the Numerators
Now subtract the numerators (9 − 8 = 1) and keep the common denominator 12 unchanged.
Working: 9 − 8/12 = 1/12

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 1 and 12 is 1, confirming that 1/12 cannot be reduced further—it is already in its simplest irreducible form.
Working: 1/12

Step 5: Decimal & Percentage Representation
Dividing the numerator 1 by denominator 12 produces a repeating decimal (approximately 0.083333, or 8.3333%).
Working: 1 ÷ 12 = 0.083333 (8.3333%)

Key Values:
- Simplified Fraction: 1/12
- Mixed Number Form: 1/12
- Decimal Value: 0.083333
- Percentage: 8.3333%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-4-minus-2-3/
==================================================

3/4 − 2/3 = 1/12

Simplified Fraction

1/12

Mixed Number

Proper (1/12)

Decimal Value

0.083333

Percentage

8.3333%

Reduce / Convert Fraction:

Convert Fraction:

Enter Decimal Number:

Enter Percentage: %

What is % of

From Value: To Value:

Simplify Ratio: :

First Number: Second Number:

Find All Factors of:

Dividend: ÷ Divisor:

√ Square Root of: OR Power (x^y): ^{^}

x² + x + = 0

Number (n! & log):

Circle Radius (r):

Side a: Side b:

Angle (Degrees): °

Numbers (comma separated):

Total Items (n): Choose (r):

Decimal Number:

Number (1–3999):

Step-by-Step Solution: 3/4 − 2/3

Step 1

Find the Least Common Denominator (LCD)

The denominators 4 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 4 × 3 = 12.

LCD(4, 3) = 12

Step 2

Convert to Equivalent Fractions with Common Denominator 12

Multiply the numerator and denominator of 3/4 by 3, and multiply the numerator and denominator of 2/3 by 4 so both fractions share the common base 12.

3 × 3/4 × 3 = 9/12 and 2 × 4/3 × 4 = 8/12

Step 3

Subtract the Numerators

Now subtract the numerators (9 − 8 = 1) and keep the common denominator 12 unchanged.

9 − 8/12 = 1/12

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 1 and 12 is 1, confirming that 1/12 cannot be reduced further—it is already in its simplest irreducible form.

1/12

Step 5

Decimal & Percentage Representation

Dividing the numerator 1 by denominator 12 produces a repeating decimal (approximately 0.083333, or 8.3333%).

1 ÷ 12 = 0.083333 (8.3333%)

Visual Representation

The diagram below illustrates 3/4 minus 2/3 visually:

−

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`1/12`
Mixed Number Form	`1/12`
Decimal Form	`0.083333`
Percentage	`8.3333%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 3/4 minus 2/3 as a fraction?

3/4 − 2/3 in simplest fraction form is 1/12.

What is 3/4 minus 2/3 as a decimal?

3/4 − 2/3 converted to a decimal is 0.083333.

What is 3/4 minus 2/3 as a percentage?

3/4 − 2/3 expressed as a percentage is 8.3333%.

Does 3/4 minus 2/3 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.083333...) because the denominator contains prime factors other than 2 and 5.