What is 2/9 minus 2/3? (Answer: -4/9)

Exact Answer

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Problem: What is 2/9 minus 2/3?
Formula / Expression: 2/9 − 2/3
Final Answer: -4/9
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 9 is an exact multiple of 3 (3 × 3 = 9). The Least Common Denominator (LCD) is simply 9, meaning we only need to scale one fraction.
Working: LCD(9, 3) = 9

Step 2: Convert to Equivalent Fractions with Common Denominator 9
Multiply the numerator and denominator of 2/9 by 1, and multiply the numerator and denominator of 2/3 by 3 so both fractions share the common base 9.
Working: 2 × 1/9 × 1 = 2/9 and 2 × 3/3 × 3 = 6/9

Step 3: Subtract the Numerators
Now subtract the numerators (2 − 6 = -4) and keep the common denominator 9 unchanged.
Working: 2 − 6/9 = -4/9

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 4 and 9 is 1, confirming that -4/9 cannot be reduced further—it is already in its simplest irreducible form.
Working: -4/9

Step 5: Decimal & Percentage Representation
Dividing the numerator -4 by denominator 9 produces a repeating decimal (approximately -0.444444, or -44.4444%).
Working: -4 ÷ 9 = -0.444444 (-44.4444%)

Key Values:
- Simplified Fraction: -4/9
- Mixed Number Form: -4/9
- Decimal Value: -0.444444
- Percentage: -44.4444%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-9-minus-2-3/
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2/9 − 2/3 = -4/9

Simplified Fraction

-4/9

Mixed Number

Proper (-4/9)

Decimal Value

-0.444444

Percentage

-44.4444%

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Step-by-Step Solution: 2/9 − 2/3

Step 1

Find the Least Common Denominator (LCD)

Notice that 9 is an exact multiple of 3 (3 × 3 = 9). The Least Common Denominator (LCD) is simply 9, meaning we only need to scale one fraction.

LCD(9, 3) = 9

Step 2

Convert to Equivalent Fractions with Common Denominator 9

Multiply the numerator and denominator of 2/9 by 1, and multiply the numerator and denominator of 2/3 by 3 so both fractions share the common base 9.

2 × 1/9 × 1 = 2/9 and 2 × 3/3 × 3 = 6/9

Step 3

Subtract the Numerators

Now subtract the numerators (2 − 6 = -4) and keep the common denominator 9 unchanged.

2 − 6/9 = -4/9

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 4 and 9 is 1, confirming that -4/9 cannot be reduced further—it is already in its simplest irreducible form.

-4/9

Step 5

Decimal & Percentage Representation

Dividing the numerator -4 by denominator 9 produces a repeating decimal (approximately -0.444444, or -44.4444%).

-4 ÷ 9 = -0.444444 (-44.4444%)

Visual Representation

The diagram below illustrates 2/9 minus 2/3 visually:

−

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`-4/9`
Mixed Number Form	`-4/9`
Decimal Form	`-0.444444`
Percentage	`-44.4444%`

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Frequently Asked Questions

What is 2/9 minus 2/3 as a fraction?

2/9 − 2/3 in simplest fraction form is -4/9.

What is 2/9 minus 2/3 as a decimal?

2/9 − 2/3 converted to a decimal is -0.444444.

What is 2/9 minus 2/3 as a percentage?

2/9 − 2/3 expressed as a percentage is -44.4444%.

Does 2/9 minus 2/3 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately -0.444444...) because the denominator contains prime factors other than 2 and 5.