What is 2/5 minus 2/3? (Answer: -4/15)

Exact Answer

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Problem: What is 2/5 minus 2/3?
Formula / Expression: 2/5 − 2/3
Final Answer: -4/15
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 5 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 5 × 3 = 15.
Working: LCD(5, 3) = 15

Step 2: Convert to Equivalent Fractions with Common Denominator 15
Multiply the numerator and denominator of 2/5 by 3, and multiply the numerator and denominator of 2/3 by 5 so both fractions share the common base 15.
Working: 2 × 3/5 × 3 = 6/15 and 2 × 5/3 × 5 = 10/15

Step 3: Subtract the Numerators
Now subtract the numerators (6 − 10 = -4) and keep the common denominator 15 unchanged.
Working: 6 − 10/15 = -4/15

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 4 and 15 is 1, confirming that -4/15 cannot be reduced further—it is already in its simplest irreducible form.
Working: -4/15

Step 5: Decimal & Percentage Representation
Dividing the numerator -4 by denominator 15 produces a repeating decimal (approximately -0.266667, or -26.6667%).
Working: -4 ÷ 15 = -0.266667 (-26.6667%)

Key Values:
- Simplified Fraction: -4/15
- Mixed Number Form: -4/15
- Decimal Value: -0.266667
- Percentage: -26.6667%

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Solved with FractionsCalc:
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2/5 − 2/3 = -4/15

Simplified Fraction

-4/15

Mixed Number

Proper (-4/15)

Decimal Value

-0.266667

Percentage

-26.6667%

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Step-by-Step Solution: 2/5 − 2/3

Step 1

Find the Least Common Denominator (LCD)

The denominators 5 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 5 × 3 = 15.

LCD(5, 3) = 15

Step 2

Convert to Equivalent Fractions with Common Denominator 15

Multiply the numerator and denominator of 2/5 by 3, and multiply the numerator and denominator of 2/3 by 5 so both fractions share the common base 15.

2 × 3/5 × 3 = 6/15 and 2 × 5/3 × 5 = 10/15

Step 3

Subtract the Numerators

Now subtract the numerators (6 − 10 = -4) and keep the common denominator 15 unchanged.

6 − 10/15 = -4/15

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 4 and 15 is 1, confirming that -4/15 cannot be reduced further—it is already in its simplest irreducible form.

-4/15

Step 5

Decimal & Percentage Representation

Dividing the numerator -4 by denominator 15 produces a repeating decimal (approximately -0.266667, or -26.6667%).

-4 ÷ 15 = -0.266667 (-26.6667%)

Visual Representation

The diagram below illustrates 2/5 minus 2/3 visually:

−

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`-4/15`
Mixed Number Form	`-4/15`
Decimal Form	`-0.266667`
Percentage	`-26.6667%`

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Frequently Asked Questions

What is 2/5 minus 2/3 as a fraction?

2/5 − 2/3 in simplest fraction form is -4/15.

What is 2/5 minus 2/3 as a decimal?

2/5 − 2/3 converted to a decimal is -0.266667.

What is 2/5 minus 2/3 as a percentage?

2/5 − 2/3 expressed as a percentage is -26.6667%.

Does 2/5 minus 2/3 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately -0.266667...) because the denominator contains prime factors other than 2 and 5.