What is 2/5 minus 2/4? (Answer: -1/10)

Exact Answer

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Problem: What is 2/5 minus 2/4?
Formula / Expression: 2/5 − 2/4
Final Answer: -1/10
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 5 and 4 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 5 × 4 = 20.
Working: LCD(5, 4) = 20

Step 2: Convert to Equivalent Fractions with Common Denominator 20
Multiply the numerator and denominator of 2/5 by 4, and multiply the numerator and denominator of 2/4 by 5 so both fractions share the common base 20.
Working: 2 × 4/5 × 4 = 8/20 and 2 × 5/4 × 5 = 10/20

Step 3: Subtract the Numerators
Now subtract the numerators (8 − 10 = -2) and keep the common denominator 20 unchanged.
Working: 8 − 10/20 = -2/20

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 2 and 20, which is 2. Divide both the numerator and denominator by 2.
Working: -2 ÷ 2/20 ÷ 2 = -1/10

Step 5: Decimal & Percentage Representation
Dividing the numerator -1 by denominator 10 yields an exact terminating decimal of -0.1 (or -10%).
Working: -1 ÷ 10 = -0.1 (-10%)

Key Values:
- Simplified Fraction: -1/10
- Mixed Number Form: -1/10
- Decimal Value: -0.1
- Percentage: -10%

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2/5 − 2/4 = -1/10

Simplified Fraction

-1/10

Mixed Number

Proper (-1/10)

Decimal Value

-0.1

Percentage

-10%

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Step-by-Step Solution: 2/5 − 2/4

Step 1

Find the Least Common Denominator (LCD)

The denominators 5 and 4 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 5 × 4 = 20.

LCD(5, 4) = 20

Step 2

Convert to Equivalent Fractions with Common Denominator 20

Multiply the numerator and denominator of 2/5 by 4, and multiply the numerator and denominator of 2/4 by 5 so both fractions share the common base 20.

2 × 4/5 × 4 = 8/20 and 2 × 5/4 × 5 = 10/20

Step 3

Subtract the Numerators

Now subtract the numerators (8 − 10 = -2) and keep the common denominator 20 unchanged.

8 − 10/20 = -2/20

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 2 and 20, which is 2. Divide both the numerator and denominator by 2.

-2 ÷ 2/20 ÷ 2 = -1/10

Step 5

Decimal & Percentage Representation

Dividing the numerator -1 by denominator 10 yields an exact terminating decimal of -0.1 (or -10%).

-1 ÷ 10 = -0.1 (-10%)

Visual Representation

The diagram below illustrates 2/5 minus 2/4 visually:

−

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`-1/10`
Mixed Number Form	`-1/10`
Decimal Form	`-0.1`
Percentage	`-10%`

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Frequently Asked Questions

What is 2/5 minus 2/4 as a fraction?

2/5 − 2/4 in simplest fraction form is -1/10.

What is 2/5 minus 2/4 as a decimal?

2/5 − 2/4 converted to a decimal is -0.1.

What is 2/5 minus 2/4 as a percentage?

2/5 − 2/4 expressed as a percentage is -10%.

Does 2/5 minus 2/4 result in a terminating or repeating decimal?

It results in an exact terminating decimal (-0.1) because the denominator in simplest terms contains only prime factors 2 and/or 5.