What is 1/2 minus 3/5? (Answer: -1/10)

Exact Answer

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Problem: What is 1/2 minus 3/5?
Formula / Expression: 1/2 − 3/5
Final Answer: -1/10
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 2 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 2 × 5 = 10.
Working: LCD(2, 5) = 10

Step 2: Convert to Equivalent Fractions with Common Denominator 10
Multiply the numerator and denominator of 1/2 by 5, and multiply the numerator and denominator of 3/5 by 2 so both fractions share the common base 10.
Working: 1 × 5/2 × 5 = 5/10 and 3 × 2/5 × 2 = 6/10

Step 3: Subtract the Numerators
Now subtract the numerators (5 − 6 = -1) and keep the common denominator 10 unchanged.
Working: 5 − 6/10 = -1/10

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 1 and 10 is 1, confirming that -1/10 cannot be reduced further—it is already in its simplest irreducible form.
Working: -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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1/2 − 3/5 = -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: 1/2 − 3/5

Step 1

Find the Least Common Denominator (LCD)

The denominators 2 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 2 × 5 = 10.

LCD(2, 5) = 10

Step 2

Convert to Equivalent Fractions with Common Denominator 10

Multiply the numerator and denominator of 1/2 by 5, and multiply the numerator and denominator of 3/5 by 2 so both fractions share the common base 10.

1 × 5/2 × 5 = 5/10 and 3 × 2/5 × 2 = 6/10

Step 3

Subtract the Numerators

Now subtract the numerators (5 − 6 = -1) and keep the common denominator 10 unchanged.

5 − 6/10 = -1/10

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 1 and 10 is 1, confirming that -1/10 cannot be reduced further—it is already in its simplest irreducible form.

-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 1/2 minus 3/5 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 1/2 minus 3/5 as a fraction?

1/2 − 3/5 in simplest fraction form is -1/10.

What is 1/2 minus 3/5 as a decimal?

1/2 − 3/5 converted to a decimal is -0.1.

What is 1/2 minus 3/5 as a percentage?

1/2 − 3/5 expressed as a percentage is -10%.

Does 1/2 minus 3/5 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.