What is 1/2 minus 7/10? (Answer: -1/5)

Exact Answer

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Problem: What is 1/2 minus 7/10?
Formula / Expression: 1/2 − 7/10
Final Answer: -1/5
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 10 is an exact multiple of 2 (2 × 5 = 10). The Least Common Denominator (LCD) is simply 10, meaning we only need to scale one fraction.
Working: LCD(2, 10) = 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 7/10 by 1 so both fractions share the common base 10.
Working: 1 × 5/2 × 5 = 5/10 and 7 × 1/10 × 1 = 7/10

Step 3: Subtract the Numerators
Now subtract the numerators (5 − 7 = -2) and keep the common denominator 10 unchanged.
Working: 5 − 7/10 = -2/10

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 2 and 10, which is 2. Divide both the numerator and denominator by 2.
Working: -2 ÷ 2/10 ÷ 2 = -1/5

Step 5: Decimal & Percentage Representation
Dividing the numerator -1 by denominator 5 yields an exact terminating decimal of -0.2 (or -20%).
Working: -1 ÷ 5 = -0.2 (-20%)

Key Values:
- Simplified Fraction: -1/5
- Mixed Number Form: -1/5
- Decimal Value: -0.2
- Percentage: -20%

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1/2 − 7/10 = -1/5

Simplified Fraction

-1/5

Mixed Number

Proper (-1/5)

Decimal Value

-0.2

Percentage

-20%

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Step-by-Step Solution: 1/2 − 7/10

Step 1

Find the Least Common Denominator (LCD)

Notice that 10 is an exact multiple of 2 (2 × 5 = 10). The Least Common Denominator (LCD) is simply 10, meaning we only need to scale one fraction.

LCD(2, 10) = 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 7/10 by 1 so both fractions share the common base 10.

1 × 5/2 × 5 = 5/10 and 7 × 1/10 × 1 = 7/10

Step 3

Subtract the Numerators

Now subtract the numerators (5 − 7 = -2) and keep the common denominator 10 unchanged.

5 − 7/10 = -2/10

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 2 and 10, which is 2. Divide both the numerator and denominator by 2.

-2 ÷ 2/10 ÷ 2 = -1/5

Step 5

Decimal & Percentage Representation

Dividing the numerator -1 by denominator 5 yields an exact terminating decimal of -0.2 (or -20%).

-1 ÷ 5 = -0.2 (-20%)

Visual Representation

The diagram below illustrates 1/2 minus 7/10 visually:

−

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`-1/5`
Mixed Number Form	`-1/5`
Decimal Form	`-0.2`
Percentage	`-20%`

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Frequently Asked Questions

What is 1/2 minus 7/10 as a fraction?

1/2 − 7/10 in simplest fraction form is -1/5.

What is 1/2 minus 7/10 as a decimal?

1/2 − 7/10 converted to a decimal is -0.2.

What is 1/2 minus 7/10 as a percentage?

1/2 − 7/10 expressed as a percentage is -20%.

Does 1/2 minus 7/10 result in a terminating or repeating decimal?

It results in an exact terminating decimal (-0.2) because the denominator in simplest terms contains only prime factors 2 and/or 5.