What is 2/5 minus 10/21? (Answer: -8/105)

Exact Answer

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Problem: What is 2/5 minus 10/21?
Formula / Expression: 2/5 − 10/21
Final Answer: -8/105
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 5 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 5 × 21 = 105.
Working: LCD(5, 21) = 105

Step 2: Convert to Equivalent Fractions with Common Denominator 105
Multiply the numerator and denominator of 2/5 by 21, and multiply the numerator and denominator of 10/21 by 5 so both fractions share the common base 105.
Working: 2 × 21/5 × 21 = 42/105 and 10 × 5/21 × 5 = 50/105

Step 3: Subtract the Numerators
Now subtract the numerators (42 − 50 = -8) and keep the common denominator 105 unchanged.
Working: 42 − 50/105 = -8/105

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 8 and 105 is 1, confirming that -8/105 cannot be reduced further—it is already in its simplest irreducible form.
Working: -8/105

Step 5: Decimal & Percentage Representation
Dividing the numerator -8 by denominator 105 produces a repeating decimal (approximately -0.07619, or -7.619%).
Working: -8 ÷ 105 = -0.07619 (-7.619%)

Key Values:
- Simplified Fraction: -8/105
- Mixed Number Form: -8/105
- Decimal Value: -0.07619
- Percentage: -7.619%

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Solved with FractionsCalc:
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2/5 − 10/21 = -8/105

Simplified Fraction

-8/105

Mixed Number

Proper (-8/105)

Decimal Value

-0.07619

Percentage

-7.619%

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Step-by-Step Solution: 2/5 − 10/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 5 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 5 × 21 = 105.

LCD(5, 21) = 105

Step 2

Convert to Equivalent Fractions with Common Denominator 105

Multiply the numerator and denominator of 2/5 by 21, and multiply the numerator and denominator of 10/21 by 5 so both fractions share the common base 105.

2 × 21/5 × 21 = 42/105 and 10 × 5/21 × 5 = 50/105

Step 3

Subtract the Numerators

Now subtract the numerators (42 − 50 = -8) and keep the common denominator 105 unchanged.

42 − 50/105 = -8/105

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 8 and 105 is 1, confirming that -8/105 cannot be reduced further—it is already in its simplest irreducible form.

-8/105

Step 5

Decimal & Percentage Representation

Dividing the numerator -8 by denominator 105 produces a repeating decimal (approximately -0.07619, or -7.619%).

-8 ÷ 105 = -0.07619 (-7.619%)

Visual Representation

The diagram below illustrates 2/5 minus 10/21 visually:

−

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`-8/105`
Mixed Number Form	`-8/105`
Decimal Form	`-0.07619`
Percentage	`-7.619%`

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Frequently Asked Questions

What is 2/5 minus 10/21 as a fraction?

2/5 − 10/21 in simplest fraction form is -8/105.

What is 2/5 minus 10/21 as a decimal?

2/5 − 10/21 converted to a decimal is -0.07619.

What is 2/5 minus 10/21 as a percentage?

2/5 − 10/21 expressed as a percentage is -7.619%.

Does 2/5 minus 10/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately -0.07619...) because the denominator contains prime factors other than 2 and 5.