What is 2/35 minus 2/21? (Answer: -4/105)

Exact Answer

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Problem: What is 2/35 minus 2/21?
Formula / Expression: 2/35 − 2/21
Final Answer: -4/105
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 35 and 21 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 105 (which is smaller than their product 35 × 21 = 735, keeping the calculation simpler).
Working: LCD(35, 21) = 105

Step 2: Convert to Equivalent Fractions with Common Denominator 105
Multiply the numerator and denominator of 2/35 by 3, and multiply the numerator and denominator of 2/21 by 5 so both fractions share the common base 105.
Working: 2 × 3/35 × 3 = 6/105 and 2 × 5/21 × 5 = 10/105

Step 3: Subtract the Numerators
Now subtract the numerators (6 − 10 = -4) and keep the common denominator 105 unchanged.
Working: 6 − 10/105 = -4/105

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

Step 5: Decimal & Percentage Representation
Dividing the numerator -4 by denominator 105 produces a repeating decimal (approximately -0.038095, or -3.8095%).
Working: -4 ÷ 105 = -0.038095 (-3.8095%)

Key Values:
- Simplified Fraction: -4/105
- Mixed Number Form: -4/105
- Decimal Value: -0.038095
- Percentage: -3.8095%

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Solved with FractionsCalc:
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2/35 − 2/21 = -4/105

Simplified Fraction

-4/105

Mixed Number

Proper (-4/105)

Decimal Value

-0.038095

Percentage

-3.8095%

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Step-by-Step Solution: 2/35 − 2/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 35 and 21 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 105 (which is smaller than their product 35 × 21 = 735, keeping the calculation simpler).

LCD(35, 21) = 105

Step 2

Convert to Equivalent Fractions with Common Denominator 105

Multiply the numerator and denominator of 2/35 by 3, and multiply the numerator and denominator of 2/21 by 5 so both fractions share the common base 105.

2 × 3/35 × 3 = 6/105 and 2 × 5/21 × 5 = 10/105

Step 3

Subtract the Numerators

Now subtract the numerators (6 − 10 = -4) and keep the common denominator 105 unchanged.

6 − 10/105 = -4/105

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 4 and 105 is 1, confirming that -4/105 cannot be reduced further—it is already in its simplest irreducible form.

-4/105

Step 5

Decimal & Percentage Representation

Dividing the numerator -4 by denominator 105 produces a repeating decimal (approximately -0.038095, or -3.8095%).

-4 ÷ 105 = -0.038095 (-3.8095%)

Visual Representation

The diagram below illustrates 2/35 minus 2/21 visually:

−

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`-4/105`
Mixed Number Form	`-4/105`
Decimal Form	`-0.038095`
Percentage	`-3.8095%`

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Frequently Asked Questions

What is 2/35 minus 2/21 as a fraction?

2/35 − 2/21 in simplest fraction form is -4/105.

What is 2/35 minus 2/21 as a decimal?

2/35 − 2/21 converted to a decimal is -0.038095.

What is 2/35 minus 2/21 as a percentage?

2/35 − 2/21 expressed as a percentage is -3.8095%.

Does 2/35 minus 2/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately -0.038095...) because the denominator contains prime factors other than 2 and 5.