What is 2/15 minus 9/21? (Answer: -31/105)

Exact Answer

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Problem: What is 2/15 minus 9/21?
Formula / Expression: 2/15 − 9/21
Final Answer: -31/105
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 15 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 105 (which is smaller than their product 15 × 21 = 315, keeping the calculation simpler).
Working: LCD(15, 21) = 105

Step 2: Convert to Equivalent Fractions with Common Denominator 105
Multiply the numerator and denominator of 2/15 by 7, and multiply the numerator and denominator of 9/21 by 5 so both fractions share the common base 105.
Working: 2 × 7/15 × 7 = 14/105 and 9 × 5/21 × 5 = 45/105

Step 3: Subtract the Numerators
Now subtract the numerators (14 − 45 = -31) and keep the common denominator 105 unchanged.
Working: 14 − 45/105 = -31/105

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 31 and 105 is 1, confirming that -31/105 cannot be reduced further—it is already in its simplest irreducible form.
Working: -31/105

Step 5: Decimal & Percentage Representation
Dividing the numerator -31 by denominator 105 produces a repeating decimal (approximately -0.295238, or -29.5238%).
Working: -31 ÷ 105 = -0.295238 (-29.5238%)

Key Values:
- Simplified Fraction: -31/105
- Mixed Number Form: -31/105
- Decimal Value: -0.295238
- Percentage: -29.5238%

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Solved with FractionsCalc:
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2/15 − 9/21 = -31/105

Simplified Fraction

-31/105

Mixed Number

Proper (-31/105)

Decimal Value

-0.295238

Percentage

-29.5238%

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Step-by-Step Solution: 2/15 − 9/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 15 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 105 (which is smaller than their product 15 × 21 = 315, keeping the calculation simpler).

LCD(15, 21) = 105

Step 2

Convert to Equivalent Fractions with Common Denominator 105

Multiply the numerator and denominator of 2/15 by 7, and multiply the numerator and denominator of 9/21 by 5 so both fractions share the common base 105.

2 × 7/15 × 7 = 14/105 and 9 × 5/21 × 5 = 45/105

Step 3

Subtract the Numerators

Now subtract the numerators (14 − 45 = -31) and keep the common denominator 105 unchanged.

14 − 45/105 = -31/105

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 31 and 105 is 1, confirming that -31/105 cannot be reduced further—it is already in its simplest irreducible form.

-31/105

Step 5

Decimal & Percentage Representation

Dividing the numerator -31 by denominator 105 produces a repeating decimal (approximately -0.295238, or -29.5238%).

-31 ÷ 105 = -0.295238 (-29.5238%)

Visual Representation

The diagram below illustrates 2/15 minus 9/21 visually:

−

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`-31/105`
Mixed Number Form	`-31/105`
Decimal Form	`-0.295238`
Percentage	`-29.5238%`

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Frequently Asked Questions

What is 2/15 minus 9/21 as a fraction?

2/15 − 9/21 in simplest fraction form is -31/105.

What is 2/15 minus 9/21 as a decimal?

2/15 − 9/21 converted to a decimal is -0.295238.

What is 2/15 minus 9/21 as a percentage?

2/15 − 9/21 expressed as a percentage is -29.5238%.

Does 2/15 minus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately -0.295238...) because the denominator contains prime factors other than 2 and 5.