What is 2/45 minus 2/21? (Answer: -16/315)

Exact Answer

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Problem: What is 2/45 minus 2/21?
Formula / Expression: 2/45 − 2/21
Final Answer: -16/315
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 45 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 315 (which is smaller than their product 45 × 21 = 945, keeping the calculation simpler).
Working: LCD(45, 21) = 315

Step 2: Convert to Equivalent Fractions with Common Denominator 315
Multiply the numerator and denominator of 2/45 by 7, and multiply the numerator and denominator of 2/21 by 15 so both fractions share the common base 315.
Working: 2 × 7/45 × 7 = 14/315 and 2 × 15/21 × 15 = 30/315

Step 3: Subtract the Numerators
Now subtract the numerators (14 − 30 = -16) and keep the common denominator 315 unchanged.
Working: 14 − 30/315 = -16/315

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 16 and 315 is 1, confirming that -16/315 cannot be reduced further—it is already in its simplest irreducible form.
Working: -16/315

Step 5: Decimal & Percentage Representation
Dividing the numerator -16 by denominator 315 produces a repeating decimal (approximately -0.050794, or -5.0794%).
Working: -16 ÷ 315 = -0.050794 (-5.0794%)

Key Values:
- Simplified Fraction: -16/315
- Mixed Number Form: -16/315
- Decimal Value: -0.050794
- Percentage: -5.0794%

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Solved with FractionsCalc:
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2/45 − 2/21 = -16/315

Simplified Fraction

-16/315

Mixed Number

Proper (-16/315)

Decimal Value

-0.050794

Percentage

-5.0794%

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Step-by-Step Solution: 2/45 − 2/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 45 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 315 (which is smaller than their product 45 × 21 = 945, keeping the calculation simpler).

LCD(45, 21) = 315

Step 2

Convert to Equivalent Fractions with Common Denominator 315

Multiply the numerator and denominator of 2/45 by 7, and multiply the numerator and denominator of 2/21 by 15 so both fractions share the common base 315.

2 × 7/45 × 7 = 14/315 and 2 × 15/21 × 15 = 30/315

Step 3

Subtract the Numerators

Now subtract the numerators (14 − 30 = -16) and keep the common denominator 315 unchanged.

14 − 30/315 = -16/315

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 16 and 315 is 1, confirming that -16/315 cannot be reduced further—it is already in its simplest irreducible form.

-16/315

Step 5

Decimal & Percentage Representation

Dividing the numerator -16 by denominator 315 produces a repeating decimal (approximately -0.050794, or -5.0794%).

-16 ÷ 315 = -0.050794 (-5.0794%)

Visual Representation

The diagram below illustrates 2/45 minus 2/21 visually:

−

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`-16/315`
Mixed Number Form	`-16/315`
Decimal Form	`-0.050794`
Percentage	`-5.0794%`

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Frequently Asked Questions

What is 2/45 minus 2/21 as a fraction?

2/45 − 2/21 in simplest fraction form is -16/315.

What is 2/45 minus 2/21 as a decimal?

2/45 − 2/21 converted to a decimal is -0.050794.

What is 2/45 minus 2/21 as a percentage?

2/45 − 2/21 expressed as a percentage is -5.0794%.

Does 2/45 minus 2/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately -0.050794...) because the denominator contains prime factors other than 2 and 5.