What is 2/36 minus 2/21? (Answer: -5/126)

Exact Answer

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Problem: What is 2/36 minus 2/21?
Formula / Expression: 2/36 − 2/21
Final Answer: -5/126
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 36 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 252 (which is smaller than their product 36 × 21 = 756, keeping the calculation simpler).
Working: LCD(36, 21) = 252

Step 2: Convert to Equivalent Fractions with Common Denominator 252
Multiply the numerator and denominator of 2/36 by 7, and multiply the numerator and denominator of 2/21 by 12 so both fractions share the common base 252.
Working: 2 × 7/36 × 7 = 14/252 and 2 × 12/21 × 12 = 24/252

Step 3: Subtract the Numerators
Now subtract the numerators (14 − 24 = -10) and keep the common denominator 252 unchanged.
Working: 14 − 24/252 = -10/252

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 10 and 252, which is 2. Divide both the numerator and denominator by 2.
Working: -10 ÷ 2/252 ÷ 2 = -5/126

Step 5: Decimal & Percentage Representation
Dividing the numerator -5 by denominator 126 produces a repeating decimal (approximately -0.039683, or -3.9683%).
Working: -5 ÷ 126 = -0.039683 (-3.9683%)

Key Values:
- Simplified Fraction: -5/126
- Mixed Number Form: -5/126
- Decimal Value: -0.039683
- Percentage: -3.9683%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-36-minus-2-21/
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2/36 − 2/21 = -5/126

Simplified Fraction

-5/126

Mixed Number

Proper (-5/126)

Decimal Value

-0.039683

Percentage

-3.9683%

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Step-by-Step Solution: 2/36 − 2/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 36 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 252 (which is smaller than their product 36 × 21 = 756, keeping the calculation simpler).

LCD(36, 21) = 252

Step 2

Convert to Equivalent Fractions with Common Denominator 252

Multiply the numerator and denominator of 2/36 by 7, and multiply the numerator and denominator of 2/21 by 12 so both fractions share the common base 252.

2 × 7/36 × 7 = 14/252 and 2 × 12/21 × 12 = 24/252

Step 3

Subtract the Numerators

Now subtract the numerators (14 − 24 = -10) and keep the common denominator 252 unchanged.

14 − 24/252 = -10/252

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 10 and 252, which is 2. Divide both the numerator and denominator by 2.

-10 ÷ 2/252 ÷ 2 = -5/126

Step 5

Decimal & Percentage Representation

Dividing the numerator -5 by denominator 126 produces a repeating decimal (approximately -0.039683, or -3.9683%).

-5 ÷ 126 = -0.039683 (-3.9683%)

Visual Representation

The diagram below illustrates 2/36 minus 2/21 visually:

−

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`-5/126`
Mixed Number Form	`-5/126`
Decimal Form	`-0.039683`
Percentage	`-3.9683%`

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Frequently Asked Questions

What is 2/36 minus 2/21 as a fraction?

2/36 − 2/21 in simplest fraction form is -5/126.

What is 2/36 minus 2/21 as a decimal?

2/36 − 2/21 converted to a decimal is -0.039683.

What is 2/36 minus 2/21 as a percentage?

2/36 − 2/21 expressed as a percentage is -3.9683%.

Does 2/36 minus 2/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately -0.039683...) because the denominator contains prime factors other than 2 and 5.