What is 2/36 plus 2/21? (Answer: 19/126)

Exact Answer

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Problem: What is 2/36 plus 2/21?
Formula / Expression: 2/36 + 2/21
Final Answer: 19/126
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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: Add the Numerators
Now add the numerators (14 + 24 = 38) and keep the common denominator 252 unchanged.
Working: 14 + 24/252 = 38/252

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 38 and 252, which is 2. Divide both the numerator and denominator by 2.
Working: 38 ÷ 2/252 ÷ 2 = 19/126

Step 5: Decimal & Percentage Representation
Dividing the numerator 19 by denominator 126 produces a repeating decimal (approximately 0.150794, or 15.0794%).
Working: 19 ÷ 126 = 0.150794 (15.0794%)

Key Values:
- Simplified Fraction: 19/126
- Mixed Number Form: 19/126
- Decimal Value: 0.150794
- Percentage: 15.0794%

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Solved with FractionsCalc:
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2/36 + 2/21 = 19/126

Simplified Fraction

19/126

Mixed Number

Proper (19/126)

Decimal Value

0.150794

Percentage

15.0794%

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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

Add the Numerators

Now add the numerators (14 + 24 = 38) and keep the common denominator 252 unchanged.

14 + 24/252 = 38/252

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 38 and 252, which is 2. Divide both the numerator and denominator by 2.

38 ÷ 2/252 ÷ 2 = 19/126

Step 5

Decimal & Percentage Representation

Dividing the numerator 19 by denominator 126 produces a repeating decimal (approximately 0.150794, or 15.0794%).

19 ÷ 126 = 0.150794 (15.0794%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`19/126`
Mixed Number Form	`19/126`
Decimal Form	`0.150794`
Percentage	`15.0794%`

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Frequently Asked Questions

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

2/36 + 2/21 in simplest fraction form is 19/126.

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

2/36 + 2/21 converted to a decimal is 0.150794.

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

2/36 + 2/21 expressed as a percentage is 15.0794%.

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

It results in a repeating decimal (approximately 0.150794...) because the denominator contains prime factors other than 2 and 5.