What is 1/36 plus 2/21? (Answer: 31/252)

Exact Answer

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Problem: What is 1/36 plus 2/21?
Formula / Expression: 1/36 + 2/21
Final Answer: 31/252
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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 1/36 by 7, and multiply the numerator and denominator of 2/21 by 12 so both fractions share the common base 252.
Working: 1 × 7/36 × 7 = 7/252 and 2 × 12/21 × 12 = 24/252

Step 3: Add the Numerators
Now add the numerators (7 + 24 = 31) and keep the common denominator 252 unchanged.
Working: 7 + 24/252 = 31/252

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 31 and 252 is 1, confirming that 31/252 cannot be reduced further—it is already in its simplest irreducible form.
Working: 31/252

Step 5: Decimal & Percentage Representation
Dividing the numerator 31 by denominator 252 produces a repeating decimal (approximately 0.123016, or 12.3016%).
Working: 31 ÷ 252 = 0.123016 (12.3016%)

Key Values:
- Simplified Fraction: 31/252
- Mixed Number Form: 31/252
- Decimal Value: 0.123016
- Percentage: 12.3016%

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Solved with FractionsCalc:
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1/36 + 2/21 = 31/252

Simplified Fraction

31/252

Mixed Number

Proper (31/252)

Decimal Value

0.123016

Percentage

12.3016%

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Step-by-Step Solution: 1/36 + 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 1/36 by 7, and multiply the numerator and denominator of 2/21 by 12 so both fractions share the common base 252.

1 × 7/36 × 7 = 7/252 and 2 × 12/21 × 12 = 24/252

Step 3

Add the Numerators

Now add the numerators (7 + 24 = 31) and keep the common denominator 252 unchanged.

7 + 24/252 = 31/252

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 31 and 252 is 1, confirming that 31/252 cannot be reduced further—it is already in its simplest irreducible form.

31/252

Step 5

Decimal & Percentage Representation

Dividing the numerator 31 by denominator 252 produces a repeating decimal (approximately 0.123016, or 12.3016%).

31 ÷ 252 = 0.123016 (12.3016%)

Visual Representation

The diagram below illustrates 1/36 plus 2/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`31/252`
Mixed Number Form	`31/252`
Decimal Form	`0.123016`
Percentage	`12.3016%`

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Frequently Asked Questions

What is 1/36 plus 2/21 as a fraction?

1/36 + 2/21 in simplest fraction form is 31/252.

What is 1/36 plus 2/21 as a decimal?

1/36 + 2/21 converted to a decimal is 0.123016.

What is 1/36 plus 2/21 as a percentage?

1/36 + 2/21 expressed as a percentage is 12.3016%.

Does 1/36 plus 2/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.123016...) because the denominator contains prime factors other than 2 and 5.