What is 11/36 plus 8/21? (Answer: 173/252)

Exact Answer

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Problem: What is 11/36 plus 8/21?
Formula / Expression: 11/36 + 8/21
Final Answer: 173/252
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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 11/36 by 7, and multiply the numerator and denominator of 8/21 by 12 so both fractions share the common base 252.
Working: 11 × 7/36 × 7 = 77/252 and 8 × 12/21 × 12 = 96/252

Step 3: Add the Numerators
Now add the numerators (77 + 96 = 173) and keep the common denominator 252 unchanged.
Working: 77 + 96/252 = 173/252

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 173 and 252 is 1, confirming that 173/252 cannot be reduced further—it is already in its simplest irreducible form.
Working: 173/252

Step 5: Decimal & Percentage Representation
Dividing the numerator 173 by denominator 252 produces a repeating decimal (approximately 0.686508, or 68.6508%).
Working: 173 ÷ 252 = 0.686508 (68.6508%)

Key Values:
- Simplified Fraction: 173/252
- Mixed Number Form: 173/252
- Decimal Value: 0.686508
- Percentage: 68.6508%

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Solved with FractionsCalc:
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11/36 + 8/21 = 173/252

Simplified Fraction

173/252

Mixed Number

Proper (173/252)

Decimal Value

0.686508

Percentage

68.6508%

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Step-by-Step Solution: 11/36 + 8/21

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 11/36 by 7, and multiply the numerator and denominator of 8/21 by 12 so both fractions share the common base 252.

11 × 7/36 × 7 = 77/252 and 8 × 12/21 × 12 = 96/252

Step 3

Add the Numerators

Now add the numerators (77 + 96 = 173) and keep the common denominator 252 unchanged.

77 + 96/252 = 173/252

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 173 and 252 is 1, confirming that 173/252 cannot be reduced further—it is already in its simplest irreducible form.

173/252

Step 5

Decimal & Percentage Representation

Dividing the numerator 173 by denominator 252 produces a repeating decimal (approximately 0.686508, or 68.6508%).

173 ÷ 252 = 0.686508 (68.6508%)

Visual Representation

The diagram below illustrates 11/36 plus 8/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`173/252`
Mixed Number Form	`173/252`
Decimal Form	`0.686508`
Percentage	`68.6508%`

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Frequently Asked Questions

What is 11/36 plus 8/21 as a fraction?

11/36 + 8/21 in simplest fraction form is 173/252.

What is 11/36 plus 8/21 as a decimal?

11/36 + 8/21 converted to a decimal is 0.686508.

What is 11/36 plus 8/21 as a percentage?

11/36 + 8/21 expressed as a percentage is 68.6508%.

Does 11/36 plus 8/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.686508...) because the denominator contains prime factors other than 2 and 5.