What is 11/36 plus 10/21? (Answer: 197/252)

Exact Answer

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Problem: What is 11/36 plus 10/21?
Formula / Expression: 11/36 + 10/21
Final Answer: 197/252
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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 10/21 by 12 so both fractions share the common base 252.
Working: 11 × 7/36 × 7 = 77/252 and 10 × 12/21 × 12 = 120/252

Step 3: Add the Numerators
Now add the numerators (77 + 120 = 197) and keep the common denominator 252 unchanged.
Working: 77 + 120/252 = 197/252

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 197 and 252 is 1, confirming that 197/252 cannot be reduced further—it is already in its simplest irreducible form.
Working: 197/252

Step 5: Decimal & Percentage Representation
Dividing the numerator 197 by denominator 252 produces a repeating decimal (approximately 0.781746, or 78.1746%).
Working: 197 ÷ 252 = 0.781746 (78.1746%)

Key Values:
- Simplified Fraction: 197/252
- Mixed Number Form: 197/252
- Decimal Value: 0.781746
- Percentage: 78.1746%

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Solved with FractionsCalc:
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11/36 + 10/21 = 197/252

Simplified Fraction

197/252

Mixed Number

Proper (197/252)

Decimal Value

0.781746

Percentage

78.1746%

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Step-by-Step Solution: 11/36 + 10/21

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 10/21 by 12 so both fractions share the common base 252.

11 × 7/36 × 7 = 77/252 and 10 × 12/21 × 12 = 120/252

Step 3

Add the Numerators

Now add the numerators (77 + 120 = 197) and keep the common denominator 252 unchanged.

77 + 120/252 = 197/252

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 197 and 252 is 1, confirming that 197/252 cannot be reduced further—it is already in its simplest irreducible form.

197/252

Step 5

Decimal & Percentage Representation

Dividing the numerator 197 by denominator 252 produces a repeating decimal (approximately 0.781746, or 78.1746%).

197 ÷ 252 = 0.781746 (78.1746%)

Visual Representation

The diagram below illustrates 11/36 plus 10/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`197/252`
Mixed Number Form	`197/252`
Decimal Form	`0.781746`
Percentage	`78.1746%`

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Frequently Asked Questions

What is 11/36 plus 10/21 as a fraction?

11/36 + 10/21 in simplest fraction form is 197/252.

What is 11/36 plus 10/21 as a decimal?

11/36 + 10/21 converted to a decimal is 0.781746.

What is 11/36 plus 10/21 as a percentage?

11/36 + 10/21 expressed as a percentage is 78.1746%.

Does 11/36 plus 10/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.781746...) because the denominator contains prime factors other than 2 and 5.