What is 13/36 plus 11/21? (Answer: 223/252)

Exact Answer

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Problem: What is 13/36 plus 11/21?
Formula / Expression: 13/36 + 11/21
Final Answer: 223/252
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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 13/36 by 7, and multiply the numerator and denominator of 11/21 by 12 so both fractions share the common base 252.
Working: 13 × 7/36 × 7 = 91/252 and 11 × 12/21 × 12 = 132/252

Step 3: Add the Numerators
Now add the numerators (91 + 132 = 223) and keep the common denominator 252 unchanged.
Working: 91 + 132/252 = 223/252

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 223 and 252 is 1, confirming that 223/252 cannot be reduced further—it is already in its simplest irreducible form.
Working: 223/252

Step 5: Decimal & Percentage Representation
Dividing the numerator 223 by denominator 252 produces a repeating decimal (approximately 0.884921, or 88.4921%).
Working: 223 ÷ 252 = 0.884921 (88.4921%)

Key Values:
- Simplified Fraction: 223/252
- Mixed Number Form: 223/252
- Decimal Value: 0.884921
- Percentage: 88.4921%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-13-36-plus-11-21/
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13/36 + 11/21 = 223/252

Simplified Fraction

223/252

Mixed Number

Proper (223/252)

Decimal Value

0.884921

Percentage

88.4921%

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Step-by-Step Solution: 13/36 + 11/21

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 13/36 by 7, and multiply the numerator and denominator of 11/21 by 12 so both fractions share the common base 252.

13 × 7/36 × 7 = 91/252 and 11 × 12/21 × 12 = 132/252

Step 3

Add the Numerators

Now add the numerators (91 + 132 = 223) and keep the common denominator 252 unchanged.

91 + 132/252 = 223/252

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 223 and 252 is 1, confirming that 223/252 cannot be reduced further—it is already in its simplest irreducible form.

223/252

Step 5

Decimal & Percentage Representation

Dividing the numerator 223 by denominator 252 produces a repeating decimal (approximately 0.884921, or 88.4921%).

223 ÷ 252 = 0.884921 (88.4921%)

Visual Representation

The diagram below illustrates 13/36 plus 11/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`223/252`
Mixed Number Form	`223/252`
Decimal Form	`0.884921`
Percentage	`88.4921%`

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Frequently Asked Questions

What is 13/36 plus 11/21 as a fraction?

13/36 + 11/21 in simplest fraction form is 223/252.

What is 13/36 plus 11/21 as a decimal?

13/36 + 11/21 converted to a decimal is 0.884921.

What is 13/36 plus 11/21 as a percentage?

13/36 + 11/21 expressed as a percentage is 88.4921%.

Does 13/36 plus 11/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.884921...) because the denominator contains prime factors other than 2 and 5.