What is 13/36 plus 12/21? (Answer: 235/252)

Exact Answer

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Problem: What is 13/36 plus 12/21?
Formula / Expression: 13/36 + 12/21
Final Answer: 235/252
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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 12/21 by 12 so both fractions share the common base 252.
Working: 13 × 7/36 × 7 = 91/252 and 12 × 12/21 × 12 = 144/252

Step 3: Add the Numerators
Now add the numerators (91 + 144 = 235) and keep the common denominator 252 unchanged.
Working: 91 + 144/252 = 235/252

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 235 and 252 is 1, confirming that 235/252 cannot be reduced further—it is already in its simplest irreducible form.
Working: 235/252

Step 5: Decimal & Percentage Representation
Dividing the numerator 235 by denominator 252 produces a repeating decimal (approximately 0.93254, or 93.254%).
Working: 235 ÷ 252 = 0.93254 (93.254%)

Key Values:
- Simplified Fraction: 235/252
- Mixed Number Form: 235/252
- Decimal Value: 0.93254
- Percentage: 93.254%

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Solved with FractionsCalc:
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13/36 + 12/21 = 235/252

Simplified Fraction

235/252

Mixed Number

Proper (235/252)

Decimal Value

0.93254

Percentage

93.254%

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Step-by-Step Solution: 13/36 + 12/21

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

13 × 7/36 × 7 = 91/252 and 12 × 12/21 × 12 = 144/252

Step 3

Add the Numerators

Now add the numerators (91 + 144 = 235) and keep the common denominator 252 unchanged.

91 + 144/252 = 235/252

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 235 and 252 is 1, confirming that 235/252 cannot be reduced further—it is already in its simplest irreducible form.

235/252

Step 5

Decimal & Percentage Representation

Dividing the numerator 235 by denominator 252 produces a repeating decimal (approximately 0.93254, or 93.254%).

235 ÷ 252 = 0.93254 (93.254%)

Visual Representation

The diagram below illustrates 13/36 plus 12/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`235/252`
Mixed Number Form	`235/252`
Decimal Form	`0.93254`
Percentage	`93.254%`

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Frequently Asked Questions

What is 13/36 plus 12/21 as a fraction?

13/36 + 12/21 in simplest fraction form is 235/252.

What is 13/36 plus 12/21 as a decimal?

13/36 + 12/21 converted to a decimal is 0.93254.

What is 13/36 plus 12/21 as a percentage?

13/36 + 12/21 expressed as a percentage is 93.254%.

Does 13/36 plus 12/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.93254...) because the denominator contains prime factors other than 2 and 5.