What is 17/36 plus 12/21? (Answer: 263/252)

Exact Answer

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Problem: What is 17/36 plus 12/21?
Formula / Expression: 17/36 + 12/21
Final Answer: 1 11/252 (263/252)
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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 17/36 by 7, and multiply the numerator and denominator of 12/21 by 12 so both fractions share the common base 252.
Working: 17 × 7/36 × 7 = 119/252 and 12 × 12/21 × 12 = 144/252

Step 3: Add the Numerators
Now add the numerators (119 + 144 = 263) and keep the common denominator 252 unchanged.
Working: 119 + 144/252 = 263/252

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 263 and 252 is 1, confirming that 263/252 cannot be reduced further—it is already in its simplest irreducible form.
Working: 263/252

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (263) is greater than the denominator (252), divide 263 by 252: it goes in 1 whole time(s) with a remainder of 11, giving the mixed number 1 11/252.
Working: 263/252 = 1 11/252

Step 6: Decimal & Percentage Representation
Dividing the numerator 263 by denominator 252 produces a repeating decimal (approximately 1.043651, or 104.3651%).
Working: 263 ÷ 252 = 1.043651 (104.3651%)

Key Values:
- Simplified Fraction: 263/252
- Mixed Number Form: 1 11/252
- Decimal Value: 1.043651
- Percentage: 104.3651%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-17-36-plus-12-21/
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17/36 + 12/21 = 263/252

Simplified Fraction

263/252

Mixed Number

1 11/252

Decimal Value

1.043651

Percentage

104.3651%

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Step-by-Step Solution: 17/36 + 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 17/36 by 7, and multiply the numerator and denominator of 12/21 by 12 so both fractions share the common base 252.

17 × 7/36 × 7 = 119/252 and 12 × 12/21 × 12 = 144/252

Step 3

Add the Numerators

Now add the numerators (119 + 144 = 263) and keep the common denominator 252 unchanged.

119 + 144/252 = 263/252

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 263 and 252 is 1, confirming that 263/252 cannot be reduced further—it is already in its simplest irreducible form.

263/252

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (263) is greater than the denominator (252), divide 263 by 252: it goes in 1 whole time(s) with a remainder of 11, giving the mixed number 1 11/252.

263/252 = 111/252

Step 6

Decimal & Percentage Representation

Dividing the numerator 263 by denominator 252 produces a repeating decimal (approximately 1.043651, or 104.3651%).

263 ÷ 252 = 1.043651 (104.3651%)

Visual Representation

The diagram below illustrates 17/36 plus 12/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`263/252`
Mixed Number Form	`1 11/252`
Decimal Form	`1.043651`
Percentage	`104.3651%`

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Frequently Asked Questions

What is 17/36 plus 12/21 as a fraction?

17/36 + 12/21 in simplest fraction form is 263/252 (or 1 11/252 as a mixed number).

What is 17/36 plus 12/21 as a decimal?

17/36 + 12/21 converted to a decimal is 1.043651.

What is 17/36 plus 12/21 as a percentage?

17/36 + 12/21 expressed as a percentage is 104.3651%.

How do you write 17/36 plus 12/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 263/252 can be written as the mixed number 1 11/252.

Does 17/36 plus 12/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.043651...) because the denominator contains prime factors other than 2 and 5.