What is 13/36 plus 8/21? (Answer: 187/252)

Exact Answer

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Problem: What is 13/36 plus 8/21?
Formula / Expression: 13/36 + 8/21
Final Answer: 187/252
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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 8/21 by 12 so both fractions share the common base 252.
Working: 13 × 7/36 × 7 = 91/252 and 8 × 12/21 × 12 = 96/252

Step 3: Add the Numerators
Now add the numerators (91 + 96 = 187) and keep the common denominator 252 unchanged.
Working: 91 + 96/252 = 187/252

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 187 and 252 is 1, confirming that 187/252 cannot be reduced further—it is already in its simplest irreducible form.
Working: 187/252

Step 5: Decimal & Percentage Representation
Dividing the numerator 187 by denominator 252 produces a repeating decimal (approximately 0.742063, or 74.2063%).
Working: 187 ÷ 252 = 0.742063 (74.2063%)

Key Values:
- Simplified Fraction: 187/252
- Mixed Number Form: 187/252
- Decimal Value: 0.742063
- Percentage: 74.2063%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-13-36-plus-8-21/
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13/36 + 8/21 = 187/252

Simplified Fraction

187/252

Mixed Number

Proper (187/252)

Decimal Value

0.742063

Percentage

74.2063%

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Step-by-Step Solution: 13/36 + 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 13/36 by 7, and multiply the numerator and denominator of 8/21 by 12 so both fractions share the common base 252.

13 × 7/36 × 7 = 91/252 and 8 × 12/21 × 12 = 96/252

Step 3

Add the Numerators

Now add the numerators (91 + 96 = 187) and keep the common denominator 252 unchanged.

91 + 96/252 = 187/252

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 187 and 252 is 1, confirming that 187/252 cannot be reduced further—it is already in its simplest irreducible form.

187/252

Step 5

Decimal & Percentage Representation

Dividing the numerator 187 by denominator 252 produces a repeating decimal (approximately 0.742063, or 74.2063%).

187 ÷ 252 = 0.742063 (74.2063%)

Visual Representation

The diagram below illustrates 13/36 plus 8/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`187/252`
Mixed Number Form	`187/252`
Decimal Form	`0.742063`
Percentage	`74.2063%`

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Frequently Asked Questions

What is 13/36 plus 8/21 as a fraction?

13/36 + 8/21 in simplest fraction form is 187/252.

What is 13/36 plus 8/21 as a decimal?

13/36 + 8/21 converted to a decimal is 0.742063.

What is 13/36 plus 8/21 as a percentage?

13/36 + 8/21 expressed as a percentage is 74.2063%.

Does 13/36 plus 8/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.742063...) because the denominator contains prime factors other than 2 and 5.