What is 5/36 plus 6/21? (Answer: 107/252)

Exact Answer

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Problem: What is 5/36 plus 6/21?
Formula / Expression: 5/36 + 6/21
Final Answer: 107/252
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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 5/36 by 7, and multiply the numerator and denominator of 6/21 by 12 so both fractions share the common base 252.
Working: 5 × 7/36 × 7 = 35/252 and 6 × 12/21 × 12 = 72/252

Step 3: Add the Numerators
Now add the numerators (35 + 72 = 107) and keep the common denominator 252 unchanged.
Working: 35 + 72/252 = 107/252

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 107 and 252 is 1, confirming that 107/252 cannot be reduced further—it is already in its simplest irreducible form.
Working: 107/252

Step 5: Decimal & Percentage Representation
Dividing the numerator 107 by denominator 252 produces a repeating decimal (approximately 0.424603, or 42.4603%).
Working: 107 ÷ 252 = 0.424603 (42.4603%)

Key Values:
- Simplified Fraction: 107/252
- Mixed Number Form: 107/252
- Decimal Value: 0.424603
- Percentage: 42.4603%

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Solved with FractionsCalc:
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5/36 + 6/21 = 107/252

Simplified Fraction

107/252

Mixed Number

Proper (107/252)

Decimal Value

0.424603

Percentage

42.4603%

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Step-by-Step Solution: 5/36 + 6/21

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 5/36 by 7, and multiply the numerator and denominator of 6/21 by 12 so both fractions share the common base 252.

5 × 7/36 × 7 = 35/252 and 6 × 12/21 × 12 = 72/252

Step 3

Add the Numerators

Now add the numerators (35 + 72 = 107) and keep the common denominator 252 unchanged.

35 + 72/252 = 107/252

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 107 and 252 is 1, confirming that 107/252 cannot be reduced further—it is already in its simplest irreducible form.

107/252

Step 5

Decimal & Percentage Representation

Dividing the numerator 107 by denominator 252 produces a repeating decimal (approximately 0.424603, or 42.4603%).

107 ÷ 252 = 0.424603 (42.4603%)

Visual Representation

The diagram below illustrates 5/36 plus 6/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`107/252`
Mixed Number Form	`107/252`
Decimal Form	`0.424603`
Percentage	`42.4603%`

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Frequently Asked Questions

What is 5/36 plus 6/21 as a fraction?

5/36 + 6/21 in simplest fraction form is 107/252.

What is 5/36 plus 6/21 as a decimal?

5/36 + 6/21 converted to a decimal is 0.424603.

What is 5/36 plus 6/21 as a percentage?

5/36 + 6/21 expressed as a percentage is 42.4603%.

Does 5/36 plus 6/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.424603...) because the denominator contains prime factors other than 2 and 5.