What is 8/36 plus 6/21? (Answer: 32/63)

Exact Answer

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Problem: What is 8/36 plus 6/21?
Formula / Expression: 8/36 + 6/21
Final Answer: 32/63
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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 8/36 by 7, and multiply the numerator and denominator of 6/21 by 12 so both fractions share the common base 252.
Working: 8 × 7/36 × 7 = 56/252 and 6 × 12/21 × 12 = 72/252

Step 3: Add the Numerators
Now add the numerators (56 + 72 = 128) and keep the common denominator 252 unchanged.
Working: 56 + 72/252 = 128/252

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 128 and 252, which is 4. Divide both the numerator and denominator by 4.
Working: 128 ÷ 4/252 ÷ 4 = 32/63

Step 5: Decimal & Percentage Representation
Dividing the numerator 32 by denominator 63 produces a repeating decimal (approximately 0.507937, or 50.7937%).
Working: 32 ÷ 63 = 0.507937 (50.7937%)

Key Values:
- Simplified Fraction: 32/63
- Mixed Number Form: 32/63
- Decimal Value: 0.507937
- Percentage: 50.7937%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-8-36-plus-6-21/
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8/36 + 6/21 = 32/63

Simplified Fraction

32/63

Mixed Number

Proper (32/63)

Decimal Value

0.507937

Percentage

50.7937%

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Step-by-Step Solution: 8/36 + 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 8/36 by 7, and multiply the numerator and denominator of 6/21 by 12 so both fractions share the common base 252.

8 × 7/36 × 7 = 56/252 and 6 × 12/21 × 12 = 72/252

Step 3

Add the Numerators

Now add the numerators (56 + 72 = 128) and keep the common denominator 252 unchanged.

56 + 72/252 = 128/252

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 128 and 252, which is 4. Divide both the numerator and denominator by 4.

128 ÷ 4/252 ÷ 4 = 32/63

Step 5

Decimal & Percentage Representation

Dividing the numerator 32 by denominator 63 produces a repeating decimal (approximately 0.507937, or 50.7937%).

32 ÷ 63 = 0.507937 (50.7937%)

Visual Representation

The diagram below illustrates 8/36 plus 6/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`32/63`
Mixed Number Form	`32/63`
Decimal Form	`0.507937`
Percentage	`50.7937%`

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Frequently Asked Questions

What is 8/36 plus 6/21 as a fraction?

8/36 + 6/21 in simplest fraction form is 32/63.

What is 8/36 plus 6/21 as a decimal?

8/36 + 6/21 converted to a decimal is 0.507937.

What is 8/36 plus 6/21 as a percentage?

8/36 + 6/21 expressed as a percentage is 50.7937%.

Does 8/36 plus 6/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.507937...) because the denominator contains prime factors other than 2 and 5.