What is 3/36 plus 6/21? (Answer: 31/84)

Exact Answer

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Problem: What is 3/36 plus 6/21?
Formula / Expression: 3/36 + 6/21
Final Answer: 31/84
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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 3/36 by 7, and multiply the numerator and denominator of 6/21 by 12 so both fractions share the common base 252.
Working: 3 × 7/36 × 7 = 21/252 and 6 × 12/21 × 12 = 72/252

Step 3: Add the Numerators
Now add the numerators (21 + 72 = 93) and keep the common denominator 252 unchanged.
Working: 21 + 72/252 = 93/252

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 93 and 252, which is 3. Divide both the numerator and denominator by 3.
Working: 93 ÷ 3/252 ÷ 3 = 31/84

Step 5: Decimal & Percentage Representation
Dividing the numerator 31 by denominator 84 produces a repeating decimal (approximately 0.369048, or 36.9048%).
Working: 31 ÷ 84 = 0.369048 (36.9048%)

Key Values:
- Simplified Fraction: 31/84
- Mixed Number Form: 31/84
- Decimal Value: 0.369048
- Percentage: 36.9048%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-36-plus-6-21/
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3/36 + 6/21 = 31/84

Simplified Fraction

31/84

Mixed Number

Proper (31/84)

Decimal Value

0.369048

Percentage

36.9048%

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Step-by-Step Solution: 3/36 + 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 3/36 by 7, and multiply the numerator and denominator of 6/21 by 12 so both fractions share the common base 252.

3 × 7/36 × 7 = 21/252 and 6 × 12/21 × 12 = 72/252

Step 3

Add the Numerators

Now add the numerators (21 + 72 = 93) and keep the common denominator 252 unchanged.

21 + 72/252 = 93/252

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 93 and 252, which is 3. Divide both the numerator and denominator by 3.

93 ÷ 3/252 ÷ 3 = 31/84

Step 5

Decimal & Percentage Representation

Dividing the numerator 31 by denominator 84 produces a repeating decimal (approximately 0.369048, or 36.9048%).

31 ÷ 84 = 0.369048 (36.9048%)

Visual Representation

The diagram below illustrates 3/36 plus 6/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`31/84`
Mixed Number Form	`31/84`
Decimal Form	`0.369048`
Percentage	`36.9048%`

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Frequently Asked Questions

What is 3/36 plus 6/21 as a fraction?

3/36 + 6/21 in simplest fraction form is 31/84.

What is 3/36 plus 6/21 as a decimal?

3/36 + 6/21 converted to a decimal is 0.369048.

What is 3/36 plus 6/21 as a percentage?

3/36 + 6/21 expressed as a percentage is 36.9048%.

Does 3/36 plus 6/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.369048...) because the denominator contains prime factors other than 2 and 5.