What is 1/12 plus 6/21? (Answer: 31/84)

Exact Answer

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Problem: What is 1/12 plus 6/21?
Formula / Expression: 1/12 + 6/21
Final Answer: 31/84
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 12 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 84 (which is smaller than their product 12 × 21 = 252, keeping the calculation simpler).
Working: LCD(12, 21) = 84

Step 2: Convert to Equivalent Fractions with Common Denominator 84
Multiply the numerator and denominator of 1/12 by 7, and multiply the numerator and denominator of 6/21 by 4 so both fractions share the common base 84.
Working: 1 × 7/12 × 7 = 7/84 and 6 × 4/21 × 4 = 24/84

Step 3: Add the Numerators
Now add the numerators (7 + 24 = 31) and keep the common denominator 84 unchanged.
Working: 7 + 24/84 = 31/84

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 31 and 84 is 1, confirming that 31/84 cannot be reduced further—it is already in its simplest irreducible form.
Working: 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-1-12-plus-6-21/
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1/12 + 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: 1/12 + 6/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 12 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 84 (which is smaller than their product 12 × 21 = 252, keeping the calculation simpler).

LCD(12, 21) = 84

Step 2

Convert to Equivalent Fractions with Common Denominator 84

Multiply the numerator and denominator of 1/12 by 7, and multiply the numerator and denominator of 6/21 by 4 so both fractions share the common base 84.

1 × 7/12 × 7 = 7/84 and 6 × 4/21 × 4 = 24/84

Step 3

Add the Numerators

Now add the numerators (7 + 24 = 31) and keep the common denominator 84 unchanged.

7 + 24/84 = 31/84

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 31 and 84 is 1, confirming that 31/84 cannot be reduced further—it is already in its simplest irreducible form.

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 1/12 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 1/12 plus 6/21 as a fraction?

1/12 + 6/21 in simplest fraction form is 31/84.

What is 1/12 plus 6/21 as a decimal?

1/12 + 6/21 converted to a decimal is 0.369048.

What is 1/12 plus 6/21 as a percentage?

1/12 + 6/21 expressed as a percentage is 36.9048%.

Does 1/12 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.