What is 1/12 plus 9/21? (Answer: 43/84)

Exact Answer

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Problem: What is 1/12 plus 9/21?
Formula / Expression: 1/12 + 9/21
Final Answer: 43/84
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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 9/21 by 4 so both fractions share the common base 84.
Working: 1 × 7/12 × 7 = 7/84 and 9 × 4/21 × 4 = 36/84

Step 3: Add the Numerators
Now add the numerators (7 + 36 = 43) and keep the common denominator 84 unchanged.
Working: 7 + 36/84 = 43/84

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 43 and 84 is 1, confirming that 43/84 cannot be reduced further—it is already in its simplest irreducible form.
Working: 43/84

Step 5: Decimal & Percentage Representation
Dividing the numerator 43 by denominator 84 produces a repeating decimal (approximately 0.511905, or 51.1905%).
Working: 43 ÷ 84 = 0.511905 (51.1905%)

Key Values:
- Simplified Fraction: 43/84
- Mixed Number Form: 43/84
- Decimal Value: 0.511905
- Percentage: 51.1905%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-12-plus-9-21/
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1/12 + 9/21 = 43/84

Simplified Fraction

43/84

Mixed Number

Proper (43/84)

Decimal Value

0.511905

Percentage

51.1905%

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Step-by-Step Solution: 1/12 + 9/21

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 9/21 by 4 so both fractions share the common base 84.

1 × 7/12 × 7 = 7/84 and 9 × 4/21 × 4 = 36/84

Step 3

Add the Numerators

Now add the numerators (7 + 36 = 43) and keep the common denominator 84 unchanged.

7 + 36/84 = 43/84

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 43 and 84 is 1, confirming that 43/84 cannot be reduced further—it is already in its simplest irreducible form.

43/84

Step 5

Decimal & Percentage Representation

Dividing the numerator 43 by denominator 84 produces a repeating decimal (approximately 0.511905, or 51.1905%).

43 ÷ 84 = 0.511905 (51.1905%)

Visual Representation

The diagram below illustrates 1/12 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`43/84`
Mixed Number Form	`43/84`
Decimal Form	`0.511905`
Percentage	`51.1905%`

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Frequently Asked Questions

What is 1/12 plus 9/21 as a fraction?

1/12 + 9/21 in simplest fraction form is 43/84.

What is 1/12 plus 9/21 as a decimal?

1/12 + 9/21 converted to a decimal is 0.511905.

What is 1/12 plus 9/21 as a percentage?

1/12 + 9/21 expressed as a percentage is 51.1905%.

Does 1/12 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.511905...) because the denominator contains prime factors other than 2 and 5.