What is 1/12 plus 7/21? (Answer: 5/12)

Exact Answer

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Problem: What is 1/12 plus 7/21?
Formula / Expression: 1/12 + 7/21
Final Answer: 5/12
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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 7/21 by 4 so both fractions share the common base 84.
Working: 1 × 7/12 × 7 = 7/84 and 7 × 4/21 × 4 = 28/84

Step 3: Add the Numerators
Now add the numerators (7 + 28 = 35) and keep the common denominator 84 unchanged.
Working: 7 + 28/84 = 35/84

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 35 and 84, which is 7. Divide both the numerator and denominator by 7.
Working: 35 ÷ 7/84 ÷ 7 = 5/12

Step 5: Decimal & Percentage Representation
Dividing the numerator 5 by denominator 12 produces a repeating decimal (approximately 0.416667, or 41.6667%).
Working: 5 ÷ 12 = 0.416667 (41.6667%)

Key Values:
- Simplified Fraction: 5/12
- Mixed Number Form: 5/12
- Decimal Value: 0.416667
- Percentage: 41.6667%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-12-plus-7-21/
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1/12 + 7/21 = 5/12

Simplified Fraction

5/12

Mixed Number

Proper (5/12)

Decimal Value

0.416667

Percentage

41.6667%

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Step-by-Step Solution: 1/12 + 7/21

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 7/21 by 4 so both fractions share the common base 84.

1 × 7/12 × 7 = 7/84 and 7 × 4/21 × 4 = 28/84

Step 3

Add the Numerators

Now add the numerators (7 + 28 = 35) and keep the common denominator 84 unchanged.

7 + 28/84 = 35/84

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 35 and 84, which is 7. Divide both the numerator and denominator by 7.

35 ÷ 7/84 ÷ 7 = 5/12

Step 5

Decimal & Percentage Representation

Dividing the numerator 5 by denominator 12 produces a repeating decimal (approximately 0.416667, or 41.6667%).

5 ÷ 12 = 0.416667 (41.6667%)

Visual Representation

The diagram below illustrates 1/12 plus 7/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`5/12`
Mixed Number Form	`5/12`
Decimal Form	`0.416667`
Percentage	`41.6667%`

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Frequently Asked Questions

What is 1/12 plus 7/21 as a fraction?

1/12 + 7/21 in simplest fraction form is 5/12.

What is 1/12 plus 7/21 as a decimal?

1/12 + 7/21 converted to a decimal is 0.416667.

What is 1/12 plus 7/21 as a percentage?

1/12 + 7/21 expressed as a percentage is 41.6667%.

Does 1/12 plus 7/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.416667...) because the denominator contains prime factors other than 2 and 5.