What is 2/7 plus 7/12? (Answer: 73/84)

Exact Answer

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Problem: What is 2/7 plus 7/12?
Formula / Expression: 2/7 + 7/12
Final Answer: 73/84
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 7 and 12 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 7 × 12 = 84.
Working: LCD(7, 12) = 84

Step 2: Convert to Equivalent Fractions with Common Denominator 84
Multiply the numerator and denominator of 2/7 by 12, and multiply the numerator and denominator of 7/12 by 7 so both fractions share the common base 84.
Working: 2 × 12/7 × 12 = 24/84 and 7 × 7/12 × 7 = 49/84

Step 3: Add the Numerators
Now add the numerators (24 + 49 = 73) and keep the common denominator 84 unchanged.
Working: 24 + 49/84 = 73/84

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 73 and 84 is 1, confirming that 73/84 cannot be reduced further—it is already in its simplest irreducible form.
Working: 73/84

Step 5: Decimal & Percentage Representation
Dividing the numerator 73 by denominator 84 produces a repeating decimal (approximately 0.869048, or 86.9048%).
Working: 73 ÷ 84 = 0.869048 (86.9048%)

Key Values:
- Simplified Fraction: 73/84
- Mixed Number Form: 73/84
- Decimal Value: 0.869048
- Percentage: 86.9048%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-7-plus-7-12/
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2/7 + 7/12 = 73/84

Simplified Fraction

73/84

Mixed Number

Proper (73/84)

Decimal Value

0.869048

Percentage

86.9048%

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Step-by-Step Solution: 2/7 + 7/12

Step 1

Find the Least Common Denominator (LCD)

The denominators 7 and 12 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 7 × 12 = 84.

LCD(7, 12) = 84

Step 2

Convert to Equivalent Fractions with Common Denominator 84

Multiply the numerator and denominator of 2/7 by 12, and multiply the numerator and denominator of 7/12 by 7 so both fractions share the common base 84.

2 × 12/7 × 12 = 24/84 and 7 × 7/12 × 7 = 49/84

Step 3

Add the Numerators

Now add the numerators (24 + 49 = 73) and keep the common denominator 84 unchanged.

24 + 49/84 = 73/84

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 73 and 84 is 1, confirming that 73/84 cannot be reduced further—it is already in its simplest irreducible form.

73/84

Step 5

Decimal & Percentage Representation

Dividing the numerator 73 by denominator 84 produces a repeating decimal (approximately 0.869048, or 86.9048%).

73 ÷ 84 = 0.869048 (86.9048%)

Visual Representation

The diagram below illustrates 2/7 plus 7/12 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`73/84`
Mixed Number Form	`73/84`
Decimal Form	`0.869048`
Percentage	`86.9048%`

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Frequently Asked Questions

What is 2/7 plus 7/12 as a fraction?

2/7 + 7/12 in simplest fraction form is 73/84.

What is 2/7 plus 7/12 as a decimal?

2/7 + 7/12 converted to a decimal is 0.869048.

What is 2/7 plus 7/12 as a percentage?

2/7 + 7/12 expressed as a percentage is 86.9048%.

Does 2/7 plus 7/12 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.869048...) because the denominator contains prime factors other than 2 and 5.