What is 2/7 plus 5/12? (Answer: 59/84)

Exact Answer

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Problem: What is 2/7 plus 5/12?
Formula / Expression: 2/7 + 5/12
Final Answer: 59/84
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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 5/12 by 7 so both fractions share the common base 84.
Working: 2 × 12/7 × 12 = 24/84 and 5 × 7/12 × 7 = 35/84

Step 3: Add the Numerators
Now add the numerators (24 + 35 = 59) and keep the common denominator 84 unchanged.
Working: 24 + 35/84 = 59/84

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 59 and 84 is 1, confirming that 59/84 cannot be reduced further—it is already in its simplest irreducible form.
Working: 59/84

Step 5: Decimal & Percentage Representation
Dividing the numerator 59 by denominator 84 produces a repeating decimal (approximately 0.702381, or 70.2381%).
Working: 59 ÷ 84 = 0.702381 (70.2381%)

Key Values:
- Simplified Fraction: 59/84
- Mixed Number Form: 59/84
- Decimal Value: 0.702381
- Percentage: 70.2381%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-7-plus-5-12/
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2/7 + 5/12 = 59/84

Simplified Fraction

59/84

Mixed Number

Proper (59/84)

Decimal Value

0.702381

Percentage

70.2381%

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Step-by-Step Solution: 2/7 + 5/12

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 5/12 by 7 so both fractions share the common base 84.

2 × 12/7 × 12 = 24/84 and 5 × 7/12 × 7 = 35/84

Step 3

Add the Numerators

Now add the numerators (24 + 35 = 59) and keep the common denominator 84 unchanged.

24 + 35/84 = 59/84

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 59 and 84 is 1, confirming that 59/84 cannot be reduced further—it is already in its simplest irreducible form.

59/84

Step 5

Decimal & Percentage Representation

Dividing the numerator 59 by denominator 84 produces a repeating decimal (approximately 0.702381, or 70.2381%).

59 ÷ 84 = 0.702381 (70.2381%)

Visual Representation

The diagram below illustrates 2/7 plus 5/12 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`59/84`
Mixed Number Form	`59/84`
Decimal Form	`0.702381`
Percentage	`70.2381%`

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Frequently Asked Questions

What is 2/7 plus 5/12 as a fraction?

2/7 + 5/12 in simplest fraction form is 59/84.

What is 2/7 plus 5/12 as a decimal?

2/7 + 5/12 converted to a decimal is 0.702381.

What is 2/7 plus 5/12 as a percentage?

2/7 + 5/12 expressed as a percentage is 70.2381%.

Does 2/7 plus 5/12 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.702381...) because the denominator contains prime factors other than 2 and 5.