What is 2/14 plus 3/5? (Answer: 26/35)

Exact Answer

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Problem: What is 2/14 plus 3/5?
Formula / Expression: 2/14 + 3/5
Final Answer: 26/35
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 14 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 14 × 5 = 70.
Working: LCD(14, 5) = 70

Step 2: Convert to Equivalent Fractions with Common Denominator 70
Multiply the numerator and denominator of 2/14 by 5, and multiply the numerator and denominator of 3/5 by 14 so both fractions share the common base 70.
Working: 2 × 5/14 × 5 = 10/70 and 3 × 14/5 × 14 = 42/70

Step 3: Add the Numerators
Now add the numerators (10 + 42 = 52) and keep the common denominator 70 unchanged.
Working: 10 + 42/70 = 52/70

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 52 and 70, which is 2. Divide both the numerator and denominator by 2.
Working: 52 ÷ 2/70 ÷ 2 = 26/35

Step 5: Decimal & Percentage Representation
Dividing the numerator 26 by denominator 35 produces a repeating decimal (approximately 0.742857, or 74.2857%).
Working: 26 ÷ 35 = 0.742857 (74.2857%)

Key Values:
- Simplified Fraction: 26/35
- Mixed Number Form: 26/35
- Decimal Value: 0.742857
- Percentage: 74.2857%

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Solved with FractionsCalc:
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2/14 + 3/5 = 26/35

Simplified Fraction

26/35

Mixed Number

Proper (26/35)

Decimal Value

0.742857

Percentage

74.2857%

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Step-by-Step Solution: 2/14 + 3/5

Step 1

Find the Least Common Denominator (LCD)

The denominators 14 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 14 × 5 = 70.

LCD(14, 5) = 70

Step 2

Convert to Equivalent Fractions with Common Denominator 70

Multiply the numerator and denominator of 2/14 by 5, and multiply the numerator and denominator of 3/5 by 14 so both fractions share the common base 70.

2 × 5/14 × 5 = 10/70 and 3 × 14/5 × 14 = 42/70

Step 3

Add the Numerators

Now add the numerators (10 + 42 = 52) and keep the common denominator 70 unchanged.

10 + 42/70 = 52/70

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 52 and 70, which is 2. Divide both the numerator and denominator by 2.

52 ÷ 2/70 ÷ 2 = 26/35

Step 5

Decimal & Percentage Representation

Dividing the numerator 26 by denominator 35 produces a repeating decimal (approximately 0.742857, or 74.2857%).

26 ÷ 35 = 0.742857 (74.2857%)

Visual Representation

The diagram below illustrates 2/14 plus 3/5 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`26/35`
Mixed Number Form	`26/35`
Decimal Form	`0.742857`
Percentage	`74.2857%`

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Frequently Asked Questions

What is 2/14 plus 3/5 as a fraction?

2/14 + 3/5 in simplest fraction form is 26/35.

What is 2/14 plus 3/5 as a decimal?

2/14 + 3/5 converted to a decimal is 0.742857.

What is 2/14 plus 3/5 as a percentage?

2/14 + 3/5 expressed as a percentage is 74.2857%.

Does 2/14 plus 3/5 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.742857...) because the denominator contains prime factors other than 2 and 5.