What is 2/14 plus 2/5? (Answer: 19/35)

Exact Answer

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Problem: What is 2/14 plus 2/5?
Formula / Expression: 2/14 + 2/5
Final Answer: 19/35
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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 2/5 by 14 so both fractions share the common base 70.
Working: 2 × 5/14 × 5 = 10/70 and 2 × 14/5 × 14 = 28/70

Step 3: Add the Numerators
Now add the numerators (10 + 28 = 38) and keep the common denominator 70 unchanged.
Working: 10 + 28/70 = 38/70

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 38 and 70, which is 2. Divide both the numerator and denominator by 2.
Working: 38 ÷ 2/70 ÷ 2 = 19/35

Step 5: Decimal & Percentage Representation
Dividing the numerator 19 by denominator 35 produces a repeating decimal (approximately 0.542857, or 54.2857%).
Working: 19 ÷ 35 = 0.542857 (54.2857%)

Key Values:
- Simplified Fraction: 19/35
- Mixed Number Form: 19/35
- Decimal Value: 0.542857
- Percentage: 54.2857%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-14-plus-2-5/
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2/14 + 2/5 = 19/35

Simplified Fraction

19/35

Mixed Number

Proper (19/35)

Decimal Value

0.542857

Percentage

54.2857%

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

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 2/5 by 14 so both fractions share the common base 70.

2 × 5/14 × 5 = 10/70 and 2 × 14/5 × 14 = 28/70

Step 3

Add the Numerators

Now add the numerators (10 + 28 = 38) and keep the common denominator 70 unchanged.

10 + 28/70 = 38/70

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 38 and 70, which is 2. Divide both the numerator and denominator by 2.

38 ÷ 2/70 ÷ 2 = 19/35

Step 5

Decimal & Percentage Representation

Dividing the numerator 19 by denominator 35 produces a repeating decimal (approximately 0.542857, or 54.2857%).

19 ÷ 35 = 0.542857 (54.2857%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`19/35`
Mixed Number Form	`19/35`
Decimal Form	`0.542857`
Percentage	`54.2857%`

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Frequently Asked Questions

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

2/14 + 2/5 in simplest fraction form is 19/35.

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

2/14 + 2/5 converted to a decimal is 0.542857.

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

2/14 + 2/5 expressed as a percentage is 54.2857%.

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

It results in a repeating decimal (approximately 0.542857...) because the denominator contains prime factors other than 2 and 5.