What is 5/14 plus 2/5? (Answer: 53/70)

Exact Answer

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Problem: What is 5/14 plus 2/5?
Formula / Expression: 5/14 + 2/5
Final Answer: 53/70
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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 5/14 by 5, and multiply the numerator and denominator of 2/5 by 14 so both fractions share the common base 70.
Working: 5 × 5/14 × 5 = 25/70 and 2 × 14/5 × 14 = 28/70

Step 3: Add the Numerators
Now add the numerators (25 + 28 = 53) and keep the common denominator 70 unchanged.
Working: 25 + 28/70 = 53/70

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 53 and 70 is 1, confirming that 53/70 cannot be reduced further—it is already in its simplest irreducible form.
Working: 53/70

Step 5: Decimal & Percentage Representation
Dividing the numerator 53 by denominator 70 produces a repeating decimal (approximately 0.757143, or 75.7143%).
Working: 53 ÷ 70 = 0.757143 (75.7143%)

Key Values:
- Simplified Fraction: 53/70
- Mixed Number Form: 53/70
- Decimal Value: 0.757143
- Percentage: 75.7143%

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Solved with FractionsCalc:
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5/14 + 2/5 = 53/70

Simplified Fraction

53/70

Mixed Number

Proper (53/70)

Decimal Value

0.757143

Percentage

75.7143%

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Step-by-Step Solution: 5/14 + 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 5/14 by 5, and multiply the numerator and denominator of 2/5 by 14 so both fractions share the common base 70.

5 × 5/14 × 5 = 25/70 and 2 × 14/5 × 14 = 28/70

Step 3

Add the Numerators

Now add the numerators (25 + 28 = 53) and keep the common denominator 70 unchanged.

25 + 28/70 = 53/70

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 53 and 70 is 1, confirming that 53/70 cannot be reduced further—it is already in its simplest irreducible form.

53/70

Step 5

Decimal & Percentage Representation

Dividing the numerator 53 by denominator 70 produces a repeating decimal (approximately 0.757143, or 75.7143%).

53 ÷ 70 = 0.757143 (75.7143%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`53/70`
Mixed Number Form	`53/70`
Decimal Form	`0.757143`
Percentage	`75.7143%`

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Frequently Asked Questions

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

5/14 + 2/5 in simplest fraction form is 53/70.

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

5/14 + 2/5 converted to a decimal is 0.757143.

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

5/14 + 2/5 expressed as a percentage is 75.7143%.

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

It results in a repeating decimal (approximately 0.757143...) because the denominator contains prime factors other than 2 and 5.