What is 3/14 plus 2/5? (Answer: 43/70)

Exact Answer

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Problem: What is 3/14 plus 2/5?
Formula / Expression: 3/14 + 2/5
Final Answer: 43/70
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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 3/14 by 5, and multiply the numerator and denominator of 2/5 by 14 so both fractions share the common base 70.
Working: 3 × 5/14 × 5 = 15/70 and 2 × 14/5 × 14 = 28/70

Step 3: Add the Numerators
Now add the numerators (15 + 28 = 43) and keep the common denominator 70 unchanged.
Working: 15 + 28/70 = 43/70

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 43 and 70 is 1, confirming that 43/70 cannot be reduced further—it is already in its simplest irreducible form.
Working: 43/70

Step 5: Decimal & Percentage Representation
Dividing the numerator 43 by denominator 70 produces a repeating decimal (approximately 0.614286, or 61.4286%).
Working: 43 ÷ 70 = 0.614286 (61.4286%)

Key Values:
- Simplified Fraction: 43/70
- Mixed Number Form: 43/70
- Decimal Value: 0.614286
- Percentage: 61.4286%

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3/14 + 2/5 = 43/70

Simplified Fraction

43/70

Mixed Number

Proper (43/70)

Decimal Value

0.614286

Percentage

61.4286%

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Step-by-Step Solution: 3/14 + 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 3/14 by 5, and multiply the numerator and denominator of 2/5 by 14 so both fractions share the common base 70.

3 × 5/14 × 5 = 15/70 and 2 × 14/5 × 14 = 28/70

Step 3

Add the Numerators

Now add the numerators (15 + 28 = 43) and keep the common denominator 70 unchanged.

15 + 28/70 = 43/70

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 43 and 70 is 1, confirming that 43/70 cannot be reduced further—it is already in its simplest irreducible form.

43/70

Step 5

Decimal & Percentage Representation

Dividing the numerator 43 by denominator 70 produces a repeating decimal (approximately 0.614286, or 61.4286%).

43 ÷ 70 = 0.614286 (61.4286%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`43/70`
Mixed Number Form	`43/70`
Decimal Form	`0.614286`
Percentage	`61.4286%`

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Frequently Asked Questions

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

3/14 + 2/5 in simplest fraction form is 43/70.

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

3/14 + 2/5 converted to a decimal is 0.614286.

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

3/14 + 2/5 expressed as a percentage is 61.4286%.

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

It results in a repeating decimal (approximately 0.614286...) because the denominator contains prime factors other than 2 and 5.