What is 2/5 plus 3/7? (Answer: 29/35)

Exact Answer

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Problem: What is 2/5 plus 3/7?
Formula / Expression: 2/5 + 3/7
Final Answer: 29/35
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 5 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 5 × 7 = 35.
Working: LCD(5, 7) = 35

Step 2: Convert to Equivalent Fractions with Common Denominator 35
Multiply the numerator and denominator of 2/5 by 7, and multiply the numerator and denominator of 3/7 by 5 so both fractions share the common base 35.
Working: 2 × 7/5 × 7 = 14/35 and 3 × 5/7 × 5 = 15/35

Step 3: Add the Numerators
Now add the numerators (14 + 15 = 29) and keep the common denominator 35 unchanged.
Working: 14 + 15/35 = 29/35

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 29 and 35 is 1, confirming that 29/35 cannot be reduced further—it is already in its simplest irreducible form.
Working: 29/35

Step 5: Decimal & Percentage Representation
Dividing the numerator 29 by denominator 35 produces a repeating decimal (approximately 0.828571, or 82.8571%).
Working: 29 ÷ 35 = 0.828571 (82.8571%)

Key Values:
- Simplified Fraction: 29/35
- Mixed Number Form: 29/35
- Decimal Value: 0.828571
- Percentage: 82.8571%

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Solved with FractionsCalc:
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2/5 + 3/7 = 29/35

Simplified Fraction

29/35

Mixed Number

Proper (29/35)

Decimal Value

0.828571

Percentage

82.8571%

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Step-by-Step Solution: 2/5 + 3/7

Step 1

Find the Least Common Denominator (LCD)

The denominators 5 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 5 × 7 = 35.

LCD(5, 7) = 35

Step 2

Convert to Equivalent Fractions with Common Denominator 35

Multiply the numerator and denominator of 2/5 by 7, and multiply the numerator and denominator of 3/7 by 5 so both fractions share the common base 35.

2 × 7/5 × 7 = 14/35 and 3 × 5/7 × 5 = 15/35

Step 3

Add the Numerators

Now add the numerators (14 + 15 = 29) and keep the common denominator 35 unchanged.

14 + 15/35 = 29/35

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 29 and 35 is 1, confirming that 29/35 cannot be reduced further—it is already in its simplest irreducible form.

29/35

Step 5

Decimal & Percentage Representation

Dividing the numerator 29 by denominator 35 produces a repeating decimal (approximately 0.828571, or 82.8571%).

29 ÷ 35 = 0.828571 (82.8571%)

Visual Representation

The diagram below illustrates 2/5 plus 3/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`29/35`
Mixed Number Form	`29/35`
Decimal Form	`0.828571`
Percentage	`82.8571%`

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Frequently Asked Questions

What is 2/5 plus 3/7 as a fraction?

2/5 + 3/7 in simplest fraction form is 29/35.

What is 2/5 plus 3/7 as a decimal?

2/5 + 3/7 converted to a decimal is 0.828571.

What is 2/5 plus 3/7 as a percentage?

2/5 + 3/7 expressed as a percentage is 82.8571%.

Does 2/5 plus 3/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.828571...) because the denominator contains prime factors other than 2 and 5.