What is 2/7 plus 3/5? (Answer: 31/35)

Exact Answer

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Problem: What is 2/7 plus 3/5?
Formula / Expression: 2/7 + 3/5
Final Answer: 31/35
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 35
Multiply the numerator and denominator of 2/7 by 5, and multiply the numerator and denominator of 3/5 by 7 so both fractions share the common base 35.
Working: 2 × 5/7 × 5 = 10/35 and 3 × 7/5 × 7 = 21/35

Step 3: Add the Numerators
Now add the numerators (10 + 21 = 31) and keep the common denominator 35 unchanged.
Working: 10 + 21/35 = 31/35

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 31 and 35 is 1, confirming that 31/35 cannot be reduced further—it is already in its simplest irreducible form.
Working: 31/35

Step 5: Decimal & Percentage Representation
Dividing the numerator 31 by denominator 35 produces a repeating decimal (approximately 0.885714, or 88.5714%).
Working: 31 ÷ 35 = 0.885714 (88.5714%)

Key Values:
- Simplified Fraction: 31/35
- Mixed Number Form: 31/35
- Decimal Value: 0.885714
- Percentage: 88.5714%

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2/7 + 3/5 = 31/35

Simplified Fraction

31/35

Mixed Number

Proper (31/35)

Decimal Value

0.885714

Percentage

88.5714%

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

Step 1

Find the Least Common Denominator (LCD)

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

LCD(7, 5) = 35

Step 2

Convert to Equivalent Fractions with Common Denominator 35

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

2 × 5/7 × 5 = 10/35 and 3 × 7/5 × 7 = 21/35

Step 3

Add the Numerators

Now add the numerators (10 + 21 = 31) and keep the common denominator 35 unchanged.

10 + 21/35 = 31/35

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 31 and 35 is 1, confirming that 31/35 cannot be reduced further—it is already in its simplest irreducible form.

31/35

Step 5

Decimal & Percentage Representation

Dividing the numerator 31 by denominator 35 produces a repeating decimal (approximately 0.885714, or 88.5714%).

31 ÷ 35 = 0.885714 (88.5714%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`31/35`
Mixed Number Form	`31/35`
Decimal Form	`0.885714`
Percentage	`88.5714%`

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Frequently Asked Questions

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

2/7 + 3/5 in simplest fraction form is 31/35.

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

2/7 + 3/5 converted to a decimal is 0.885714.

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

2/7 + 3/5 expressed as a percentage is 88.5714%.

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

It results in a repeating decimal (approximately 0.885714...) because the denominator contains prime factors other than 2 and 5.