What is 2/7 plus 3/10? (Answer: 41/70)

Exact Answer

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Problem: What is 2/7 plus 3/10?
Formula / Expression: 2/7 + 3/10
Final Answer: 41/70
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 7 and 10 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 7 × 10 = 70.
Working: LCD(7, 10) = 70

Step 2: Convert to Equivalent Fractions with Common Denominator 70
Multiply the numerator and denominator of 2/7 by 10, and multiply the numerator and denominator of 3/10 by 7 so both fractions share the common base 70.
Working: 2 × 10/7 × 10 = 20/70 and 3 × 7/10 × 7 = 21/70

Step 3: Add the Numerators
Now add the numerators (20 + 21 = 41) and keep the common denominator 70 unchanged.
Working: 20 + 21/70 = 41/70

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 41 and 70 is 1, confirming that 41/70 cannot be reduced further—it is already in its simplest irreducible form.
Working: 41/70

Step 5: Decimal & Percentage Representation
Dividing the numerator 41 by denominator 70 produces a repeating decimal (approximately 0.585714, or 58.5714%).
Working: 41 ÷ 70 = 0.585714 (58.5714%)

Key Values:
- Simplified Fraction: 41/70
- Mixed Number Form: 41/70
- Decimal Value: 0.585714
- Percentage: 58.5714%

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Solved with FractionsCalc:
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2/7 + 3/10 = 41/70

Simplified Fraction

41/70

Mixed Number

Proper (41/70)

Decimal Value

0.585714

Percentage

58.5714%

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Step-by-Step Solution: 2/7 + 3/10

Step 1

Find the Least Common Denominator (LCD)

The denominators 7 and 10 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 7 × 10 = 70.

LCD(7, 10) = 70

Step 2

Convert to Equivalent Fractions with Common Denominator 70

Multiply the numerator and denominator of 2/7 by 10, and multiply the numerator and denominator of 3/10 by 7 so both fractions share the common base 70.

2 × 10/7 × 10 = 20/70 and 3 × 7/10 × 7 = 21/70

Step 3

Add the Numerators

Now add the numerators (20 + 21 = 41) and keep the common denominator 70 unchanged.

20 + 21/70 = 41/70

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 41 and 70 is 1, confirming that 41/70 cannot be reduced further—it is already in its simplest irreducible form.

41/70

Step 5

Decimal & Percentage Representation

Dividing the numerator 41 by denominator 70 produces a repeating decimal (approximately 0.585714, or 58.5714%).

41 ÷ 70 = 0.585714 (58.5714%)

Visual Representation

The diagram below illustrates 2/7 plus 3/10 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`41/70`
Mixed Number Form	`41/70`
Decimal Form	`0.585714`
Percentage	`58.5714%`

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Frequently Asked Questions

What is 2/7 plus 3/10 as a fraction?

2/7 + 3/10 in simplest fraction form is 41/70.

What is 2/7 plus 3/10 as a decimal?

2/7 + 3/10 converted to a decimal is 0.585714.

What is 2/7 plus 3/10 as a percentage?

2/7 + 3/10 expressed as a percentage is 58.5714%.

Does 2/7 plus 3/10 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.585714...) because the denominator contains prime factors other than 2 and 5.