What is 2/7 plus 7/10? (Answer: 69/70)

Exact Answer

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Problem: What is 2/7 plus 7/10?
Formula / Expression: 2/7 + 7/10
Final Answer: 69/70
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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 7/10 by 7 so both fractions share the common base 70.
Working: 2 × 10/7 × 10 = 20/70 and 7 × 7/10 × 7 = 49/70

Step 3: Add the Numerators
Now add the numerators (20 + 49 = 69) and keep the common denominator 70 unchanged.
Working: 20 + 49/70 = 69/70

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 69 and 70 is 1, confirming that 69/70 cannot be reduced further—it is already in its simplest irreducible form.
Working: 69/70

Step 5: Decimal & Percentage Representation
Dividing the numerator 69 by denominator 70 produces a repeating decimal (approximately 0.985714, or 98.5714%).
Working: 69 ÷ 70 = 0.985714 (98.5714%)

Key Values:
- Simplified Fraction: 69/70
- Mixed Number Form: 69/70
- Decimal Value: 0.985714
- Percentage: 98.5714%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-7-plus-7-10/
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2/7 + 7/10 = 69/70

Simplified Fraction

69/70

Mixed Number

Proper (69/70)

Decimal Value

0.985714

Percentage

98.5714%

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

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 7/10 by 7 so both fractions share the common base 70.

2 × 10/7 × 10 = 20/70 and 7 × 7/10 × 7 = 49/70

Step 3

Add the Numerators

Now add the numerators (20 + 49 = 69) and keep the common denominator 70 unchanged.

20 + 49/70 = 69/70

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 69 and 70 is 1, confirming that 69/70 cannot be reduced further—it is already in its simplest irreducible form.

69/70

Step 5

Decimal & Percentage Representation

Dividing the numerator 69 by denominator 70 produces a repeating decimal (approximately 0.985714, or 98.5714%).

69 ÷ 70 = 0.985714 (98.5714%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`69/70`
Mixed Number Form	`69/70`
Decimal Form	`0.985714`
Percentage	`98.5714%`

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Frequently Asked Questions

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

2/7 + 7/10 in simplest fraction form is 69/70.

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

2/7 + 7/10 converted to a decimal is 0.985714.

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

2/7 + 7/10 expressed as a percentage is 98.5714%.

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

It results in a repeating decimal (approximately 0.985714...) because the denominator contains prime factors other than 2 and 5.