What is 1/7 plus 2/10? (Answer: 12/35)

Exact Answer

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Problem: What is 1/7 plus 2/10?
Formula / Expression: 1/7 + 2/10
Final Answer: 12/35
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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 1/7 by 10, and multiply the numerator and denominator of 2/10 by 7 so both fractions share the common base 70.
Working: 1 × 10/7 × 10 = 10/70 and 2 × 7/10 × 7 = 14/70

Step 3: Add the Numerators
Now add the numerators (10 + 14 = 24) and keep the common denominator 70 unchanged.
Working: 10 + 14/70 = 24/70

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 24 and 70, which is 2. Divide both the numerator and denominator by 2.
Working: 24 ÷ 2/70 ÷ 2 = 12/35

Step 5: Decimal & Percentage Representation
Dividing the numerator 12 by denominator 35 produces a repeating decimal (approximately 0.342857, or 34.2857%).
Working: 12 ÷ 35 = 0.342857 (34.2857%)

Key Values:
- Simplified Fraction: 12/35
- Mixed Number Form: 12/35
- Decimal Value: 0.342857
- Percentage: 34.2857%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-7-plus-2-10/
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1/7 + 2/10 = 12/35

Simplified Fraction

12/35

Mixed Number

Proper (12/35)

Decimal Value

0.342857

Percentage

34.2857%

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Step-by-Step Solution: 1/7 + 2/10

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 1/7 by 10, and multiply the numerator and denominator of 2/10 by 7 so both fractions share the common base 70.

1 × 10/7 × 10 = 10/70 and 2 × 7/10 × 7 = 14/70

Step 3

Add the Numerators

Now add the numerators (10 + 14 = 24) and keep the common denominator 70 unchanged.

10 + 14/70 = 24/70

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 24 and 70, which is 2. Divide both the numerator and denominator by 2.

24 ÷ 2/70 ÷ 2 = 12/35

Step 5

Decimal & Percentage Representation

Dividing the numerator 12 by denominator 35 produces a repeating decimal (approximately 0.342857, or 34.2857%).

12 ÷ 35 = 0.342857 (34.2857%)

Visual Representation

The diagram below illustrates 1/7 plus 2/10 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`12/35`
Mixed Number Form	`12/35`
Decimal Form	`0.342857`
Percentage	`34.2857%`

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Frequently Asked Questions

What is 1/7 plus 2/10 as a fraction?

1/7 + 2/10 in simplest fraction form is 12/35.

What is 1/7 plus 2/10 as a decimal?

1/7 + 2/10 converted to a decimal is 0.342857.

What is 1/7 plus 2/10 as a percentage?

1/7 + 2/10 expressed as a percentage is 34.2857%.

Does 1/7 plus 2/10 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.342857...) because the denominator contains prime factors other than 2 and 5.