What is 1/7 plus 2/5? (Answer: 19/35)

Exact Answer

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Problem: What is 1/7 plus 2/5?
Formula / Expression: 1/7 + 2/5
Final Answer: 19/35
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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 1/7 by 5, and multiply the numerator and denominator of 2/5 by 7 so both fractions share the common base 35.
Working: 1 × 5/7 × 5 = 5/35 and 2 × 7/5 × 7 = 14/35

Step 3: Add the Numerators
Now add the numerators (5 + 14 = 19) and keep the common denominator 35 unchanged.
Working: 5 + 14/35 = 19/35

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 19 and 35 is 1, confirming that 19/35 cannot be reduced further—it is already in its simplest irreducible form.
Working: 19/35

Step 5: Decimal & Percentage Representation
Dividing the numerator 19 by denominator 35 produces a repeating decimal (approximately 0.542857, or 54.2857%).
Working: 19 ÷ 35 = 0.542857 (54.2857%)

Key Values:
- Simplified Fraction: 19/35
- Mixed Number Form: 19/35
- Decimal Value: 0.542857
- Percentage: 54.2857%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-7-plus-2-5/
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1/7 + 2/5 = 19/35

Simplified Fraction

19/35

Mixed Number

Proper (19/35)

Decimal Value

0.542857

Percentage

54.2857%

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Step-by-Step Solution: 1/7 + 2/5

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 1/7 by 5, and multiply the numerator and denominator of 2/5 by 7 so both fractions share the common base 35.

1 × 5/7 × 5 = 5/35 and 2 × 7/5 × 7 = 14/35

Step 3

Add the Numerators

Now add the numerators (5 + 14 = 19) and keep the common denominator 35 unchanged.

5 + 14/35 = 19/35

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 19 and 35 is 1, confirming that 19/35 cannot be reduced further—it is already in its simplest irreducible form.

19/35

Step 5

Decimal & Percentage Representation

Dividing the numerator 19 by denominator 35 produces a repeating decimal (approximately 0.542857, or 54.2857%).

19 ÷ 35 = 0.542857 (54.2857%)

Visual Representation

The diagram below illustrates 1/7 plus 2/5 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`19/35`
Mixed Number Form	`19/35`
Decimal Form	`0.542857`
Percentage	`54.2857%`

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Frequently Asked Questions

What is 1/7 plus 2/5 as a fraction?

1/7 + 2/5 in simplest fraction form is 19/35.

What is 1/7 plus 2/5 as a decimal?

1/7 + 2/5 converted to a decimal is 0.542857.

What is 1/7 plus 2/5 as a percentage?

1/7 + 2/5 expressed as a percentage is 54.2857%.

Does 1/7 plus 2/5 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.542857...) because the denominator contains prime factors other than 2 and 5.