What is 1/7 plus 3/5? (Answer: 26/35)

Exact Answer

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Problem: What is 1/7 plus 3/5?
Formula / Expression: 1/7 + 3/5
Final Answer: 26/35
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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 3/5 by 7 so both fractions share the common base 35.
Working: 1 × 5/7 × 5 = 5/35 and 3 × 7/5 × 7 = 21/35

Step 3: Add the Numerators
Now add the numerators (5 + 21 = 26) and keep the common denominator 35 unchanged.
Working: 5 + 21/35 = 26/35

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 26 and 35 is 1, confirming that 26/35 cannot be reduced further—it is already in its simplest irreducible form.
Working: 26/35

Step 5: Decimal & Percentage Representation
Dividing the numerator 26 by denominator 35 produces a repeating decimal (approximately 0.742857, or 74.2857%).
Working: 26 ÷ 35 = 0.742857 (74.2857%)

Key Values:
- Simplified Fraction: 26/35
- Mixed Number Form: 26/35
- Decimal Value: 0.742857
- Percentage: 74.2857%

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1/7 + 3/5 = 26/35

Simplified Fraction

26/35

Mixed Number

Proper (26/35)

Decimal Value

0.742857

Percentage

74.2857%

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Step-by-Step Solution: 1/7 + 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 1/7 by 5, and multiply the numerator and denominator of 3/5 by 7 so both fractions share the common base 35.

1 × 5/7 × 5 = 5/35 and 3 × 7/5 × 7 = 21/35

Step 3

Add the Numerators

Now add the numerators (5 + 21 = 26) and keep the common denominator 35 unchanged.

5 + 21/35 = 26/35

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 26 and 35 is 1, confirming that 26/35 cannot be reduced further—it is already in its simplest irreducible form.

26/35

Step 5

Decimal & Percentage Representation

Dividing the numerator 26 by denominator 35 produces a repeating decimal (approximately 0.742857, or 74.2857%).

26 ÷ 35 = 0.742857 (74.2857%)

Visual Representation

The diagram below illustrates 1/7 plus 3/5 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`26/35`
Mixed Number Form	`26/35`
Decimal Form	`0.742857`
Percentage	`74.2857%`

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Frequently Asked Questions

What is 1/7 plus 3/5 as a fraction?

1/7 + 3/5 in simplest fraction form is 26/35.

What is 1/7 plus 3/5 as a decimal?

1/7 + 3/5 converted to a decimal is 0.742857.

What is 1/7 plus 3/5 as a percentage?

1/7 + 3/5 expressed as a percentage is 74.2857%.

Does 1/7 plus 3/5 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.742857...) because the denominator contains prime factors other than 2 and 5.