What is 3/35 plus 2/7? (Answer: 13/35)

Exact Answer

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Problem: What is 3/35 plus 2/7?
Formula / Expression: 3/35 + 2/7
Final Answer: 13/35
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 35 is an exact multiple of 7 (7 × 5 = 35). The Least Common Denominator (LCD) is simply 35, meaning we only need to scale one fraction.
Working: LCD(35, 7) = 35

Step 2: Convert to Equivalent Fractions with Common Denominator 35
Multiply the numerator and denominator of 3/35 by 1, and multiply the numerator and denominator of 2/7 by 5 so both fractions share the common base 35.
Working: 3 × 1/35 × 1 = 3/35 and 2 × 5/7 × 5 = 10/35

Step 3: Add the Numerators
Now add the numerators (3 + 10 = 13) and keep the common denominator 35 unchanged.
Working: 3 + 10/35 = 13/35

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 13 and 35 is 1, confirming that 13/35 cannot be reduced further—it is already in its simplest irreducible form.
Working: 13/35

Step 5: Decimal & Percentage Representation
Dividing the numerator 13 by denominator 35 produces a repeating decimal (approximately 0.371429, or 37.1429%).
Working: 13 ÷ 35 = 0.371429 (37.1429%)

Key Values:
- Simplified Fraction: 13/35
- Mixed Number Form: 13/35
- Decimal Value: 0.371429
- Percentage: 37.1429%

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Solved with FractionsCalc:
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3/35 + 2/7 = 13/35

Simplified Fraction

13/35

Mixed Number

Proper (13/35)

Decimal Value

0.371429

Percentage

37.1429%

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Step-by-Step Solution: 3/35 + 2/7

Step 1

Find the Least Common Denominator (LCD)

Notice that 35 is an exact multiple of 7 (7 × 5 = 35). The Least Common Denominator (LCD) is simply 35, meaning we only need to scale one fraction.

LCD(35, 7) = 35

Step 2

Convert to Equivalent Fractions with Common Denominator 35

Multiply the numerator and denominator of 3/35 by 1, and multiply the numerator and denominator of 2/7 by 5 so both fractions share the common base 35.

3 × 1/35 × 1 = 3/35 and 2 × 5/7 × 5 = 10/35

Step 3

Add the Numerators

Now add the numerators (3 + 10 = 13) and keep the common denominator 35 unchanged.

3 + 10/35 = 13/35

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 13 and 35 is 1, confirming that 13/35 cannot be reduced further—it is already in its simplest irreducible form.

13/35

Step 5

Decimal & Percentage Representation

Dividing the numerator 13 by denominator 35 produces a repeating decimal (approximately 0.371429, or 37.1429%).

13 ÷ 35 = 0.371429 (37.1429%)

Visual Representation

The diagram below illustrates 3/35 plus 2/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`13/35`
Mixed Number Form	`13/35`
Decimal Form	`0.371429`
Percentage	`37.1429%`

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Frequently Asked Questions

What is 3/35 plus 2/7 as a fraction?

3/35 + 2/7 in simplest fraction form is 13/35.

What is 3/35 plus 2/7 as a decimal?

3/35 + 2/7 converted to a decimal is 0.371429.

What is 3/35 plus 2/7 as a percentage?

3/35 + 2/7 expressed as a percentage is 37.1429%.

Does 3/35 plus 2/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.371429...) because the denominator contains prime factors other than 2 and 5.