What is 3/15 plus 2/7? (Answer: 17/35)

Exact Answer

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Problem: What is 3/15 plus 2/7?
Formula / Expression: 3/15 + 2/7
Final Answer: 17/35
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 15 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 15 × 7 = 105.
Working: LCD(15, 7) = 105

Step 2: Convert to Equivalent Fractions with Common Denominator 105
Multiply the numerator and denominator of 3/15 by 7, and multiply the numerator and denominator of 2/7 by 15 so both fractions share the common base 105.
Working: 3 × 7/15 × 7 = 21/105 and 2 × 15/7 × 15 = 30/105

Step 3: Add the Numerators
Now add the numerators (21 + 30 = 51) and keep the common denominator 105 unchanged.
Working: 21 + 30/105 = 51/105

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 51 and 105, which is 3. Divide both the numerator and denominator by 3.
Working: 51 ÷ 3/105 ÷ 3 = 17/35

Step 5: Decimal & Percentage Representation
Dividing the numerator 17 by denominator 35 produces a repeating decimal (approximately 0.485714, or 48.5714%).
Working: 17 ÷ 35 = 0.485714 (48.5714%)

Key Values:
- Simplified Fraction: 17/35
- Mixed Number Form: 17/35
- Decimal Value: 0.485714
- Percentage: 48.5714%

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Solved with FractionsCalc:
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3/15 + 2/7 = 17/35

Simplified Fraction

17/35

Mixed Number

Proper (17/35)

Decimal Value

0.485714

Percentage

48.5714%

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Step-by-Step Solution: 3/15 + 2/7

Step 1

Find the Least Common Denominator (LCD)

The denominators 15 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 15 × 7 = 105.

LCD(15, 7) = 105

Step 2

Convert to Equivalent Fractions with Common Denominator 105

Multiply the numerator and denominator of 3/15 by 7, and multiply the numerator and denominator of 2/7 by 15 so both fractions share the common base 105.

3 × 7/15 × 7 = 21/105 and 2 × 15/7 × 15 = 30/105

Step 3

Add the Numerators

Now add the numerators (21 + 30 = 51) and keep the common denominator 105 unchanged.

21 + 30/105 = 51/105

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 51 and 105, which is 3. Divide both the numerator and denominator by 3.

51 ÷ 3/105 ÷ 3 = 17/35

Step 5

Decimal & Percentage Representation

Dividing the numerator 17 by denominator 35 produces a repeating decimal (approximately 0.485714, or 48.5714%).

17 ÷ 35 = 0.485714 (48.5714%)

Visual Representation

The diagram below illustrates 3/15 plus 2/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`17/35`
Mixed Number Form	`17/35`
Decimal Form	`0.485714`
Percentage	`48.5714%`

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Frequently Asked Questions

What is 3/15 plus 2/7 as a fraction?

3/15 + 2/7 in simplest fraction form is 17/35.

What is 3/15 plus 2/7 as a decimal?

3/15 + 2/7 converted to a decimal is 0.485714.

What is 3/15 plus 2/7 as a percentage?

3/15 + 2/7 expressed as a percentage is 48.5714%.

Does 3/15 plus 2/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.485714...) because the denominator contains prime factors other than 2 and 5.