What is 2/35 plus 2/15? (Answer: 4/21)

Exact Answer

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Problem: What is 2/35 plus 2/15?
Formula / Expression: 2/35 + 2/15
Final Answer: 4/21
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 35 and 15 share a common factor (GCD = 5). Finding their Least Common Multiple gives an LCD of 105 (which is smaller than their product 35 × 15 = 525, keeping the calculation simpler).
Working: LCD(35, 15) = 105

Step 2: Convert to Equivalent Fractions with Common Denominator 105
Multiply the numerator and denominator of 2/35 by 3, and multiply the numerator and denominator of 2/15 by 7 so both fractions share the common base 105.
Working: 2 × 3/35 × 3 = 6/105 and 2 × 7/15 × 7 = 14/105

Step 3: Add the Numerators
Now add the numerators (6 + 14 = 20) and keep the common denominator 105 unchanged.
Working: 6 + 14/105 = 20/105

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 20 and 105, which is 5. Divide both the numerator and denominator by 5.
Working: 20 ÷ 5/105 ÷ 5 = 4/21

Step 5: Decimal & Percentage Representation
Dividing the numerator 4 by denominator 21 produces a repeating decimal (approximately 0.190476, or 19.0476%).
Working: 4 ÷ 21 = 0.190476 (19.0476%)

Key Values:
- Simplified Fraction: 4/21
- Mixed Number Form: 4/21
- Decimal Value: 0.190476
- Percentage: 19.0476%

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Solved with FractionsCalc:
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2/35 + 2/15 = 4/21

Simplified Fraction

4/21

Mixed Number

Proper (4/21)

Decimal Value

0.190476

Percentage

19.0476%

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Step-by-Step Solution: 2/35 + 2/15

Step 1

Find the Least Common Denominator (LCD)

The denominators 35 and 15 share a common factor (GCD = 5). Finding their Least Common Multiple gives an LCD of 105 (which is smaller than their product 35 × 15 = 525, keeping the calculation simpler).

LCD(35, 15) = 105

Step 2

Convert to Equivalent Fractions with Common Denominator 105

Multiply the numerator and denominator of 2/35 by 3, and multiply the numerator and denominator of 2/15 by 7 so both fractions share the common base 105.

2 × 3/35 × 3 = 6/105 and 2 × 7/15 × 7 = 14/105

Step 3

Add the Numerators

Now add the numerators (6 + 14 = 20) and keep the common denominator 105 unchanged.

6 + 14/105 = 20/105

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 20 and 105, which is 5. Divide both the numerator and denominator by 5.

20 ÷ 5/105 ÷ 5 = 4/21

Step 5

Decimal & Percentage Representation

Dividing the numerator 4 by denominator 21 produces a repeating decimal (approximately 0.190476, or 19.0476%).

4 ÷ 21 = 0.190476 (19.0476%)

Visual Representation

The diagram below illustrates 2/35 plus 2/15 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`4/21`
Mixed Number Form	`4/21`
Decimal Form	`0.190476`
Percentage	`19.0476%`

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Frequently Asked Questions

What is 2/35 plus 2/15 as a fraction?

2/35 + 2/15 in simplest fraction form is 4/21.

What is 2/35 plus 2/15 as a decimal?

2/35 + 2/15 converted to a decimal is 0.190476.

What is 2/35 plus 2/15 as a percentage?

2/35 + 2/15 expressed as a percentage is 19.0476%.

Does 2/35 plus 2/15 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.190476...) because the denominator contains prime factors other than 2 and 5.