What is 2/15 plus 2/10? (Answer: 1/3)

Exact Answer

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Problem: What is 2/15 plus 2/10?
Formula / Expression: 2/15 + 2/10
Final Answer: 1/3
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 15 and 10 share a common factor (GCD = 5). Finding their Least Common Multiple gives an LCD of 30 (which is smaller than their product 15 × 10 = 150, keeping the calculation simpler).
Working: LCD(15, 10) = 30

Step 2: Convert to Equivalent Fractions with Common Denominator 30
Multiply the numerator and denominator of 2/15 by 2, and multiply the numerator and denominator of 2/10 by 3 so both fractions share the common base 30.
Working: 2 × 2/15 × 2 = 4/30 and 2 × 3/10 × 3 = 6/30

Step 3: Add the Numerators
Now add the numerators (4 + 6 = 10) and keep the common denominator 30 unchanged.
Working: 4 + 6/30 = 10/30

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 10 and 30, which is 10. Divide both the numerator and denominator by 10.
Working: 10 ÷ 10/30 ÷ 10 = 1/3

Step 5: Decimal & Percentage Representation
Dividing the numerator 1 by denominator 3 produces a repeating decimal (approximately 0.333333, or 33.3333%).
Working: 1 ÷ 3 = 0.333333 (33.3333%)

Key Values:
- Simplified Fraction: 1/3
- Mixed Number Form: 1/3
- Decimal Value: 0.333333
- Percentage: 33.3333%

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Solved with FractionsCalc:
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2/15 + 2/10 = 1/3

Simplified Fraction

1/3

Mixed Number

Proper (1/3)

Decimal Value

0.333333

Percentage

33.3333%

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Step-by-Step Solution: 2/15 + 2/10

Step 1

Find the Least Common Denominator (LCD)

The denominators 15 and 10 share a common factor (GCD = 5). Finding their Least Common Multiple gives an LCD of 30 (which is smaller than their product 15 × 10 = 150, keeping the calculation simpler).

LCD(15, 10) = 30

Step 2

Convert to Equivalent Fractions with Common Denominator 30

Multiply the numerator and denominator of 2/15 by 2, and multiply the numerator and denominator of 2/10 by 3 so both fractions share the common base 30.

2 × 2/15 × 2 = 4/30 and 2 × 3/10 × 3 = 6/30

Step 3

Add the Numerators

Now add the numerators (4 + 6 = 10) and keep the common denominator 30 unchanged.

4 + 6/30 = 10/30

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 10 and 30, which is 10. Divide both the numerator and denominator by 10.

10 ÷ 10/30 ÷ 10 = 1/3

Step 5

Decimal & Percentage Representation

Dividing the numerator 1 by denominator 3 produces a repeating decimal (approximately 0.333333, or 33.3333%).

1 ÷ 3 = 0.333333 (33.3333%)

Visual Representation

The diagram below illustrates 2/15 plus 2/10 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`1/3`
Mixed Number Form	`1/3`
Decimal Form	`0.333333`
Percentage	`33.3333%`

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Frequently Asked Questions

What is 2/15 plus 2/10 as a fraction?

2/15 + 2/10 in simplest fraction form is 1/3.

What is 2/15 plus 2/10 as a decimal?

2/15 + 2/10 converted to a decimal is 0.333333.

What is 2/15 plus 2/10 as a percentage?

2/15 + 2/10 expressed as a percentage is 33.3333%.

Does 2/15 plus 2/10 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.333333...) because the denominator contains prime factors other than 2 and 5.