What is 3/15 plus 2/5? (Answer: 3/5)

Exact Answer

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Problem: What is 3/15 plus 2/5?
Formula / Expression: 3/15 + 2/5
Final Answer: 3/5
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 15 is an exact multiple of 5 (5 × 3 = 15). The Least Common Denominator (LCD) is simply 15, meaning we only need to scale one fraction.
Working: LCD(15, 5) = 15

Step 2: Convert to Equivalent Fractions with Common Denominator 15
Multiply the numerator and denominator of 3/15 by 1, and multiply the numerator and denominator of 2/5 by 3 so both fractions share the common base 15.
Working: 3 × 1/15 × 1 = 3/15 and 2 × 3/5 × 3 = 6/15

Step 3: Add the Numerators
Now add the numerators (3 + 6 = 9) and keep the common denominator 15 unchanged.
Working: 3 + 6/15 = 9/15

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 9 and 15, which is 3. Divide both the numerator and denominator by 3.
Working: 9 ÷ 3/15 ÷ 3 = 3/5

Step 5: Decimal & Percentage Representation
Dividing the numerator 3 by denominator 5 yields an exact terminating decimal of 0.6 (or 60%).
Working: 3 ÷ 5 = 0.6 (60%)

Key Values:
- Simplified Fraction: 3/5
- Mixed Number Form: 3/5
- Decimal Value: 0.6
- Percentage: 60%

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Solved with FractionsCalc:
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3/15 + 2/5 = 3/5

Simplified Fraction

3/5

Mixed Number

Proper (3/5)

Decimal Value

0.6

Percentage

60%

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Step-by-Step Solution: 3/15 + 2/5

Step 1

Find the Least Common Denominator (LCD)

Notice that 15 is an exact multiple of 5 (5 × 3 = 15). The Least Common Denominator (LCD) is simply 15, meaning we only need to scale one fraction.

LCD(15, 5) = 15

Step 2

Convert to Equivalent Fractions with Common Denominator 15

Multiply the numerator and denominator of 3/15 by 1, and multiply the numerator and denominator of 2/5 by 3 so both fractions share the common base 15.

3 × 1/15 × 1 = 3/15 and 2 × 3/5 × 3 = 6/15

Step 3

Add the Numerators

Now add the numerators (3 + 6 = 9) and keep the common denominator 15 unchanged.

3 + 6/15 = 9/15

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 9 and 15, which is 3. Divide both the numerator and denominator by 3.

9 ÷ 3/15 ÷ 3 = 3/5

Step 5

Decimal & Percentage Representation

Dividing the numerator 3 by denominator 5 yields an exact terminating decimal of 0.6 (or 60%).

3 ÷ 5 = 0.6 (60%)

Visual Representation

The diagram below illustrates 3/15 plus 2/5 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`3/5`
Mixed Number Form	`3/5`
Decimal Form	`0.6`
Percentage	`60%`

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Frequently Asked Questions

What is 3/15 plus 2/5 as a fraction?

3/15 + 2/5 in simplest fraction form is 3/5.

What is 3/15 plus 2/5 as a decimal?

3/15 + 2/5 converted to a decimal is 0.6.

What is 3/15 plus 2/5 as a percentage?

3/15 + 2/5 expressed as a percentage is 60%.

Does 3/15 plus 2/5 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.6) because the denominator in simplest terms contains only prime factors 2 and/or 5.