What is 1/3 plus 3/5? (Answer: 14/15)

Exact Answer

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Problem: What is 1/3 plus 3/5?
Formula / Expression: 1/3 + 3/5
Final Answer: 14/15
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 3 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 3 × 5 = 15.
Working: LCD(3, 5) = 15

Step 2: Convert to Equivalent Fractions with Common Denominator 15
Multiply the numerator and denominator of 1/3 by 5, and multiply the numerator and denominator of 3/5 by 3 so both fractions share the common base 15.
Working: 1 × 5/3 × 5 = 5/15 and 3 × 3/5 × 3 = 9/15

Step 3: Add the Numerators
Now add the numerators (5 + 9 = 14) and keep the common denominator 15 unchanged.
Working: 5 + 9/15 = 14/15

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 14 and 15 is 1, confirming that 14/15 cannot be reduced further—it is already in its simplest irreducible form.
Working: 14/15

Step 5: Decimal & Percentage Representation
Dividing the numerator 14 by denominator 15 produces a repeating decimal (approximately 0.933333, or 93.3333%).
Working: 14 ÷ 15 = 0.933333 (93.3333%)

Key Values:
- Simplified Fraction: 14/15
- Mixed Number Form: 14/15
- Decimal Value: 0.933333
- Percentage: 93.3333%

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1/3 + 3/5 = 14/15

Simplified Fraction

14/15

Mixed Number

Proper (14/15)

Decimal Value

0.933333

Percentage

93.3333%

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Step-by-Step Solution: 1/3 + 3/5

Step 1

Find the Least Common Denominator (LCD)

The denominators 3 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 3 × 5 = 15.

LCD(3, 5) = 15

Step 2

Convert to Equivalent Fractions with Common Denominator 15

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

1 × 5/3 × 5 = 5/15 and 3 × 3/5 × 3 = 9/15

Step 3

Add the Numerators

Now add the numerators (5 + 9 = 14) and keep the common denominator 15 unchanged.

5 + 9/15 = 14/15

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 14 and 15 is 1, confirming that 14/15 cannot be reduced further—it is already in its simplest irreducible form.

14/15

Step 5

Decimal & Percentage Representation

Dividing the numerator 14 by denominator 15 produces a repeating decimal (approximately 0.933333, or 93.3333%).

14 ÷ 15 = 0.933333 (93.3333%)

Visual Representation

The diagram below illustrates 1/3 plus 3/5 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`14/15`
Mixed Number Form	`14/15`
Decimal Form	`0.933333`
Percentage	`93.3333%`

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Frequently Asked Questions

What is 1/3 plus 3/5 as a fraction?

1/3 + 3/5 in simplest fraction form is 14/15.

What is 1/3 plus 3/5 as a decimal?

1/3 + 3/5 converted to a decimal is 0.933333.

What is 1/3 plus 3/5 as a percentage?

1/3 + 3/5 expressed as a percentage is 93.3333%.

Does 1/3 plus 3/5 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.933333...) because the denominator contains prime factors other than 2 and 5.