What is 3/5 plus 2/3? (Answer: 19/15)

Exact Answer

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Problem: What is 3/5 plus 2/3?
Formula / Expression: 3/5 + 2/3
Final Answer: 1 4/15 (19/15)
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 15
Multiply the numerator and denominator of 3/5 by 3, and multiply the numerator and denominator of 2/3 by 5 so both fractions share the common base 15.
Working: 3 × 3/5 × 3 = 9/15 and 2 × 5/3 × 5 = 10/15

Step 3: Add the Numerators
Now add the numerators (9 + 10 = 19) and keep the common denominator 15 unchanged.
Working: 9 + 10/15 = 19/15

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 19 and 15 is 1, confirming that 19/15 cannot be reduced further—it is already in its simplest irreducible form.
Working: 19/15

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (19) is greater than the denominator (15), divide 19 by 15: it goes in 1 whole time(s) with a remainder of 4, giving the mixed number 1 4/15.
Working: 19/15 = 1 4/15

Step 6: Decimal & Percentage Representation
Dividing the numerator 19 by denominator 15 produces a repeating decimal (approximately 1.266667, or 126.6667%).
Working: 19 ÷ 15 = 1.266667 (126.6667%)

Key Values:
- Simplified Fraction: 19/15
- Mixed Number Form: 1 4/15
- Decimal Value: 1.266667
- Percentage: 126.6667%

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3/5 + 2/3 = 19/15

Simplified Fraction

19/15

Mixed Number

1 4/15

Decimal Value

1.266667

Percentage

126.6667%

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

Step 1

Find the Least Common Denominator (LCD)

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

LCD(5, 3) = 15

Step 2

Convert to Equivalent Fractions with Common Denominator 15

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

3 × 3/5 × 3 = 9/15 and 2 × 5/3 × 5 = 10/15

Step 3

Add the Numerators

Now add the numerators (9 + 10 = 19) and keep the common denominator 15 unchanged.

9 + 10/15 = 19/15

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 19 and 15 is 1, confirming that 19/15 cannot be reduced further—it is already in its simplest irreducible form.

19/15

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (19) is greater than the denominator (15), divide 19 by 15: it goes in 1 whole time(s) with a remainder of 4, giving the mixed number 1 4/15.

19/15 = 14/15

Step 6

Decimal & Percentage Representation

Dividing the numerator 19 by denominator 15 produces a repeating decimal (approximately 1.266667, or 126.6667%).

19 ÷ 15 = 1.266667 (126.6667%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`19/15`
Mixed Number Form	`1 4/15`
Decimal Form	`1.266667`
Percentage	`126.6667%`

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Frequently Asked Questions

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

3/5 + 2/3 in simplest fraction form is 19/15 (or 1 4/15 as a mixed number).

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

3/5 + 2/3 converted to a decimal is 1.266667.

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

3/5 + 2/3 expressed as a percentage is 126.6667%.

How do you write 3/5 plus 2/3 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 19/15 can be written as the mixed number 1 4/15.

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

It results in a repeating decimal (approximately 1.266667...) because the denominator contains prime factors other than 2 and 5.