What is 2/5 plus 2/3? (Answer: 16/15)

Exact Answer

==================================================
Problem: What is 2/5 plus 2/3?
Formula / Expression: 2/5 + 2/3
Final Answer: 1 1/15 (16/15)
==================================================

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 2/5 by 3, and multiply the numerator and denominator of 2/3 by 5 so both fractions share the common base 15.
Working: 2 × 3/5 × 3 = 6/15 and 2 × 5/3 × 5 = 10/15

Step 3: Add the Numerators
Now add the numerators (6 + 10 = 16) and keep the common denominator 15 unchanged.
Working: 6 + 10/15 = 16/15

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 16 and 15 is 1, confirming that 16/15 cannot be reduced further—it is already in its simplest irreducible form.
Working: 16/15

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (16) is greater than the denominator (15), divide 16 by 15: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/15.
Working: 16/15 = 1 1/15

Step 6: Decimal & Percentage Representation
Dividing the numerator 16 by denominator 15 produces a repeating decimal (approximately 1.066667, or 106.6667%).
Working: 16 ÷ 15 = 1.066667 (106.6667%)

Key Values:
- Simplified Fraction: 16/15
- Mixed Number Form: 1 1/15
- Decimal Value: 1.066667
- Percentage: 106.6667%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-5-plus-2-3/
==================================================

2/5 + 2/3 = 16/15

Simplified Fraction

16/15

Mixed Number

1 1/15

Decimal Value

1.066667

Percentage

106.6667%

Reduce / Convert Fraction:

Convert Fraction:

Enter Decimal Number:

Enter Percentage: %

What is % of

From Value: To Value:

Simplify Ratio: :

First Number: Second Number:

Find All Factors of:

Dividend: ÷ Divisor:

√ Square Root of: OR Power (x^y): ^{^}

x² + x + = 0

Number (n! & log):

Circle Radius (r):

Side a: Side b:

Angle (Degrees): °

Numbers (comma separated):

Total Items (n): Choose (r):

Decimal Number:

Number (1–3999):

Step-by-Step Solution: 2/5 + 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 2/5 by 3, and multiply the numerator and denominator of 2/3 by 5 so both fractions share the common base 15.

2 × 3/5 × 3 = 6/15 and 2 × 5/3 × 5 = 10/15

Step 3

Add the Numerators

Now add the numerators (6 + 10 = 16) and keep the common denominator 15 unchanged.

6 + 10/15 = 16/15

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 16 and 15 is 1, confirming that 16/15 cannot be reduced further—it is already in its simplest irreducible form.

16/15

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (16) is greater than the denominator (15), divide 16 by 15: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/15.

16/15 = 11/15

Step 6

Decimal & Percentage Representation

Dividing the numerator 16 by denominator 15 produces a repeating decimal (approximately 1.066667, or 106.6667%).

16 ÷ 15 = 1.066667 (106.6667%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`16/15`
Mixed Number Form	`1 1/15`
Decimal Form	`1.066667`
Percentage	`106.6667%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

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

2/5 + 2/3 in simplest fraction form is 16/15 (or 1 1/15 as a mixed number).

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

2/5 + 2/3 converted to a decimal is 1.066667.

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

2/5 + 2/3 expressed as a percentage is 106.6667%.

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

Because the numerator is greater than the denominator, the improper fraction 16/15 can be written as the mixed number 1 1/15.

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

It results in a repeating decimal (approximately 1.066667...) because the denominator contains prime factors other than 2 and 5.