What is 7/15 plus 2/3? (Answer: 17/15)

Exact Answer

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Problem: What is 7/15 plus 2/3?
Formula / Expression: 7/15 + 2/3
Final Answer: 1 2/15 (17/15)
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 15
Multiply the numerator and denominator of 7/15 by 1, and multiply the numerator and denominator of 2/3 by 5 so both fractions share the common base 15.
Working: 7 × 1/15 × 1 = 7/15 and 2 × 5/3 × 5 = 10/15

Step 3: Add the Numerators
Now add the numerators (7 + 10 = 17) and keep the common denominator 15 unchanged.
Working: 7 + 10/15 = 17/15

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 17 and 15 is 1, confirming that 17/15 cannot be reduced further—it is already in its simplest irreducible form.
Working: 17/15

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (17) is greater than the denominator (15), divide 17 by 15: it goes in 1 whole time(s) with a remainder of 2, giving the mixed number 1 2/15.
Working: 17/15 = 1 2/15

Step 6: Decimal & Percentage Representation
Dividing the numerator 17 by denominator 15 produces a repeating decimal (approximately 1.133333, or 113.3333%).
Working: 17 ÷ 15 = 1.133333 (113.3333%)

Key Values:
- Simplified Fraction: 17/15
- Mixed Number Form: 1 2/15
- Decimal Value: 1.133333
- Percentage: 113.3333%

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Solved with FractionsCalc:
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7/15 + 2/3 = 17/15

Simplified Fraction

17/15

Mixed Number

1 2/15

Decimal Value

1.133333

Percentage

113.3333%

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Step-by-Step Solution: 7/15 + 2/3

Step 1

Find the Least Common Denominator (LCD)

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

LCD(15, 3) = 15

Step 2

Convert to Equivalent Fractions with Common Denominator 15

Multiply the numerator and denominator of 7/15 by 1, and multiply the numerator and denominator of 2/3 by 5 so both fractions share the common base 15.

7 × 1/15 × 1 = 7/15 and 2 × 5/3 × 5 = 10/15

Step 3

Add the Numerators

Now add the numerators (7 + 10 = 17) and keep the common denominator 15 unchanged.

7 + 10/15 = 17/15

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 17 and 15 is 1, confirming that 17/15 cannot be reduced further—it is already in its simplest irreducible form.

17/15

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (17) is greater than the denominator (15), divide 17 by 15: it goes in 1 whole time(s) with a remainder of 2, giving the mixed number 1 2/15.

17/15 = 12/15

Step 6

Decimal & Percentage Representation

Dividing the numerator 17 by denominator 15 produces a repeating decimal (approximately 1.133333, or 113.3333%).

17 ÷ 15 = 1.133333 (113.3333%)

Visual Representation

The diagram below illustrates 7/15 plus 2/3 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`17/15`
Mixed Number Form	`1 2/15`
Decimal Form	`1.133333`
Percentage	`113.3333%`

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Frequently Asked Questions

What is 7/15 plus 2/3 as a fraction?

7/15 + 2/3 in simplest fraction form is 17/15 (or 1 2/15 as a mixed number).

What is 7/15 plus 2/3 as a decimal?

7/15 + 2/3 converted to a decimal is 1.133333.

What is 7/15 plus 2/3 as a percentage?

7/15 + 2/3 expressed as a percentage is 113.3333%.

How do you write 7/15 plus 2/3 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 17/15 can be written as the mixed number 1 2/15.

Does 7/15 plus 2/3 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.133333...) because the denominator contains prime factors other than 2 and 5.