What is 4/15 plus 2/3? (Answer: 14/15)

Exact Answer

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Problem: What is 4/15 plus 2/3?
Formula / Expression: 4/15 + 2/3
Final Answer: 14/15
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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 4/15 by 1, and multiply the numerator and denominator of 2/3 by 5 so both fractions share the common base 15.
Working: 4 × 1/15 × 1 = 4/15 and 2 × 5/3 × 5 = 10/15

Step 3: Add the Numerators
Now add the numerators (4 + 10 = 14) and keep the common denominator 15 unchanged.
Working: 4 + 10/15 = 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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Solved with FractionsCalc:
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4/15 + 2/3 = 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: 4/15 + 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 4/15 by 1, and multiply the numerator and denominator of 2/3 by 5 so both fractions share the common base 15.

4 × 1/15 × 1 = 4/15 and 2 × 5/3 × 5 = 10/15

Step 3

Add the Numerators

Now add the numerators (4 + 10 = 14) and keep the common denominator 15 unchanged.

4 + 10/15 = 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 4/15 plus 2/3 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 4/15 plus 2/3 as a fraction?

4/15 + 2/3 in simplest fraction form is 14/15.

What is 4/15 plus 2/3 as a decimal?

4/15 + 2/3 converted to a decimal is 0.933333.

What is 4/15 plus 2/3 as a percentage?

4/15 + 2/3 expressed as a percentage is 93.3333%.

Does 4/15 plus 2/3 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.