What is 2/15 plus 3/4? (Answer: 53/60)

Exact Answer

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Problem: What is 2/15 plus 3/4?
Formula / Expression: 2/15 + 3/4
Final Answer: 53/60
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 15 and 4 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 15 × 4 = 60.
Working: LCD(15, 4) = 60

Step 2: Convert to Equivalent Fractions with Common Denominator 60
Multiply the numerator and denominator of 2/15 by 4, and multiply the numerator and denominator of 3/4 by 15 so both fractions share the common base 60.
Working: 2 × 4/15 × 4 = 8/60 and 3 × 15/4 × 15 = 45/60

Step 3: Add the Numerators
Now add the numerators (8 + 45 = 53) and keep the common denominator 60 unchanged.
Working: 8 + 45/60 = 53/60

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 53 and 60 is 1, confirming that 53/60 cannot be reduced further—it is already in its simplest irreducible form.
Working: 53/60

Step 5: Decimal & Percentage Representation
Dividing the numerator 53 by denominator 60 produces a repeating decimal (approximately 0.883333, or 88.3333%).
Working: 53 ÷ 60 = 0.883333 (88.3333%)

Key Values:
- Simplified Fraction: 53/60
- Mixed Number Form: 53/60
- Decimal Value: 0.883333
- Percentage: 88.3333%

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Solved with FractionsCalc:
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2/15 + 3/4 = 53/60

Simplified Fraction

53/60

Mixed Number

Proper (53/60)

Decimal Value

0.883333

Percentage

88.3333%

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Step-by-Step Solution: 2/15 + 3/4

Step 1

Find the Least Common Denominator (LCD)

The denominators 15 and 4 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 15 × 4 = 60.

LCD(15, 4) = 60

Step 2

Convert to Equivalent Fractions with Common Denominator 60

Multiply the numerator and denominator of 2/15 by 4, and multiply the numerator and denominator of 3/4 by 15 so both fractions share the common base 60.

2 × 4/15 × 4 = 8/60 and 3 × 15/4 × 15 = 45/60

Step 3

Add the Numerators

Now add the numerators (8 + 45 = 53) and keep the common denominator 60 unchanged.

8 + 45/60 = 53/60

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 53 and 60 is 1, confirming that 53/60 cannot be reduced further—it is already in its simplest irreducible form.

53/60

Step 5

Decimal & Percentage Representation

Dividing the numerator 53 by denominator 60 produces a repeating decimal (approximately 0.883333, or 88.3333%).

53 ÷ 60 = 0.883333 (88.3333%)

Visual Representation

The diagram below illustrates 2/15 plus 3/4 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`53/60`
Mixed Number Form	`53/60`
Decimal Form	`0.883333`
Percentage	`88.3333%`

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Frequently Asked Questions

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

2/15 + 3/4 in simplest fraction form is 53/60.

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

2/15 + 3/4 converted to a decimal is 0.883333.

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

2/15 + 3/4 expressed as a percentage is 88.3333%.

Does 2/15 plus 3/4 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.883333...) because the denominator contains prime factors other than 2 and 5.