What is 4/15 plus 3/4? (Answer: 61/60)

Exact Answer

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Problem: What is 4/15 plus 3/4?
Formula / Expression: 4/15 + 3/4
Final Answer: 1 1/60 (61/60)
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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 4/15 by 4, and multiply the numerator and denominator of 3/4 by 15 so both fractions share the common base 60.
Working: 4 × 4/15 × 4 = 16/60 and 3 × 15/4 × 15 = 45/60

Step 3: Add the Numerators
Now add the numerators (16 + 45 = 61) and keep the common denominator 60 unchanged.
Working: 16 + 45/60 = 61/60

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 61 and 60 is 1, confirming that 61/60 cannot be reduced further—it is already in its simplest irreducible form.
Working: 61/60

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (61) is greater than the denominator (60), divide 61 by 60: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/60.
Working: 61/60 = 1 1/60

Step 6: Decimal & Percentage Representation
Dividing the numerator 61 by denominator 60 produces a repeating decimal (approximately 1.016667, or 101.6667%).
Working: 61 ÷ 60 = 1.016667 (101.6667%)

Key Values:
- Simplified Fraction: 61/60
- Mixed Number Form: 1 1/60
- Decimal Value: 1.016667
- Percentage: 101.6667%

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Solved with FractionsCalc:
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4/15 + 3/4 = 61/60

Simplified Fraction

61/60

Mixed Number

1 1/60

Decimal Value

1.016667

Percentage

101.6667%

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Step-by-Step Solution: 4/15 + 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 4/15 by 4, and multiply the numerator and denominator of 3/4 by 15 so both fractions share the common base 60.

4 × 4/15 × 4 = 16/60 and 3 × 15/4 × 15 = 45/60

Step 3

Add the Numerators

Now add the numerators (16 + 45 = 61) and keep the common denominator 60 unchanged.

16 + 45/60 = 61/60

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 61 and 60 is 1, confirming that 61/60 cannot be reduced further—it is already in its simplest irreducible form.

61/60

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (61) is greater than the denominator (60), divide 61 by 60: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/60.

61/60 = 11/60

Step 6

Decimal & Percentage Representation

Dividing the numerator 61 by denominator 60 produces a repeating decimal (approximately 1.016667, or 101.6667%).

61 ÷ 60 = 1.016667 (101.6667%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`61/60`
Mixed Number Form	`1 1/60`
Decimal Form	`1.016667`
Percentage	`101.6667%`

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Frequently Asked Questions

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

4/15 + 3/4 in simplest fraction form is 61/60 (or 1 1/60 as a mixed number).

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

4/15 + 3/4 converted to a decimal is 1.016667.

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

4/15 + 3/4 expressed as a percentage is 101.6667%.

How do you write 4/15 plus 3/4 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 61/60 can be written as the mixed number 1 1/60.

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

It results in a repeating decimal (approximately 1.016667...) because the denominator contains prime factors other than 2 and 5.