What is 5/9 plus 3/4? (Answer: 47/36)

Exact Answer

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Problem: What is 5/9 plus 3/4?
Formula / Expression: 5/9 + 3/4
Final Answer: 1 11/36 (47/36)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 9 and 4 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 4 = 36.
Working: LCD(9, 4) = 36

Step 2: Convert to Equivalent Fractions with Common Denominator 36
Multiply the numerator and denominator of 5/9 by 4, and multiply the numerator and denominator of 3/4 by 9 so both fractions share the common base 36.
Working: 5 × 4/9 × 4 = 20/36 and 3 × 9/4 × 9 = 27/36

Step 3: Add the Numerators
Now add the numerators (20 + 27 = 47) and keep the common denominator 36 unchanged.
Working: 20 + 27/36 = 47/36

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 47 and 36 is 1, confirming that 47/36 cannot be reduced further—it is already in its simplest irreducible form.
Working: 47/36

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (47) is greater than the denominator (36), divide 47 by 36: it goes in 1 whole time(s) with a remainder of 11, giving the mixed number 1 11/36.
Working: 47/36 = 1 11/36

Step 6: Decimal & Percentage Representation
Dividing the numerator 47 by denominator 36 produces a repeating decimal (approximately 1.305556, or 130.5556%).
Working: 47 ÷ 36 = 1.305556 (130.5556%)

Key Values:
- Simplified Fraction: 47/36
- Mixed Number Form: 1 11/36
- Decimal Value: 1.305556
- Percentage: 130.5556%

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Solved with FractionsCalc:
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5/9 + 3/4 = 47/36

Simplified Fraction

47/36

Mixed Number

1 11/36

Decimal Value

1.305556

Percentage

130.5556%

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Step-by-Step Solution: 5/9 + 3/4

Step 1

Find the Least Common Denominator (LCD)

The denominators 9 and 4 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 4 = 36.

LCD(9, 4) = 36

Step 2

Convert to Equivalent Fractions with Common Denominator 36

Multiply the numerator and denominator of 5/9 by 4, and multiply the numerator and denominator of 3/4 by 9 so both fractions share the common base 36.

5 × 4/9 × 4 = 20/36 and 3 × 9/4 × 9 = 27/36

Step 3

Add the Numerators

Now add the numerators (20 + 27 = 47) and keep the common denominator 36 unchanged.

20 + 27/36 = 47/36

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 47 and 36 is 1, confirming that 47/36 cannot be reduced further—it is already in its simplest irreducible form.

47/36

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (47) is greater than the denominator (36), divide 47 by 36: it goes in 1 whole time(s) with a remainder of 11, giving the mixed number 1 11/36.

47/36 = 111/36

Step 6

Decimal & Percentage Representation

Dividing the numerator 47 by denominator 36 produces a repeating decimal (approximately 1.305556, or 130.5556%).

47 ÷ 36 = 1.305556 (130.5556%)

Visual Representation

The diagram below illustrates 5/9 plus 3/4 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`47/36`
Mixed Number Form	`1 11/36`
Decimal Form	`1.305556`
Percentage	`130.5556%`

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Frequently Asked Questions

What is 5/9 plus 3/4 as a fraction?

5/9 + 3/4 in simplest fraction form is 47/36 (or 1 11/36 as a mixed number).

What is 5/9 plus 3/4 as a decimal?

5/9 + 3/4 converted to a decimal is 1.305556.

What is 5/9 plus 3/4 as a percentage?

5/9 + 3/4 expressed as a percentage is 130.5556%.

How do you write 5/9 plus 3/4 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 47/36 can be written as the mixed number 1 11/36.

Does 5/9 plus 3/4 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.305556...) because the denominator contains prime factors other than 2 and 5.