What is 3/9 plus 3/4? (Answer: 13/12)

Exact Answer

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Problem: What is 3/9 plus 3/4?
Formula / Expression: 3/9 + 3/4
Final Answer: 1 1/12 (13/12)
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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 3/9 by 4, and multiply the numerator and denominator of 3/4 by 9 so both fractions share the common base 36.
Working: 3 × 4/9 × 4 = 12/36 and 3 × 9/4 × 9 = 27/36

Step 3: Add the Numerators
Now add the numerators (12 + 27 = 39) and keep the common denominator 36 unchanged.
Working: 12 + 27/36 = 39/36

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 39 and 36, which is 3. Divide both the numerator and denominator by 3.
Working: 39 ÷ 3/36 ÷ 3 = 13/12

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (13) is greater than the denominator (12), divide 13 by 12: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/12.
Working: 13/12 = 1 1/12

Step 6: Decimal & Percentage Representation
Dividing the numerator 13 by denominator 12 produces a repeating decimal (approximately 1.083333, or 108.3333%).
Working: 13 ÷ 12 = 1.083333 (108.3333%)

Key Values:
- Simplified Fraction: 13/12
- Mixed Number Form: 1 1/12
- Decimal Value: 1.083333
- Percentage: 108.3333%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-9-plus-3-4/
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3/9 + 3/4 = 13/12

Simplified Fraction

13/12

Mixed Number

1 1/12

Decimal Value

1.083333

Percentage

108.3333%

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Step-by-Step Solution: 3/9 + 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 3/9 by 4, and multiply the numerator and denominator of 3/4 by 9 so both fractions share the common base 36.

3 × 4/9 × 4 = 12/36 and 3 × 9/4 × 9 = 27/36

Step 3

Add the Numerators

Now add the numerators (12 + 27 = 39) and keep the common denominator 36 unchanged.

12 + 27/36 = 39/36

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 39 and 36, which is 3. Divide both the numerator and denominator by 3.

39 ÷ 3/36 ÷ 3 = 13/12

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (13) is greater than the denominator (12), divide 13 by 12: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/12.

13/12 = 11/12

Step 6

Decimal & Percentage Representation

Dividing the numerator 13 by denominator 12 produces a repeating decimal (approximately 1.083333, or 108.3333%).

13 ÷ 12 = 1.083333 (108.3333%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`13/12`
Mixed Number Form	`1 1/12`
Decimal Form	`1.083333`
Percentage	`108.3333%`

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Frequently Asked Questions

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

3/9 + 3/4 in simplest fraction form is 13/12 (or 1 1/12 as a mixed number).

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

3/9 + 3/4 converted to a decimal is 1.083333.

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

3/9 + 3/4 expressed as a percentage is 108.3333%.

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

Because the numerator is greater than the denominator, the improper fraction 13/12 can be written as the mixed number 1 1/12.

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

It results in a repeating decimal (approximately 1.083333...) because the denominator contains prime factors other than 2 and 5.