What is 9/27 plus 3/4?
9/27 plus 3/4 equals 13/12 (or 1 1/12 as a mixed number) (or 1.083333 in decimal form). Learn the step-by-step solution to add 9/27 and 3/4 using Least Common Denominator and simplification.
Exact Answer
9/27 + 3/4 = 13/12
Simplified Fraction
13/12
Mixed Number
1 1/12
Decimal Value
1.083333
Percentage
108.3333%
Step-by-Step Solution: 9/27 + 3/4
Step 1
Find the Least Common Denominator (LCD)
The denominators 27 and 4 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 27 × 4 = 108.
LCD(27, 4) = 108
Step 2
Convert to Equivalent Fractions with Common Denominator 108
Multiply the numerator and denominator of 9/27 by 4, and multiply the numerator and denominator of 3/4 by 27 so both fractions share the common base 108.
9 × 4/27 × 4 = 36/108 and 3 × 27/4 × 27 = 81/108
Step 3
Add the Numerators
Now add the numerators (36 + 81 = 117) and keep the common denominator 108 unchanged.
36 + 81/108 = 117/108
Step 4
Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 117 and 108, which is 9. Divide both the numerator and denominator by 9.
117 ÷ 9/108 ÷ 9 = 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 9/27 plus 3/4 visually:
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=
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 9/27 plus 3/4 as a fraction?
9/27 + 3/4 in simplest fraction form is 13/12 (or 1 1/12 as a mixed number).
What is 9/27 plus 3/4 as a decimal?
9/27 + 3/4 converted to a decimal is 1.083333.
What is 9/27 plus 3/4 as a percentage?
9/27 + 3/4 expressed as a percentage is 108.3333%.
How do you write 9/27 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 9/27 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.