What is 6/9 plus 3/4?
6/9 plus 3/4 equals 17/12 (or 1 5/12 as a mixed number) (or 1.416667 in decimal form). Learn the step-by-step solution to add 6/9 and 3/4 using Least Common Denominator and simplification.
Exact Answer
6/9 + 3/4 = 17/12
Simplified Fraction
17/12
Mixed Number
1 5/12
Decimal Value
1.416667
Percentage
141.6667%
Step-by-Step Solution: 6/9 + 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 6/9 by 4, and multiply the numerator and denominator of 3/4 by 9 so both fractions share the common base 36.
6 × 4/9 × 4 = 24/36 and 3 × 9/4 × 9 = 27/36
Step 3
Add the Numerators
Now add the numerators (24 + 27 = 51) and keep the common denominator 36 unchanged.
24 + 27/36 = 51/36
Step 4
Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 51 and 36, which is 3. Divide both the numerator and denominator by 3.
51 ÷ 3/36 ÷ 3 = 17/12
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (17) is greater than the denominator (12), divide 17 by 12: it goes in 1 whole time(s) with a remainder of 5, giving the mixed number 1 5/12.
17/12 = 15/12
Step 6
Decimal & Percentage Representation
Dividing the numerator 17 by denominator 12 produces a repeating decimal (approximately 1.416667, or 141.6667%).
17 ÷ 12 = 1.416667 (141.6667%)
Visual Representation
The diagram below illustrates 6/9 plus 3/4 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 17/12 |
| Mixed Number Form | 1 5/12 |
| Decimal Form | 1.416667 |
| Percentage | 141.6667% |
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Frequently Asked Questions
What is 6/9 plus 3/4 as a fraction?
6/9 + 3/4 in simplest fraction form is 17/12 (or 1 5/12 as a mixed number).
What is 6/9 plus 3/4 as a decimal?
6/9 + 3/4 converted to a decimal is 1.416667.
What is 6/9 plus 3/4 as a percentage?
6/9 + 3/4 expressed as a percentage is 141.6667%.
How do you write 6/9 plus 3/4 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 17/12 can be written as the mixed number 1 5/12.
Does 6/9 plus 3/4 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.416667...) because the denominator contains prime factors other than 2 and 5.