What is 2/3 plus 7/9?
2/3 plus 7/9 equals 13/9 (or 1 4/9 as a mixed number) (or 1.444444 in decimal form). Learn the step-by-step solution to add 2/3 and 7/9 using Least Common Denominator and simplification.
Exact Answer
2/3 + 7/9 = 13/9
Simplified Fraction
13/9
Mixed Number
1 4/9
Decimal Value
1.444444
Percentage
144.4444%
Step-by-Step Solution: 2/3 + 7/9
Step 1
Find the Least Common Denominator (LCD)
Notice that 9 is an exact multiple of 3 (3 × 3 = 9). The Least Common Denominator (LCD) is simply 9, meaning we only need to scale one fraction.
LCD(3, 9) = 9
Step 2
Convert to Equivalent Fractions with Common Denominator 9
Multiply the numerator and denominator of 2/3 by 3, and multiply the numerator and denominator of 7/9 by 1 so both fractions share the common base 9.
2 × 3/3 × 3 = 6/9 and 7 × 1/9 × 1 = 7/9
Step 3
Add the Numerators
Now add the numerators (6 + 7 = 13) and keep the common denominator 9 unchanged.
6 + 7/9 = 13/9
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 13 and 9 is 1, confirming that 13/9 cannot be reduced further—it is already in its simplest irreducible form.
13/9
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (13) is greater than the denominator (9), divide 13 by 9: it goes in 1 whole time(s) with a remainder of 4, giving the mixed number 1 4/9.
13/9 = 14/9
Step 6
Decimal & Percentage Representation
Dividing the numerator 13 by denominator 9 produces a repeating decimal (approximately 1.444444, or 144.4444%).
13 ÷ 9 = 1.444444 (144.4444%)
Visual Representation
The diagram below illustrates 2/3 plus 7/9 visually:
+
=
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 13/9 |
| Mixed Number Form | 1 4/9 |
| Decimal Form | 1.444444 |
| Percentage | 144.4444% |
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Frequently Asked Questions
What is 2/3 plus 7/9 as a fraction?
2/3 + 7/9 in simplest fraction form is 13/9 (or 1 4/9 as a mixed number).
What is 2/3 plus 7/9 as a decimal?
2/3 + 7/9 converted to a decimal is 1.444444.
What is 2/3 plus 7/9 as a percentage?
2/3 + 7/9 expressed as a percentage is 144.4444%.
How do you write 2/3 plus 7/9 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 13/9 can be written as the mixed number 1 4/9.
Does 2/3 plus 7/9 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.444444...) because the denominator contains prime factors other than 2 and 5.