What is 3/9 plus 6/7?
3/9 plus 6/7 equals 25/21 (or 1 4/21 as a mixed number) (or 1.190476 in decimal form). Learn the step-by-step solution to add 3/9 and 6/7 using Least Common Denominator and simplification.
Exact Answer
3/9 + 6/7 = 25/21
Simplified Fraction
25/21
Mixed Number
1 4/21
Decimal Value
1.190476
Percentage
119.0476%
Step-by-Step Solution: 3/9 + 6/7
Step 1
Find the Least Common Denominator (LCD)
The denominators 9 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 7 = 63.
LCD(9, 7) = 63
Step 2
Convert to Equivalent Fractions with Common Denominator 63
Multiply the numerator and denominator of 3/9 by 7, and multiply the numerator and denominator of 6/7 by 9 so both fractions share the common base 63.
3 × 7/9 × 7 = 21/63 and 6 × 9/7 × 9 = 54/63
Step 3
Add the Numerators
Now add the numerators (21 + 54 = 75) and keep the common denominator 63 unchanged.
21 + 54/63 = 75/63
Step 4
Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 75 and 63, which is 3. Divide both the numerator and denominator by 3.
75 ÷ 3/63 ÷ 3 = 25/21
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (25) is greater than the denominator (21), divide 25 by 21: it goes in 1 whole time(s) with a remainder of 4, giving the mixed number 1 4/21.
25/21 = 14/21
Step 6
Decimal & Percentage Representation
Dividing the numerator 25 by denominator 21 produces a repeating decimal (approximately 1.190476, or 119.0476%).
25 ÷ 21 = 1.190476 (119.0476%)
Visual Representation
The diagram below illustrates 3/9 plus 6/7 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 25/21 |
| Mixed Number Form | 1 4/21 |
| Decimal Form | 1.190476 |
| Percentage | 119.0476% |
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Frequently Asked Questions
What is 3/9 plus 6/7 as a fraction?
3/9 + 6/7 in simplest fraction form is 25/21 (or 1 4/21 as a mixed number).
What is 3/9 plus 6/7 as a decimal?
3/9 + 6/7 converted to a decimal is 1.190476.
What is 3/9 plus 6/7 as a percentage?
3/9 + 6/7 expressed as a percentage is 119.0476%.
How do you write 3/9 plus 6/7 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 25/21 can be written as the mixed number 1 4/21.
Does 3/9 plus 6/7 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.190476...) because the denominator contains prime factors other than 2 and 5.