What is 9/21 plus 6/9?
9/21 plus 6/9 equals 23/21 (or 1 2/21 as a mixed number) (or 1.095238 in decimal form). Learn the step-by-step solution to add 9/21 and 6/9 using Least Common Denominator and simplification.
Exact Answer
9/21 + 6/9 = 23/21
Simplified Fraction
23/21
Mixed Number
1 2/21
Decimal Value
1.095238
Percentage
109.5238%
Step-by-Step Solution: 9/21 + 6/9
Step 1
Find the Least Common Denominator (LCD)
The denominators 21 and 9 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 63 (which is smaller than their product 21 × 9 = 189, keeping the calculation simpler).
LCD(21, 9) = 63
Step 2
Convert to Equivalent Fractions with Common Denominator 63
Multiply the numerator and denominator of 9/21 by 3, and multiply the numerator and denominator of 6/9 by 7 so both fractions share the common base 63.
9 × 3/21 × 3 = 27/63 and 6 × 7/9 × 7 = 42/63
Step 3
Add the Numerators
Now add the numerators (27 + 42 = 69) and keep the common denominator 63 unchanged.
27 + 42/63 = 69/63
Step 4
Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 69 and 63, which is 3. Divide both the numerator and denominator by 3.
69 ÷ 3/63 ÷ 3 = 23/21
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (23) is greater than the denominator (21), divide 23 by 21: it goes in 1 whole time(s) with a remainder of 2, giving the mixed number 1 2/21.
23/21 = 12/21
Step 6
Decimal & Percentage Representation
Dividing the numerator 23 by denominator 21 produces a repeating decimal (approximately 1.095238, or 109.5238%).
23 ÷ 21 = 1.095238 (109.5238%)
Visual Representation
The diagram below illustrates 9/21 plus 6/9 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 23/21 |
| Mixed Number Form | 1 2/21 |
| Decimal Form | 1.095238 |
| Percentage | 109.5238% |
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Frequently Asked Questions
What is 9/21 plus 6/9 as a fraction?
9/21 + 6/9 in simplest fraction form is 23/21 (or 1 2/21 as a mixed number).
What is 9/21 plus 6/9 as a decimal?
9/21 + 6/9 converted to a decimal is 1.095238.
What is 9/21 plus 6/9 as a percentage?
9/21 + 6/9 expressed as a percentage is 109.5238%.
How do you write 9/21 plus 6/9 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 23/21 can be written as the mixed number 1 2/21.
Does 9/21 plus 6/9 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.095238...) because the denominator contains prime factors other than 2 and 5.