What is 10/21 plus 9/13?
10/21 plus 9/13 equals 319/273 (or 1 46/273 as a mixed number) (or 1.168498 in decimal form). Learn the step-by-step solution to add 10/21 and 9/13 using Least Common Denominator and simplification.
Exact Answer
10/21 + 9/13 = 319/273
Simplified Fraction
319/273
Mixed Number
1 46/273
Decimal Value
1.168498
Percentage
116.8498%
Step-by-Step Solution: 10/21 + 9/13
Step 1
Find the Least Common Denominator (LCD)
The denominators 21 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 21 × 13 = 273.
LCD(21, 13) = 273
Step 2
Convert to Equivalent Fractions with Common Denominator 273
Multiply the numerator and denominator of 10/21 by 13, and multiply the numerator and denominator of 9/13 by 21 so both fractions share the common base 273.
10 × 13/21 × 13 = 130/273 and 9 × 21/13 × 21 = 189/273
Step 3
Add the Numerators
Now add the numerators (130 + 189 = 319) and keep the common denominator 273 unchanged.
130 + 189/273 = 319/273
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 319 and 273 is 1, confirming that 319/273 cannot be reduced further—it is already in its simplest irreducible form.
319/273
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (319) is greater than the denominator (273), divide 319 by 273: it goes in 1 whole time(s) with a remainder of 46, giving the mixed number 1 46/273.
319/273 = 146/273
Step 6
Decimal & Percentage Representation
Dividing the numerator 319 by denominator 273 produces a repeating decimal (approximately 1.168498, or 116.8498%).
319 ÷ 273 = 1.168498 (116.8498%)
Visual Representation
The diagram below illustrates 10/21 plus 9/13 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 319/273 |
| Mixed Number Form | 1 46/273 |
| Decimal Form | 1.168498 |
| Percentage | 116.8498% |
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Frequently Asked Questions
What is 10/21 plus 9/13 as a fraction?
10/21 + 9/13 in simplest fraction form is 319/273 (or 1 46/273 as a mixed number).
What is 10/21 plus 9/13 as a decimal?
10/21 + 9/13 converted to a decimal is 1.168498.
What is 10/21 plus 9/13 as a percentage?
10/21 + 9/13 expressed as a percentage is 116.8498%.
How do you write 10/21 plus 9/13 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 319/273 can be written as the mixed number 1 46/273.
Does 10/21 plus 9/13 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.168498...) because the denominator contains prime factors other than 2 and 5.