What is 9/32 plus 10/13?
9/32 plus 10/13 equals 437/416 (or 1 21/416 as a mixed number) (or 1.050481 in decimal form). Learn the step-by-step solution to add 9/32 and 10/13 using Least Common Denominator and simplification.
Exact Answer
9/32 + 10/13 = 437/416
Simplified Fraction
437/416
Mixed Number
1 21/416
Decimal Value
1.050481
Percentage
105.0481%
Step-by-Step Solution: 9/32 + 10/13
Step 1
Find the Least Common Denominator (LCD)
The denominators 32 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 32 × 13 = 416.
LCD(32, 13) = 416
Step 2
Convert to Equivalent Fractions with Common Denominator 416
Multiply the numerator and denominator of 9/32 by 13, and multiply the numerator and denominator of 10/13 by 32 so both fractions share the common base 416.
9 × 13/32 × 13 = 117/416 and 10 × 32/13 × 32 = 320/416
Step 3
Add the Numerators
Now add the numerators (117 + 320 = 437) and keep the common denominator 416 unchanged.
117 + 320/416 = 437/416
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 437 and 416 is 1, confirming that 437/416 cannot be reduced further—it is already in its simplest irreducible form.
437/416
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (437) is greater than the denominator (416), divide 437 by 416: it goes in 1 whole time(s) with a remainder of 21, giving the mixed number 1 21/416.
437/416 = 121/416
Step 6
Decimal & Percentage Representation
Dividing the numerator 437 by denominator 416 produces a repeating decimal (approximately 1.050481, or 105.0481%).
437 ÷ 416 = 1.050481 (105.0481%)
Visual Representation
The diagram below illustrates 9/32 plus 10/13 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 437/416 |
| Mixed Number Form | 1 21/416 |
| Decimal Form | 1.050481 |
| Percentage | 105.0481% |
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Frequently Asked Questions
What is 9/32 plus 10/13 as a fraction?
9/32 + 10/13 in simplest fraction form is 437/416 (or 1 21/416 as a mixed number).
What is 9/32 plus 10/13 as a decimal?
9/32 + 10/13 converted to a decimal is 1.050481.
What is 9/32 plus 10/13 as a percentage?
9/32 + 10/13 expressed as a percentage is 105.0481%.
How do you write 9/32 plus 10/13 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 437/416 can be written as the mixed number 1 21/416.
Does 9/32 plus 10/13 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.050481...) because the denominator contains prime factors other than 2 and 5.