What is 3/8 plus 9/11?
3/8 plus 9/11 equals 105/88 (or 1 17/88 as a mixed number) (or 1.193182 in decimal form). Learn the step-by-step solution to add 3/8 and 9/11 using Least Common Denominator and simplification.
Exact Answer
3/8 + 9/11 = 105/88
Simplified Fraction
105/88
Mixed Number
1 17/88
Decimal Value
1.193182
Percentage
119.3182%
Step-by-Step Solution: 3/8 + 9/11
Step 1
Find the Least Common Denominator (LCD)
The denominators 8 and 11 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 8 × 11 = 88.
LCD(8, 11) = 88
Step 2
Convert to Equivalent Fractions with Common Denominator 88
Multiply the numerator and denominator of 3/8 by 11, and multiply the numerator and denominator of 9/11 by 8 so both fractions share the common base 88.
3 × 11/8 × 11 = 33/88 and 9 × 8/11 × 8 = 72/88
Step 3
Add the Numerators
Now add the numerators (33 + 72 = 105) and keep the common denominator 88 unchanged.
33 + 72/88 = 105/88
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 105 and 88 is 1, confirming that 105/88 cannot be reduced further—it is already in its simplest irreducible form.
105/88
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (105) is greater than the denominator (88), divide 105 by 88: it goes in 1 whole time(s) with a remainder of 17, giving the mixed number 1 17/88.
105/88 = 117/88
Step 6
Decimal & Percentage Representation
Dividing the numerator 105 by denominator 88 produces a repeating decimal (approximately 1.193182, or 119.3182%).
105 ÷ 88 = 1.193182 (119.3182%)
Visual Representation
The diagram below illustrates 3/8 plus 9/11 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 105/88 |
| Mixed Number Form | 1 17/88 |
| Decimal Form | 1.193182 |
| Percentage | 119.3182% |
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Frequently Asked Questions
What is 3/8 plus 9/11 as a fraction?
3/8 + 9/11 in simplest fraction form is 105/88 (or 1 17/88 as a mixed number).
What is 3/8 plus 9/11 as a decimal?
3/8 + 9/11 converted to a decimal is 1.193182.
What is 3/8 plus 9/11 as a percentage?
3/8 + 9/11 expressed as a percentage is 119.3182%.
How do you write 3/8 plus 9/11 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 105/88 can be written as the mixed number 1 17/88.
Does 3/8 plus 9/11 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.193182...) because the denominator contains prime factors other than 2 and 5.