What is 9/22 plus 5/8?
9/22 plus 5/8 equals 91/88 (or 1 3/88 as a mixed number) (or 1.034091 in decimal form). Learn the step-by-step solution to add 9/22 and 5/8 using Least Common Denominator and simplification.
Exact Answer
9/22 + 5/8 = 91/88
Simplified Fraction
91/88
Mixed Number
1 3/88
Decimal Value
1.034091
Percentage
103.4091%
Step-by-Step Solution: 9/22 + 5/8
Step 1
Find the Least Common Denominator (LCD)
The denominators 22 and 8 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 88 (which is smaller than their product 22 × 8 = 176, keeping the calculation simpler).
LCD(22, 8) = 88
Step 2
Convert to Equivalent Fractions with Common Denominator 88
Multiply the numerator and denominator of 9/22 by 4, and multiply the numerator and denominator of 5/8 by 11 so both fractions share the common base 88.
9 × 4/22 × 4 = 36/88 and 5 × 11/8 × 11 = 55/88
Step 3
Add the Numerators
Now add the numerators (36 + 55 = 91) and keep the common denominator 88 unchanged.
36 + 55/88 = 91/88
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 91 and 88 is 1, confirming that 91/88 cannot be reduced further—it is already in its simplest irreducible form.
91/88
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (91) is greater than the denominator (88), divide 91 by 88: it goes in 1 whole time(s) with a remainder of 3, giving the mixed number 1 3/88.
91/88 = 13/88
Step 6
Decimal & Percentage Representation
Dividing the numerator 91 by denominator 88 produces a repeating decimal (approximately 1.034091, or 103.4091%).
91 ÷ 88 = 1.034091 (103.4091%)
Visual Representation
The diagram below illustrates 9/22 plus 5/8 visually:
+
=
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 91/88 |
| Mixed Number Form | 1 3/88 |
| Decimal Form | 1.034091 |
| Percentage | 103.4091% |
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Frequently Asked Questions
What is 9/22 plus 5/8 as a fraction?
9/22 + 5/8 in simplest fraction form is 91/88 (or 1 3/88 as a mixed number).
What is 9/22 plus 5/8 as a decimal?
9/22 + 5/8 converted to a decimal is 1.034091.
What is 9/22 plus 5/8 as a percentage?
9/22 + 5/8 expressed as a percentage is 103.4091%.
How do you write 9/22 plus 5/8 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 91/88 can be written as the mixed number 1 3/88.
Does 9/22 plus 5/8 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.034091...) because the denominator contains prime factors other than 2 and 5.