What is 9/16 plus 2/3?
9/16 plus 2/3 equals 59/48 (or 1 11/48 as a mixed number) (or 1.229167 in decimal form). Learn the step-by-step solution to add 9/16 and 2/3 using Least Common Denominator and simplification.
Exact Answer
9/16 + 2/3 = 59/48
Simplified Fraction
59/48
Mixed Number
1 11/48
Decimal Value
1.229167
Percentage
122.9167%
Step-by-Step Solution: 9/16 + 2/3
Step 1
Find the Least Common Denominator (LCD)
The denominators 16 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 16 × 3 = 48.
LCD(16, 3) = 48
Step 2
Convert to Equivalent Fractions with Common Denominator 48
Multiply the numerator and denominator of 9/16 by 3, and multiply the numerator and denominator of 2/3 by 16 so both fractions share the common base 48.
9 × 3/16 × 3 = 27/48 and 2 × 16/3 × 16 = 32/48
Step 3
Add the Numerators
Now add the numerators (27 + 32 = 59) and keep the common denominator 48 unchanged.
27 + 32/48 = 59/48
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 59 and 48 is 1, confirming that 59/48 cannot be reduced further—it is already in its simplest irreducible form.
59/48
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (59) is greater than the denominator (48), divide 59 by 48: it goes in 1 whole time(s) with a remainder of 11, giving the mixed number 1 11/48.
59/48 = 111/48
Step 6
Decimal & Percentage Representation
Dividing the numerator 59 by denominator 48 produces a repeating decimal (approximately 1.229167, or 122.9167%).
59 ÷ 48 = 1.229167 (122.9167%)
Visual Representation
The diagram below illustrates 9/16 plus 2/3 visually:
+
=
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 59/48 |
| Mixed Number Form | 1 11/48 |
| Decimal Form | 1.229167 |
| Percentage | 122.9167% |
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Frequently Asked Questions
What is 9/16 plus 2/3 as a fraction?
9/16 + 2/3 in simplest fraction form is 59/48 (or 1 11/48 as a mixed number).
What is 9/16 plus 2/3 as a decimal?
9/16 + 2/3 converted to a decimal is 1.229167.
What is 9/16 plus 2/3 as a percentage?
9/16 + 2/3 expressed as a percentage is 122.9167%.
How do you write 9/16 plus 2/3 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 59/48 can be written as the mixed number 1 11/48.
Does 9/16 plus 2/3 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.229167...) because the denominator contains prime factors other than 2 and 5.