What is 9/16 plus 4/5?
9/16 plus 4/5 equals 109/80 (or 1 29/80 as a mixed number) (or 1.3625 in decimal form). Learn the step-by-step solution to add 9/16 and 4/5 using Least Common Denominator and simplification.
Exact Answer
9/16 + 4/5 = 109/80
Simplified Fraction
109/80
Mixed Number
1 29/80
Decimal Value
1.3625
Percentage
136.25%
Step-by-Step Solution: 9/16 + 4/5
Step 1
Find the Least Common Denominator (LCD)
The denominators 16 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 16 × 5 = 80.
LCD(16, 5) = 80
Step 2
Convert to Equivalent Fractions with Common Denominator 80
Multiply the numerator and denominator of 9/16 by 5, and multiply the numerator and denominator of 4/5 by 16 so both fractions share the common base 80.
9 × 5/16 × 5 = 45/80 and 4 × 16/5 × 16 = 64/80
Step 3
Add the Numerators
Now add the numerators (45 + 64 = 109) and keep the common denominator 80 unchanged.
45 + 64/80 = 109/80
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 109 and 80 is 1, confirming that 109/80 cannot be reduced further—it is already in its simplest irreducible form.
109/80
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (109) is greater than the denominator (80), divide 109 by 80: it goes in 1 whole time(s) with a remainder of 29, giving the mixed number 1 29/80.
109/80 = 129/80
Step 6
Decimal & Percentage Representation
Dividing the numerator 109 by denominator 80 yields an exact terminating decimal of 1.3625 (or 136.25%).
109 ÷ 80 = 1.3625 (136.25%)
Visual Representation
The diagram below illustrates 9/16 plus 4/5 visually:
+
=
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 109/80 |
| Mixed Number Form | 1 29/80 |
| Decimal Form | 1.3625 |
| Percentage | 136.25% |
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Frequently Asked Questions
What is 9/16 plus 4/5 as a fraction?
9/16 + 4/5 in simplest fraction form is 109/80 (or 1 29/80 as a mixed number).
What is 9/16 plus 4/5 as a decimal?
9/16 + 4/5 converted to a decimal is 1.3625.
What is 9/16 plus 4/5 as a percentage?
9/16 + 4/5 expressed as a percentage is 136.25%.
How do you write 9/16 plus 4/5 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 109/80 can be written as the mixed number 1 29/80.
Does 9/16 plus 4/5 result in a terminating or repeating decimal?
It results in an exact terminating decimal (1.3625) because the denominator in simplest terms contains only prime factors 2 and/or 5.