What is 1/3 plus 4/5?
1/3 plus 4/5 equals 17/15 (or 1 2/15 as a mixed number) (or 1.133333 in decimal form). Learn the step-by-step solution to add 1/3 and 4/5 using Least Common Denominator and simplification.
Exact Answer
1/3 + 4/5 = 17/15
Simplified Fraction
17/15
Mixed Number
1 2/15
Decimal Value
1.133333
Percentage
113.3333%
Step-by-Step Solution: 1/3 + 4/5
Step 1
Find the Least Common Denominator (LCD)
The denominators 3 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 3 × 5 = 15.
LCD(3, 5) = 15
Step 2
Convert to Equivalent Fractions with Common Denominator 15
Multiply the numerator and denominator of 1/3 by 5, and multiply the numerator and denominator of 4/5 by 3 so both fractions share the common base 15.
1 × 5/3 × 5 = 5/15 and 4 × 3/5 × 3 = 12/15
Step 3
Add the Numerators
Now add the numerators (5 + 12 = 17) and keep the common denominator 15 unchanged.
5 + 12/15 = 17/15
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 17 and 15 is 1, confirming that 17/15 cannot be reduced further—it is already in its simplest irreducible form.
17/15
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (17) is greater than the denominator (15), divide 17 by 15: it goes in 1 whole time(s) with a remainder of 2, giving the mixed number 1 2/15.
17/15 = 12/15
Step 6
Decimal & Percentage Representation
Dividing the numerator 17 by denominator 15 produces a repeating decimal (approximately 1.133333, or 113.3333%).
17 ÷ 15 = 1.133333 (113.3333%)
Visual Representation
The diagram below illustrates 1/3 plus 4/5 visually:
+
=
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 17/15 |
| Mixed Number Form | 1 2/15 |
| Decimal Form | 1.133333 |
| Percentage | 113.3333% |
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Frequently Asked Questions
What is 1/3 plus 4/5 as a fraction?
1/3 + 4/5 in simplest fraction form is 17/15 (or 1 2/15 as a mixed number).
What is 1/3 plus 4/5 as a decimal?
1/3 + 4/5 converted to a decimal is 1.133333.
What is 1/3 plus 4/5 as a percentage?
1/3 + 4/5 expressed as a percentage is 113.3333%.
How do you write 1/3 plus 4/5 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 17/15 can be written as the mixed number 1 2/15.
Does 1/3 plus 4/5 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.133333...) because the denominator contains prime factors other than 2 and 5.