What is 4/15 plus 10/13?
4/15 plus 10/13 equals 202/195 (or 1 7/195 as a mixed number) (or 1.035897 in decimal form). Learn the step-by-step solution to add 4/15 and 10/13 using Least Common Denominator and simplification.
Exact Answer
4/15 + 10/13 = 202/195
Simplified Fraction
202/195
Mixed Number
1 7/195
Decimal Value
1.035897
Percentage
103.5897%
Step-by-Step Solution: 4/15 + 10/13
Step 1
Find the Least Common Denominator (LCD)
The denominators 15 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 15 × 13 = 195.
LCD(15, 13) = 195
Step 2
Convert to Equivalent Fractions with Common Denominator 195
Multiply the numerator and denominator of 4/15 by 13, and multiply the numerator and denominator of 10/13 by 15 so both fractions share the common base 195.
4 × 13/15 × 13 = 52/195 and 10 × 15/13 × 15 = 150/195
Step 3
Add the Numerators
Now add the numerators (52 + 150 = 202) and keep the common denominator 195 unchanged.
52 + 150/195 = 202/195
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 202 and 195 is 1, confirming that 202/195 cannot be reduced further—it is already in its simplest irreducible form.
202/195
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (202) is greater than the denominator (195), divide 202 by 195: it goes in 1 whole time(s) with a remainder of 7, giving the mixed number 1 7/195.
202/195 = 17/195
Step 6
Decimal & Percentage Representation
Dividing the numerator 202 by denominator 195 produces a repeating decimal (approximately 1.035897, or 103.5897%).
202 ÷ 195 = 1.035897 (103.5897%)
Visual Representation
The diagram below illustrates 4/15 plus 10/13 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 202/195 |
| Mixed Number Form | 1 7/195 |
| Decimal Form | 1.035897 |
| Percentage | 103.5897% |
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Frequently Asked Questions
What is 4/15 plus 10/13 as a fraction?
4/15 + 10/13 in simplest fraction form is 202/195 (or 1 7/195 as a mixed number).
What is 4/15 plus 10/13 as a decimal?
4/15 + 10/13 converted to a decimal is 1.035897.
What is 4/15 plus 10/13 as a percentage?
4/15 + 10/13 expressed as a percentage is 103.5897%.
How do you write 4/15 plus 10/13 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 202/195 can be written as the mixed number 1 7/195.
Does 4/15 plus 10/13 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.035897...) because the denominator contains prime factors other than 2 and 5.