What is 9/13 plus 7/10?
9/13 plus 7/10 equals 181/130 (or 1 51/130 as a mixed number) (or 1.392308 in decimal form). Learn the step-by-step solution to add 9/13 and 7/10 using Least Common Denominator and simplification.
Exact Answer
9/13 + 7/10 = 181/130
Simplified Fraction
181/130
Mixed Number
1 51/130
Decimal Value
1.392308
Percentage
139.2308%
Step-by-Step Solution: 9/13 + 7/10
Step 1
Find the Least Common Denominator (LCD)
The denominators 13 and 10 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 10 = 130.
LCD(13, 10) = 130
Step 2
Convert to Equivalent Fractions with Common Denominator 130
Multiply the numerator and denominator of 9/13 by 10, and multiply the numerator and denominator of 7/10 by 13 so both fractions share the common base 130.
9 × 10/13 × 10 = 90/130 and 7 × 13/10 × 13 = 91/130
Step 3
Add the Numerators
Now add the numerators (90 + 91 = 181) and keep the common denominator 130 unchanged.
90 + 91/130 = 181/130
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 181 and 130 is 1, confirming that 181/130 cannot be reduced further—it is already in its simplest irreducible form.
181/130
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (181) is greater than the denominator (130), divide 181 by 130: it goes in 1 whole time(s) with a remainder of 51, giving the mixed number 1 51/130.
181/130 = 151/130
Step 6
Decimal & Percentage Representation
Dividing the numerator 181 by denominator 130 produces a repeating decimal (approximately 1.392308, or 139.2308%).
181 ÷ 130 = 1.392308 (139.2308%)
Visual Representation
The diagram below illustrates 9/13 plus 7/10 visually:
+
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 181/130 |
| Mixed Number Form | 1 51/130 |
| Decimal Form | 1.392308 |
| Percentage | 139.2308% |
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Frequently Asked Questions
What is 9/13 plus 7/10 as a fraction?
9/13 + 7/10 in simplest fraction form is 181/130 (or 1 51/130 as a mixed number).
What is 9/13 plus 7/10 as a decimal?
9/13 + 7/10 converted to a decimal is 1.392308.
What is 9/13 plus 7/10 as a percentage?
9/13 + 7/10 expressed as a percentage is 139.2308%.
How do you write 9/13 plus 7/10 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 181/130 can be written as the mixed number 1 51/130.
Does 9/13 plus 7/10 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.392308...) because the denominator contains prime factors other than 2 and 5.