What is 9/20 plus 10/13? (Answer: 317/260)

Exact Answer

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Problem: What is 9/20 plus 10/13?
Formula / Expression: 9/20 + 10/13
Final Answer: 1 57/260 (317/260)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 20 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 20 × 13 = 260.
Working: LCD(20, 13) = 260

Step 2: Convert to Equivalent Fractions with Common Denominator 260
Multiply the numerator and denominator of 9/20 by 13, and multiply the numerator and denominator of 10/13 by 20 so both fractions share the common base 260.
Working: 9 × 13/20 × 13 = 117/260 and 10 × 20/13 × 20 = 200/260

Step 3: Add the Numerators
Now add the numerators (117 + 200 = 317) and keep the common denominator 260 unchanged.
Working: 117 + 200/260 = 317/260

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 317 and 260 is 1, confirming that 317/260 cannot be reduced further—it is already in its simplest irreducible form.
Working: 317/260

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (317) is greater than the denominator (260), divide 317 by 260: it goes in 1 whole time(s) with a remainder of 57, giving the mixed number 1 57/260.
Working: 317/260 = 1 57/260

Step 6: Decimal & Percentage Representation
Dividing the numerator 317 by denominator 260 produces a repeating decimal (approximately 1.219231, or 121.9231%).
Working: 317 ÷ 260 = 1.219231 (121.9231%)

Key Values:
- Simplified Fraction: 317/260
- Mixed Number Form: 1 57/260
- Decimal Value: 1.219231
- Percentage: 121.9231%

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9/20 + 10/13 = 317/260

Simplified Fraction

317/260

Mixed Number

1 57/260

Decimal Value

1.219231

Percentage

121.9231%

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Step-by-Step Solution: 9/20 + 10/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 20 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 20 × 13 = 260.

LCD(20, 13) = 260

Step 2

Convert to Equivalent Fractions with Common Denominator 260

Multiply the numerator and denominator of 9/20 by 13, and multiply the numerator and denominator of 10/13 by 20 so both fractions share the common base 260.

9 × 13/20 × 13 = 117/260 and 10 × 20/13 × 20 = 200/260

Step 3

Add the Numerators

Now add the numerators (117 + 200 = 317) and keep the common denominator 260 unchanged.

117 + 200/260 = 317/260

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 317 and 260 is 1, confirming that 317/260 cannot be reduced further—it is already in its simplest irreducible form.

317/260

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (317) is greater than the denominator (260), divide 317 by 260: it goes in 1 whole time(s) with a remainder of 57, giving the mixed number 1 57/260.

317/260 = 157/260

Step 6

Decimal & Percentage Representation

Dividing the numerator 317 by denominator 260 produces a repeating decimal (approximately 1.219231, or 121.9231%).

317 ÷ 260 = 1.219231 (121.9231%)

Visual Representation

The diagram below illustrates 9/20 plus 10/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`317/260`
Mixed Number Form	`1 57/260`
Decimal Form	`1.219231`
Percentage	`121.9231%`

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Frequently Asked Questions

What is 9/20 plus 10/13 as a fraction?

9/20 + 10/13 in simplest fraction form is 317/260 (or 1 57/260 as a mixed number).

What is 9/20 plus 10/13 as a decimal?

9/20 + 10/13 converted to a decimal is 1.219231.

What is 9/20 plus 10/13 as a percentage?

9/20 + 10/13 expressed as a percentage is 121.9231%.

How do you write 9/20 plus 10/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 317/260 can be written as the mixed number 1 57/260.

Does 9/20 plus 10/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.219231...) because the denominator contains prime factors other than 2 and 5.