What is 20/38 plus 9/13? (Answer: 301/247)

Exact Answer

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Problem: What is 20/38 plus 9/13?
Formula / Expression: 20/38 + 9/13
Final Answer: 1 54/247 (301/247)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 38 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 38 × 13 = 494.
Working: LCD(38, 13) = 494

Step 2: Convert to Equivalent Fractions with Common Denominator 494
Multiply the numerator and denominator of 20/38 by 13, and multiply the numerator and denominator of 9/13 by 38 so both fractions share the common base 494.
Working: 20 × 13/38 × 13 = 260/494 and 9 × 38/13 × 38 = 342/494

Step 3: Add the Numerators
Now add the numerators (260 + 342 = 602) and keep the common denominator 494 unchanged.
Working: 260 + 342/494 = 602/494

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 602 and 494, which is 2. Divide both the numerator and denominator by 2.
Working: 602 ÷ 2/494 ÷ 2 = 301/247

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (301) is greater than the denominator (247), divide 301 by 247: it goes in 1 whole time(s) with a remainder of 54, giving the mixed number 1 54/247.
Working: 301/247 = 1 54/247

Step 6: Decimal & Percentage Representation
Dividing the numerator 301 by denominator 247 produces a repeating decimal (approximately 1.218623, or 121.8623%).
Working: 301 ÷ 247 = 1.218623 (121.8623%)

Key Values:
- Simplified Fraction: 301/247
- Mixed Number Form: 1 54/247
- Decimal Value: 1.218623
- Percentage: 121.8623%

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Solved with FractionsCalc:
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20/38 + 9/13 = 301/247

Simplified Fraction

301/247

Mixed Number

1 54/247

Decimal Value

1.218623

Percentage

121.8623%

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Step-by-Step Solution: 20/38 + 9/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 38 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 38 × 13 = 494.

LCD(38, 13) = 494

Step 2

Convert to Equivalent Fractions with Common Denominator 494

Multiply the numerator and denominator of 20/38 by 13, and multiply the numerator and denominator of 9/13 by 38 so both fractions share the common base 494.

20 × 13/38 × 13 = 260/494 and 9 × 38/13 × 38 = 342/494

Step 3

Add the Numerators

Now add the numerators (260 + 342 = 602) and keep the common denominator 494 unchanged.

260 + 342/494 = 602/494

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 602 and 494, which is 2. Divide both the numerator and denominator by 2.

602 ÷ 2/494 ÷ 2 = 301/247

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (301) is greater than the denominator (247), divide 301 by 247: it goes in 1 whole time(s) with a remainder of 54, giving the mixed number 1 54/247.

301/247 = 154/247

Step 6

Decimal & Percentage Representation

Dividing the numerator 301 by denominator 247 produces a repeating decimal (approximately 1.218623, or 121.8623%).

301 ÷ 247 = 1.218623 (121.8623%)

Visual Representation

The diagram below illustrates 20/38 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`301/247`
Mixed Number Form	`1 54/247`
Decimal Form	`1.218623`
Percentage	`121.8623%`

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Frequently Asked Questions

What is 20/38 plus 9/13 as a fraction?

20/38 + 9/13 in simplest fraction form is 301/247 (or 1 54/247 as a mixed number).

What is 20/38 plus 9/13 as a decimal?

20/38 + 9/13 converted to a decimal is 1.218623.

What is 20/38 plus 9/13 as a percentage?

20/38 + 9/13 expressed as a percentage is 121.8623%.

How do you write 20/38 plus 9/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 301/247 can be written as the mixed number 1 54/247.

Does 20/38 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.218623...) because the denominator contains prime factors other than 2 and 5.