What is 13/28 plus 9/13? (Answer: 421/364)

Exact Answer

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Problem: What is 13/28 plus 9/13?
Formula / Expression: 13/28 + 9/13
Final Answer: 1 57/364 (421/364)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 28 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 28 × 13 = 364.
Working: LCD(28, 13) = 364

Step 2: Convert to Equivalent Fractions with Common Denominator 364
Multiply the numerator and denominator of 13/28 by 13, and multiply the numerator and denominator of 9/13 by 28 so both fractions share the common base 364.
Working: 13 × 13/28 × 13 = 169/364 and 9 × 28/13 × 28 = 252/364

Step 3: Add the Numerators
Now add the numerators (169 + 252 = 421) and keep the common denominator 364 unchanged.
Working: 169 + 252/364 = 421/364

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 421 and 364 is 1, confirming that 421/364 cannot be reduced further—it is already in its simplest irreducible form.
Working: 421/364

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (421) is greater than the denominator (364), divide 421 by 364: it goes in 1 whole time(s) with a remainder of 57, giving the mixed number 1 57/364.
Working: 421/364 = 1 57/364

Step 6: Decimal & Percentage Representation
Dividing the numerator 421 by denominator 364 produces a repeating decimal (approximately 1.156593, or 115.6593%).
Working: 421 ÷ 364 = 1.156593 (115.6593%)

Key Values:
- Simplified Fraction: 421/364
- Mixed Number Form: 1 57/364
- Decimal Value: 1.156593
- Percentage: 115.6593%

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Solved with FractionsCalc:
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13/28 + 9/13 = 421/364

Simplified Fraction

421/364

Mixed Number

1 57/364

Decimal Value

1.156593

Percentage

115.6593%

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Step-by-Step Solution: 13/28 + 9/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 28 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 28 × 13 = 364.

LCD(28, 13) = 364

Step 2

Convert to Equivalent Fractions with Common Denominator 364

Multiply the numerator and denominator of 13/28 by 13, and multiply the numerator and denominator of 9/13 by 28 so both fractions share the common base 364.

13 × 13/28 × 13 = 169/364 and 9 × 28/13 × 28 = 252/364

Step 3

Add the Numerators

Now add the numerators (169 + 252 = 421) and keep the common denominator 364 unchanged.

169 + 252/364 = 421/364

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 421 and 364 is 1, confirming that 421/364 cannot be reduced further—it is already in its simplest irreducible form.

421/364

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (421) is greater than the denominator (364), divide 421 by 364: it goes in 1 whole time(s) with a remainder of 57, giving the mixed number 1 57/364.

421/364 = 157/364

Step 6

Decimal & Percentage Representation

Dividing the numerator 421 by denominator 364 produces a repeating decimal (approximately 1.156593, or 115.6593%).

421 ÷ 364 = 1.156593 (115.6593%)

Visual Representation

The diagram below illustrates 13/28 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`421/364`
Mixed Number Form	`1 57/364`
Decimal Form	`1.156593`
Percentage	`115.6593%`

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Frequently Asked Questions

What is 13/28 plus 9/13 as a fraction?

13/28 + 9/13 in simplest fraction form is 421/364 (or 1 57/364 as a mixed number).

What is 13/28 plus 9/13 as a decimal?

13/28 + 9/13 converted to a decimal is 1.156593.

What is 13/28 plus 9/13 as a percentage?

13/28 + 9/13 expressed as a percentage is 115.6593%.

How do you write 13/28 plus 9/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 421/364 can be written as the mixed number 1 57/364.

Does 13/28 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.156593...) because the denominator contains prime factors other than 2 and 5.