What is 9/13 plus 21/30? (Answer: 181/130)

Exact Answer

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Problem: What is 9/13 plus 21/30?
Formula / Expression: 9/13 + 21/30
Final Answer: 1 51/130 (181/130)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 13 and 30 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 30 = 390.
Working: LCD(13, 30) = 390

Step 2: Convert to Equivalent Fractions with Common Denominator 390
Multiply the numerator and denominator of 9/13 by 30, and multiply the numerator and denominator of 21/30 by 13 so both fractions share the common base 390.
Working: 9 × 30/13 × 30 = 270/390 and 21 × 13/30 × 13 = 273/390

Step 3: Add the Numerators
Now add the numerators (270 + 273 = 543) and keep the common denominator 390 unchanged.
Working: 270 + 273/390 = 543/390

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 543 and 390, which is 3. Divide both the numerator and denominator by 3.
Working: 543 ÷ 3/390 ÷ 3 = 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.
Working: 181/130 = 1 51/130

Step 6: Decimal & Percentage Representation
Dividing the numerator 181 by denominator 130 produces a repeating decimal (approximately 1.392308, or 139.2308%).
Working: 181 ÷ 130 = 1.392308 (139.2308%)

Key Values:
- Simplified Fraction: 181/130
- Mixed Number Form: 1 51/130
- Decimal Value: 1.392308
- Percentage: 139.2308%

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Solved with FractionsCalc:
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9/13 + 21/30 = 181/130

Simplified Fraction

181/130

Mixed Number

1 51/130

Decimal Value

1.392308

Percentage

139.2308%

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Step-by-Step Solution: 9/13 + 21/30

Step 1

Find the Least Common Denominator (LCD)

The denominators 13 and 30 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 30 = 390.

LCD(13, 30) = 390

Step 2

Convert to Equivalent Fractions with Common Denominator 390

Multiply the numerator and denominator of 9/13 by 30, and multiply the numerator and denominator of 21/30 by 13 so both fractions share the common base 390.

9 × 30/13 × 30 = 270/390 and 21 × 13/30 × 13 = 273/390

Step 3

Add the Numerators

Now add the numerators (270 + 273 = 543) and keep the common denominator 390 unchanged.

270 + 273/390 = 543/390

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 543 and 390, which is 3. Divide both the numerator and denominator by 3.

543 ÷ 3/390 ÷ 3 = 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 21/30 visually:

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 21/30 as a fraction?

9/13 + 21/30 in simplest fraction form is 181/130 (or 1 51/130 as a mixed number).

What is 9/13 plus 21/30 as a decimal?

9/13 + 21/30 converted to a decimal is 1.392308.

What is 9/13 plus 21/30 as a percentage?

9/13 + 21/30 expressed as a percentage is 139.2308%.

How do you write 9/13 plus 21/30 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 21/30 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.