What is 10/30 plus 9/13? (Answer: 40/39)

Exact Answer

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Problem: What is 10/30 plus 9/13?
Formula / Expression: 10/30 + 9/13
Final Answer: 1 1/39 (40/39)
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 390
Multiply the numerator and denominator of 10/30 by 13, and multiply the numerator and denominator of 9/13 by 30 so both fractions share the common base 390.
Working: 10 × 13/30 × 13 = 130/390 and 9 × 30/13 × 30 = 270/390

Step 3: Add the Numerators
Now add the numerators (130 + 270 = 400) and keep the common denominator 390 unchanged.
Working: 130 + 270/390 = 400/390

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 400 and 390, which is 10. Divide both the numerator and denominator by 10.
Working: 400 ÷ 10/390 ÷ 10 = 40/39

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (40) is greater than the denominator (39), divide 40 by 39: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/39.
Working: 40/39 = 1 1/39

Step 6: Decimal & Percentage Representation
Dividing the numerator 40 by denominator 39 produces a repeating decimal (approximately 1.025641, or 102.5641%).
Working: 40 ÷ 39 = 1.025641 (102.5641%)

Key Values:
- Simplified Fraction: 40/39
- Mixed Number Form: 1 1/39
- Decimal Value: 1.025641
- Percentage: 102.5641%

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10/30 + 9/13 = 40/39

Simplified Fraction

40/39

Mixed Number

1 1/39

Decimal Value

1.025641

Percentage

102.5641%

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Step-by-Step Solution: 10/30 + 9/13

Step 1

Find the Least Common Denominator (LCD)

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

LCD(30, 13) = 390

Step 2

Convert to Equivalent Fractions with Common Denominator 390

Multiply the numerator and denominator of 10/30 by 13, and multiply the numerator and denominator of 9/13 by 30 so both fractions share the common base 390.

10 × 13/30 × 13 = 130/390 and 9 × 30/13 × 30 = 270/390

Step 3

Add the Numerators

Now add the numerators (130 + 270 = 400) and keep the common denominator 390 unchanged.

130 + 270/390 = 400/390

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 400 and 390, which is 10. Divide both the numerator and denominator by 10.

400 ÷ 10/390 ÷ 10 = 40/39

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (40) is greater than the denominator (39), divide 40 by 39: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/39.

40/39 = 11/39

Step 6

Decimal & Percentage Representation

Dividing the numerator 40 by denominator 39 produces a repeating decimal (approximately 1.025641, or 102.5641%).

40 ÷ 39 = 1.025641 (102.5641%)

Visual Representation

The diagram below illustrates 10/30 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`40/39`
Mixed Number Form	`1 1/39`
Decimal Form	`1.025641`
Percentage	`102.5641%`

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Frequently Asked Questions

What is 10/30 plus 9/13 as a fraction?

10/30 + 9/13 in simplest fraction form is 40/39 (or 1 1/39 as a mixed number).

What is 10/30 plus 9/13 as a decimal?

10/30 + 9/13 converted to a decimal is 1.025641.

What is 10/30 plus 9/13 as a percentage?

10/30 + 9/13 expressed as a percentage is 102.5641%.

How do you write 10/30 plus 9/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 40/39 can be written as the mixed number 1 1/39.

Does 10/30 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.025641...) because the denominator contains prime factors other than 2 and 5.