What is 4/9 plus 10/13? (Answer: 142/117)

Exact Answer

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Problem: What is 4/9 plus 10/13?
Formula / Expression: 4/9 + 10/13
Final Answer: 1 25/117 (142/117)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 9 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 13 = 117.
Working: LCD(9, 13) = 117

Step 2: Convert to Equivalent Fractions with Common Denominator 117
Multiply the numerator and denominator of 4/9 by 13, and multiply the numerator and denominator of 10/13 by 9 so both fractions share the common base 117.
Working: 4 × 13/9 × 13 = 52/117 and 10 × 9/13 × 9 = 90/117

Step 3: Add the Numerators
Now add the numerators (52 + 90 = 142) and keep the common denominator 117 unchanged.
Working: 52 + 90/117 = 142/117

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 142 and 117 is 1, confirming that 142/117 cannot be reduced further—it is already in its simplest irreducible form.
Working: 142/117

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (142) is greater than the denominator (117), divide 142 by 117: it goes in 1 whole time(s) with a remainder of 25, giving the mixed number 1 25/117.
Working: 142/117 = 1 25/117

Step 6: Decimal & Percentage Representation
Dividing the numerator 142 by denominator 117 produces a repeating decimal (approximately 1.213675, or 121.3675%).
Working: 142 ÷ 117 = 1.213675 (121.3675%)

Key Values:
- Simplified Fraction: 142/117
- Mixed Number Form: 1 25/117
- Decimal Value: 1.213675
- Percentage: 121.3675%

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Solved with FractionsCalc:
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4/9 + 10/13 = 142/117

Simplified Fraction

142/117

Mixed Number

1 25/117

Decimal Value

1.213675

Percentage

121.3675%

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Step-by-Step Solution: 4/9 + 10/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 9 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 13 = 117.

LCD(9, 13) = 117

Step 2

Convert to Equivalent Fractions with Common Denominator 117

Multiply the numerator and denominator of 4/9 by 13, and multiply the numerator and denominator of 10/13 by 9 so both fractions share the common base 117.

4 × 13/9 × 13 = 52/117 and 10 × 9/13 × 9 = 90/117

Step 3

Add the Numerators

Now add the numerators (52 + 90 = 142) and keep the common denominator 117 unchanged.

52 + 90/117 = 142/117

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 142 and 117 is 1, confirming that 142/117 cannot be reduced further—it is already in its simplest irreducible form.

142/117

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (142) is greater than the denominator (117), divide 142 by 117: it goes in 1 whole time(s) with a remainder of 25, giving the mixed number 1 25/117.

142/117 = 125/117

Step 6

Decimal & Percentage Representation

Dividing the numerator 142 by denominator 117 produces a repeating decimal (approximately 1.213675, or 121.3675%).

142 ÷ 117 = 1.213675 (121.3675%)

Visual Representation

The diagram below illustrates 4/9 plus 10/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`142/117`
Mixed Number Form	`1 25/117`
Decimal Form	`1.213675`
Percentage	`121.3675%`

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Frequently Asked Questions

What is 4/9 plus 10/13 as a fraction?

4/9 + 10/13 in simplest fraction form is 142/117 (or 1 25/117 as a mixed number).

What is 4/9 plus 10/13 as a decimal?

4/9 + 10/13 converted to a decimal is 1.213675.

What is 4/9 plus 10/13 as a percentage?

4/9 + 10/13 expressed as a percentage is 121.3675%.

How do you write 4/9 plus 10/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 142/117 can be written as the mixed number 1 25/117.

Does 4/9 plus 10/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.213675...) because the denominator contains prime factors other than 2 and 5.