What is 16/26 plus 9/13? (Answer: 17/13)

Exact Answer

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Problem: What is 16/26 plus 9/13?
Formula / Expression: 16/26 + 9/13
Final Answer: 1 4/13 (17/13)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 26 is an exact multiple of 13 (13 × 2 = 26). The Least Common Denominator (LCD) is simply 26, meaning we only need to scale one fraction.
Working: LCD(26, 13) = 26

Step 2: Convert to Equivalent Fractions with Common Denominator 26
Multiply the numerator and denominator of 16/26 by 1, and multiply the numerator and denominator of 9/13 by 2 so both fractions share the common base 26.
Working: 16 × 1/26 × 1 = 16/26 and 9 × 2/13 × 2 = 18/26

Step 3: Add the Numerators
Now add the numerators (16 + 18 = 34) and keep the common denominator 26 unchanged.
Working: 16 + 18/26 = 34/26

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 34 and 26, which is 2. Divide both the numerator and denominator by 2.
Working: 34 ÷ 2/26 ÷ 2 = 17/13

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (17) is greater than the denominator (13), divide 17 by 13: it goes in 1 whole time(s) with a remainder of 4, giving the mixed number 1 4/13.
Working: 17/13 = 1 4/13

Step 6: Decimal & Percentage Representation
Dividing the numerator 17 by denominator 13 produces a repeating decimal (approximately 1.307692, or 130.7692%).
Working: 17 ÷ 13 = 1.307692 (130.7692%)

Key Values:
- Simplified Fraction: 17/13
- Mixed Number Form: 1 4/13
- Decimal Value: 1.307692
- Percentage: 130.7692%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-16-26-plus-9-13/
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16/26 + 9/13 = 17/13

Simplified Fraction

17/13

Mixed Number

1 4/13

Decimal Value

1.307692

Percentage

130.7692%

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Step-by-Step Solution: 16/26 + 9/13

Step 1

Find the Least Common Denominator (LCD)

Notice that 26 is an exact multiple of 13 (13 × 2 = 26). The Least Common Denominator (LCD) is simply 26, meaning we only need to scale one fraction.

LCD(26, 13) = 26

Step 2

Convert to Equivalent Fractions with Common Denominator 26

Multiply the numerator and denominator of 16/26 by 1, and multiply the numerator and denominator of 9/13 by 2 so both fractions share the common base 26.

16 × 1/26 × 1 = 16/26 and 9 × 2/13 × 2 = 18/26

Step 3

Add the Numerators

Now add the numerators (16 + 18 = 34) and keep the common denominator 26 unchanged.

16 + 18/26 = 34/26

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 34 and 26, which is 2. Divide both the numerator and denominator by 2.

34 ÷ 2/26 ÷ 2 = 17/13

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (17) is greater than the denominator (13), divide 17 by 13: it goes in 1 whole time(s) with a remainder of 4, giving the mixed number 1 4/13.

17/13 = 14/13

Step 6

Decimal & Percentage Representation

Dividing the numerator 17 by denominator 13 produces a repeating decimal (approximately 1.307692, or 130.7692%).

17 ÷ 13 = 1.307692 (130.7692%)

Visual Representation

The diagram below illustrates 16/26 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`17/13`
Mixed Number Form	`1 4/13`
Decimal Form	`1.307692`
Percentage	`130.7692%`

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Frequently Asked Questions

What is 16/26 plus 9/13 as a fraction?

16/26 + 9/13 in simplest fraction form is 17/13 (or 1 4/13 as a mixed number).

What is 16/26 plus 9/13 as a decimal?

16/26 + 9/13 converted to a decimal is 1.307692.

What is 16/26 plus 9/13 as a percentage?

16/26 + 9/13 expressed as a percentage is 130.7692%.

How do you write 16/26 plus 9/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 17/13 can be written as the mixed number 1 4/13.

Does 16/26 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.307692...) because the denominator contains prime factors other than 2 and 5.