What is 3/6 plus 10/13? (Answer: 33/26)

Exact Answer

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Problem: What is 3/6 plus 10/13?
Formula / Expression: 3/6 + 10/13
Final Answer: 1 7/26 (33/26)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 6 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 6 × 13 = 78.
Working: LCD(6, 13) = 78

Step 2: Convert to Equivalent Fractions with Common Denominator 78
Multiply the numerator and denominator of 3/6 by 13, and multiply the numerator and denominator of 10/13 by 6 so both fractions share the common base 78.
Working: 3 × 13/6 × 13 = 39/78 and 10 × 6/13 × 6 = 60/78

Step 3: Add the Numerators
Now add the numerators (39 + 60 = 99) and keep the common denominator 78 unchanged.
Working: 39 + 60/78 = 99/78

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 99 and 78, which is 3. Divide both the numerator and denominator by 3.
Working: 99 ÷ 3/78 ÷ 3 = 33/26

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (33) is greater than the denominator (26), divide 33 by 26: it goes in 1 whole time(s) with a remainder of 7, giving the mixed number 1 7/26.
Working: 33/26 = 1 7/26

Step 6: Decimal & Percentage Representation
Dividing the numerator 33 by denominator 26 produces a repeating decimal (approximately 1.269231, or 126.9231%).
Working: 33 ÷ 26 = 1.269231 (126.9231%)

Key Values:
- Simplified Fraction: 33/26
- Mixed Number Form: 1 7/26
- Decimal Value: 1.269231
- Percentage: 126.9231%

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Solved with FractionsCalc:
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3/6 + 10/13 = 33/26

Simplified Fraction

33/26

Mixed Number

1 7/26

Decimal Value

1.269231

Percentage

126.9231%

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Step-by-Step Solution: 3/6 + 10/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 6 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 6 × 13 = 78.

LCD(6, 13) = 78

Step 2

Convert to Equivalent Fractions with Common Denominator 78

Multiply the numerator and denominator of 3/6 by 13, and multiply the numerator and denominator of 10/13 by 6 so both fractions share the common base 78.

3 × 13/6 × 13 = 39/78 and 10 × 6/13 × 6 = 60/78

Step 3

Add the Numerators

Now add the numerators (39 + 60 = 99) and keep the common denominator 78 unchanged.

39 + 60/78 = 99/78

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 99 and 78, which is 3. Divide both the numerator and denominator by 3.

99 ÷ 3/78 ÷ 3 = 33/26

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (33) is greater than the denominator (26), divide 33 by 26: it goes in 1 whole time(s) with a remainder of 7, giving the mixed number 1 7/26.

33/26 = 17/26

Step 6

Decimal & Percentage Representation

Dividing the numerator 33 by denominator 26 produces a repeating decimal (approximately 1.269231, or 126.9231%).

33 ÷ 26 = 1.269231 (126.9231%)

Visual Representation

The diagram below illustrates 3/6 plus 10/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`33/26`
Mixed Number Form	`1 7/26`
Decimal Form	`1.269231`
Percentage	`126.9231%`

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Frequently Asked Questions

What is 3/6 plus 10/13 as a fraction?

3/6 + 10/13 in simplest fraction form is 33/26 (or 1 7/26 as a mixed number).

What is 3/6 plus 10/13 as a decimal?

3/6 + 10/13 converted to a decimal is 1.269231.

What is 3/6 plus 10/13 as a percentage?

3/6 + 10/13 expressed as a percentage is 126.9231%.

How do you write 3/6 plus 10/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 33/26 can be written as the mixed number 1 7/26.

Does 3/6 plus 10/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.269231...) because the denominator contains prime factors other than 2 and 5.