What is 3/11 plus 10/13? (Answer: 149/143)

Exact Answer

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Problem: What is 3/11 plus 10/13?
Formula / Expression: 3/11 + 10/13
Final Answer: 1 6/143 (149/143)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 11 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 11 × 13 = 143.
Working: LCD(11, 13) = 143

Step 2: Convert to Equivalent Fractions with Common Denominator 143
Multiply the numerator and denominator of 3/11 by 13, and multiply the numerator and denominator of 10/13 by 11 so both fractions share the common base 143.
Working: 3 × 13/11 × 13 = 39/143 and 10 × 11/13 × 11 = 110/143

Step 3: Add the Numerators
Now add the numerators (39 + 110 = 149) and keep the common denominator 143 unchanged.
Working: 39 + 110/143 = 149/143

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 149 and 143 is 1, confirming that 149/143 cannot be reduced further—it is already in its simplest irreducible form.
Working: 149/143

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (149) is greater than the denominator (143), divide 149 by 143: it goes in 1 whole time(s) with a remainder of 6, giving the mixed number 1 6/143.
Working: 149/143 = 1 6/143

Step 6: Decimal & Percentage Representation
Dividing the numerator 149 by denominator 143 produces a repeating decimal (approximately 1.041958, or 104.1958%).
Working: 149 ÷ 143 = 1.041958 (104.1958%)

Key Values:
- Simplified Fraction: 149/143
- Mixed Number Form: 1 6/143
- Decimal Value: 1.041958
- Percentage: 104.1958%

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3/11 + 10/13 = 149/143

Simplified Fraction

149/143

Mixed Number

1 6/143

Decimal Value

1.041958

Percentage

104.1958%

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Step-by-Step Solution: 3/11 + 10/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 11 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 11 × 13 = 143.

LCD(11, 13) = 143

Step 2

Convert to Equivalent Fractions with Common Denominator 143

Multiply the numerator and denominator of 3/11 by 13, and multiply the numerator and denominator of 10/13 by 11 so both fractions share the common base 143.

3 × 13/11 × 13 = 39/143 and 10 × 11/13 × 11 = 110/143

Step 3

Add the Numerators

Now add the numerators (39 + 110 = 149) and keep the common denominator 143 unchanged.

39 + 110/143 = 149/143

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 149 and 143 is 1, confirming that 149/143 cannot be reduced further—it is already in its simplest irreducible form.

149/143

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (149) is greater than the denominator (143), divide 149 by 143: it goes in 1 whole time(s) with a remainder of 6, giving the mixed number 1 6/143.

149/143 = 16/143

Step 6

Decimal & Percentage Representation

Dividing the numerator 149 by denominator 143 produces a repeating decimal (approximately 1.041958, or 104.1958%).

149 ÷ 143 = 1.041958 (104.1958%)

Visual Representation

The diagram below illustrates 3/11 plus 10/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`149/143`
Mixed Number Form	`1 6/143`
Decimal Form	`1.041958`
Percentage	`104.1958%`

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Frequently Asked Questions

What is 3/11 plus 10/13 as a fraction?

3/11 + 10/13 in simplest fraction form is 149/143 (or 1 6/143 as a mixed number).

What is 3/11 plus 10/13 as a decimal?

3/11 + 10/13 converted to a decimal is 1.041958.

What is 3/11 plus 10/13 as a percentage?

3/11 + 10/13 expressed as a percentage is 104.1958%.

How do you write 3/11 plus 10/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 149/143 can be written as the mixed number 1 6/143.

Does 3/11 plus 10/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.041958...) because the denominator contains prime factors other than 2 and 5.