What is 9/13 plus 10/14? (Answer: 128/91)

Exact Answer

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Problem: What is 9/13 plus 10/14?
Formula / Expression: 9/13 + 10/14
Final Answer: 1 37/91 (128/91)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 13 and 14 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 14 = 182.
Working: LCD(13, 14) = 182

Step 2: Convert to Equivalent Fractions with Common Denominator 182
Multiply the numerator and denominator of 9/13 by 14, and multiply the numerator and denominator of 10/14 by 13 so both fractions share the common base 182.
Working: 9 × 14/13 × 14 = 126/182 and 10 × 13/14 × 13 = 130/182

Step 3: Add the Numerators
Now add the numerators (126 + 130 = 256) and keep the common denominator 182 unchanged.
Working: 126 + 130/182 = 256/182

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 256 and 182, which is 2. Divide both the numerator and denominator by 2.
Working: 256 ÷ 2/182 ÷ 2 = 128/91

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (128) is greater than the denominator (91), divide 128 by 91: it goes in 1 whole time(s) with a remainder of 37, giving the mixed number 1 37/91.
Working: 128/91 = 1 37/91

Step 6: Decimal & Percentage Representation
Dividing the numerator 128 by denominator 91 produces a repeating decimal (approximately 1.406593, or 140.6593%).
Working: 128 ÷ 91 = 1.406593 (140.6593%)

Key Values:
- Simplified Fraction: 128/91
- Mixed Number Form: 1 37/91
- Decimal Value: 1.406593
- Percentage: 140.6593%

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9/13 + 10/14 = 128/91

Simplified Fraction

128/91

Mixed Number

1 37/91

Decimal Value

1.406593

Percentage

140.6593%

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Step-by-Step Solution: 9/13 + 10/14

Step 1

Find the Least Common Denominator (LCD)

The denominators 13 and 14 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 14 = 182.

LCD(13, 14) = 182

Step 2

Convert to Equivalent Fractions with Common Denominator 182

Multiply the numerator and denominator of 9/13 by 14, and multiply the numerator and denominator of 10/14 by 13 so both fractions share the common base 182.

9 × 14/13 × 14 = 126/182 and 10 × 13/14 × 13 = 130/182

Step 3

Add the Numerators

Now add the numerators (126 + 130 = 256) and keep the common denominator 182 unchanged.

126 + 130/182 = 256/182

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 256 and 182, which is 2. Divide both the numerator and denominator by 2.

256 ÷ 2/182 ÷ 2 = 128/91

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (128) is greater than the denominator (91), divide 128 by 91: it goes in 1 whole time(s) with a remainder of 37, giving the mixed number 1 37/91.

128/91 = 137/91

Step 6

Decimal & Percentage Representation

Dividing the numerator 128 by denominator 91 produces a repeating decimal (approximately 1.406593, or 140.6593%).

128 ÷ 91 = 1.406593 (140.6593%)

Visual Representation

The diagram below illustrates 9/13 plus 10/14 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`128/91`
Mixed Number Form	`1 37/91`
Decimal Form	`1.406593`
Percentage	`140.6593%`

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Frequently Asked Questions

What is 9/13 plus 10/14 as a fraction?

9/13 + 10/14 in simplest fraction form is 128/91 (or 1 37/91 as a mixed number).

What is 9/13 plus 10/14 as a decimal?

9/13 + 10/14 converted to a decimal is 1.406593.

What is 9/13 plus 10/14 as a percentage?

9/13 + 10/14 expressed as a percentage is 140.6593%.

How do you write 9/13 plus 10/14 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 128/91 can be written as the mixed number 1 37/91.

Does 9/13 plus 10/14 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.406593...) because the denominator contains prime factors other than 2 and 5.