What is 8/22 plus 9/13? (Answer: 151/143)

Exact Answer

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Problem: What is 8/22 plus 9/13?
Formula / Expression: 8/22 + 9/13
Final Answer: 1 8/143 (151/143)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 22 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 22 × 13 = 286.
Working: LCD(22, 13) = 286

Step 2: Convert to Equivalent Fractions with Common Denominator 286
Multiply the numerator and denominator of 8/22 by 13, and multiply the numerator and denominator of 9/13 by 22 so both fractions share the common base 286.
Working: 8 × 13/22 × 13 = 104/286 and 9 × 22/13 × 22 = 198/286

Step 3: Add the Numerators
Now add the numerators (104 + 198 = 302) and keep the common denominator 286 unchanged.
Working: 104 + 198/286 = 302/286

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 302 and 286, which is 2. Divide both the numerator and denominator by 2.
Working: 302 ÷ 2/286 ÷ 2 = 151/143

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (151) is greater than the denominator (143), divide 151 by 143: it goes in 1 whole time(s) with a remainder of 8, giving the mixed number 1 8/143.
Working: 151/143 = 1 8/143

Step 6: Decimal & Percentage Representation
Dividing the numerator 151 by denominator 143 produces a repeating decimal (approximately 1.055944, or 105.5944%).
Working: 151 ÷ 143 = 1.055944 (105.5944%)

Key Values:
- Simplified Fraction: 151/143
- Mixed Number Form: 1 8/143
- Decimal Value: 1.055944
- Percentage: 105.5944%

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Solved with FractionsCalc:
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8/22 + 9/13 = 151/143

Simplified Fraction

151/143

Mixed Number

1 8/143

Decimal Value

1.055944

Percentage

105.5944%

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Step-by-Step Solution: 8/22 + 9/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 22 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 22 × 13 = 286.

LCD(22, 13) = 286

Step 2

Convert to Equivalent Fractions with Common Denominator 286

Multiply the numerator and denominator of 8/22 by 13, and multiply the numerator and denominator of 9/13 by 22 so both fractions share the common base 286.

8 × 13/22 × 13 = 104/286 and 9 × 22/13 × 22 = 198/286

Step 3

Add the Numerators

Now add the numerators (104 + 198 = 302) and keep the common denominator 286 unchanged.

104 + 198/286 = 302/286

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 302 and 286, which is 2. Divide both the numerator and denominator by 2.

302 ÷ 2/286 ÷ 2 = 151/143

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (151) is greater than the denominator (143), divide 151 by 143: it goes in 1 whole time(s) with a remainder of 8, giving the mixed number 1 8/143.

151/143 = 18/143

Step 6

Decimal & Percentage Representation

Dividing the numerator 151 by denominator 143 produces a repeating decimal (approximately 1.055944, or 105.5944%).

151 ÷ 143 = 1.055944 (105.5944%)

Visual Representation

The diagram below illustrates 8/22 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`151/143`
Mixed Number Form	`1 8/143`
Decimal Form	`1.055944`
Percentage	`105.5944%`

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Frequently Asked Questions

What is 8/22 plus 9/13 as a fraction?

8/22 + 9/13 in simplest fraction form is 151/143 (or 1 8/143 as a mixed number).

What is 8/22 plus 9/13 as a decimal?

8/22 + 9/13 converted to a decimal is 1.055944.

What is 8/22 plus 9/13 as a percentage?

8/22 + 9/13 expressed as a percentage is 105.5944%.

How do you write 8/22 plus 9/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 151/143 can be written as the mixed number 1 8/143.

Does 8/22 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.055944...) because the denominator contains prime factors other than 2 and 5.