What is 22/34 plus 9/13? (Answer: 296/221)

Exact Answer

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Problem: What is 22/34 plus 9/13?
Formula / Expression: 22/34 + 9/13
Final Answer: 1 75/221 (296/221)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 34 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 34 × 13 = 442.
Working: LCD(34, 13) = 442

Step 2: Convert to Equivalent Fractions with Common Denominator 442
Multiply the numerator and denominator of 22/34 by 13, and multiply the numerator and denominator of 9/13 by 34 so both fractions share the common base 442.
Working: 22 × 13/34 × 13 = 286/442 and 9 × 34/13 × 34 = 306/442

Step 3: Add the Numerators
Now add the numerators (286 + 306 = 592) and keep the common denominator 442 unchanged.
Working: 286 + 306/442 = 592/442

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 592 and 442, which is 2. Divide both the numerator and denominator by 2.
Working: 592 ÷ 2/442 ÷ 2 = 296/221

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (296) is greater than the denominator (221), divide 296 by 221: it goes in 1 whole time(s) with a remainder of 75, giving the mixed number 1 75/221.
Working: 296/221 = 1 75/221

Step 6: Decimal & Percentage Representation
Dividing the numerator 296 by denominator 221 produces a repeating decimal (approximately 1.339367, or 133.9367%).
Working: 296 ÷ 221 = 1.339367 (133.9367%)

Key Values:
- Simplified Fraction: 296/221
- Mixed Number Form: 1 75/221
- Decimal Value: 1.339367
- Percentage: 133.9367%

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Solved with FractionsCalc:
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22/34 + 9/13 = 296/221

Simplified Fraction

296/221

Mixed Number

1 75/221

Decimal Value

1.339367

Percentage

133.9367%

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Step-by-Step Solution: 22/34 + 9/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 34 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 34 × 13 = 442.

LCD(34, 13) = 442

Step 2

Convert to Equivalent Fractions with Common Denominator 442

Multiply the numerator and denominator of 22/34 by 13, and multiply the numerator and denominator of 9/13 by 34 so both fractions share the common base 442.

22 × 13/34 × 13 = 286/442 and 9 × 34/13 × 34 = 306/442

Step 3

Add the Numerators

Now add the numerators (286 + 306 = 592) and keep the common denominator 442 unchanged.

286 + 306/442 = 592/442

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 592 and 442, which is 2. Divide both the numerator and denominator by 2.

592 ÷ 2/442 ÷ 2 = 296/221

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (296) is greater than the denominator (221), divide 296 by 221: it goes in 1 whole time(s) with a remainder of 75, giving the mixed number 1 75/221.

296/221 = 175/221

Step 6

Decimal & Percentage Representation

Dividing the numerator 296 by denominator 221 produces a repeating decimal (approximately 1.339367, or 133.9367%).

296 ÷ 221 = 1.339367 (133.9367%)

Visual Representation

The diagram below illustrates 22/34 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`296/221`
Mixed Number Form	`1 75/221`
Decimal Form	`1.339367`
Percentage	`133.9367%`

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Frequently Asked Questions

What is 22/34 plus 9/13 as a fraction?

22/34 + 9/13 in simplest fraction form is 296/221 (or 1 75/221 as a mixed number).

What is 22/34 plus 9/13 as a decimal?

22/34 + 9/13 converted to a decimal is 1.339367.

What is 22/34 plus 9/13 as a percentage?

22/34 + 9/13 expressed as a percentage is 133.9367%.

How do you write 22/34 plus 9/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 296/221 can be written as the mixed number 1 75/221.

Does 22/34 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.339367...) because the denominator contains prime factors other than 2 and 5.