What is 22/44 plus 9/13? (Answer: 31/26)

Exact Answer

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Problem: What is 22/44 plus 9/13?
Formula / Expression: 22/44 + 9/13
Final Answer: 1 5/26 (31/26)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 44 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 44 × 13 = 572.
Working: LCD(44, 13) = 572

Step 2: Convert to Equivalent Fractions with Common Denominator 572
Multiply the numerator and denominator of 22/44 by 13, and multiply the numerator and denominator of 9/13 by 44 so both fractions share the common base 572.
Working: 22 × 13/44 × 13 = 286/572 and 9 × 44/13 × 44 = 396/572

Step 3: Add the Numerators
Now add the numerators (286 + 396 = 682) and keep the common denominator 572 unchanged.
Working: 286 + 396/572 = 682/572

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 682 and 572, which is 22. Divide both the numerator and denominator by 22.
Working: 682 ÷ 22/572 ÷ 22 = 31/26

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (31) is greater than the denominator (26), divide 31 by 26: it goes in 1 whole time(s) with a remainder of 5, giving the mixed number 1 5/26.
Working: 31/26 = 1 5/26

Step 6: Decimal & Percentage Representation
Dividing the numerator 31 by denominator 26 produces a repeating decimal (approximately 1.192308, or 119.2308%).
Working: 31 ÷ 26 = 1.192308 (119.2308%)

Key Values:
- Simplified Fraction: 31/26
- Mixed Number Form: 1 5/26
- Decimal Value: 1.192308
- Percentage: 119.2308%

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Solved with FractionsCalc:
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22/44 + 9/13 = 31/26

Simplified Fraction

31/26

Mixed Number

1 5/26

Decimal Value

1.192308

Percentage

119.2308%

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Step-by-Step Solution: 22/44 + 9/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 44 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 44 × 13 = 572.

LCD(44, 13) = 572

Step 2

Convert to Equivalent Fractions with Common Denominator 572

Multiply the numerator and denominator of 22/44 by 13, and multiply the numerator and denominator of 9/13 by 44 so both fractions share the common base 572.

22 × 13/44 × 13 = 286/572 and 9 × 44/13 × 44 = 396/572

Step 3

Add the Numerators

Now add the numerators (286 + 396 = 682) and keep the common denominator 572 unchanged.

286 + 396/572 = 682/572

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 682 and 572, which is 22. Divide both the numerator and denominator by 22.

682 ÷ 22/572 ÷ 22 = 31/26

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (31) is greater than the denominator (26), divide 31 by 26: it goes in 1 whole time(s) with a remainder of 5, giving the mixed number 1 5/26.

31/26 = 15/26

Step 6

Decimal & Percentage Representation

Dividing the numerator 31 by denominator 26 produces a repeating decimal (approximately 1.192308, or 119.2308%).

31 ÷ 26 = 1.192308 (119.2308%)

Visual Representation

The diagram below illustrates 22/44 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`31/26`
Mixed Number Form	`1 5/26`
Decimal Form	`1.192308`
Percentage	`119.2308%`

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Frequently Asked Questions

What is 22/44 plus 9/13 as a fraction?

22/44 + 9/13 in simplest fraction form is 31/26 (or 1 5/26 as a mixed number).

What is 22/44 plus 9/13 as a decimal?

22/44 + 9/13 converted to a decimal is 1.192308.

What is 22/44 plus 9/13 as a percentage?

22/44 + 9/13 expressed as a percentage is 119.2308%.

How do you write 22/44 plus 9/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 31/26 can be written as the mixed number 1 5/26.

Does 22/44 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.192308...) because the denominator contains prime factors other than 2 and 5.