What is 22/46 plus 9/13? (Answer: 350/299)

Exact Answer

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Problem: What is 22/46 plus 9/13?
Formula / Expression: 22/46 + 9/13
Final Answer: 1 51/299 (350/299)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 46 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 46 × 13 = 598.
Working: LCD(46, 13) = 598

Step 2: Convert to Equivalent Fractions with Common Denominator 598
Multiply the numerator and denominator of 22/46 by 13, and multiply the numerator and denominator of 9/13 by 46 so both fractions share the common base 598.
Working: 22 × 13/46 × 13 = 286/598 and 9 × 46/13 × 46 = 414/598

Step 3: Add the Numerators
Now add the numerators (286 + 414 = 700) and keep the common denominator 598 unchanged.
Working: 286 + 414/598 = 700/598

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 700 and 598, which is 2. Divide both the numerator and denominator by 2.
Working: 700 ÷ 2/598 ÷ 2 = 350/299

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (350) is greater than the denominator (299), divide 350 by 299: it goes in 1 whole time(s) with a remainder of 51, giving the mixed number 1 51/299.
Working: 350/299 = 1 51/299

Step 6: Decimal & Percentage Representation
Dividing the numerator 350 by denominator 299 produces a repeating decimal (approximately 1.170569, or 117.0569%).
Working: 350 ÷ 299 = 1.170569 (117.0569%)

Key Values:
- Simplified Fraction: 350/299
- Mixed Number Form: 1 51/299
- Decimal Value: 1.170569
- Percentage: 117.0569%

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Solved with FractionsCalc:
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22/46 + 9/13 = 350/299

Simplified Fraction

350/299

Mixed Number

1 51/299

Decimal Value

1.170569

Percentage

117.0569%

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Step-by-Step Solution: 22/46 + 9/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 46 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 46 × 13 = 598.

LCD(46, 13) = 598

Step 2

Convert to Equivalent Fractions with Common Denominator 598

Multiply the numerator and denominator of 22/46 by 13, and multiply the numerator and denominator of 9/13 by 46 so both fractions share the common base 598.

22 × 13/46 × 13 = 286/598 and 9 × 46/13 × 46 = 414/598

Step 3

Add the Numerators

Now add the numerators (286 + 414 = 700) and keep the common denominator 598 unchanged.

286 + 414/598 = 700/598

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 700 and 598, which is 2. Divide both the numerator and denominator by 2.

700 ÷ 2/598 ÷ 2 = 350/299

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (350) is greater than the denominator (299), divide 350 by 299: it goes in 1 whole time(s) with a remainder of 51, giving the mixed number 1 51/299.

350/299 = 151/299

Step 6

Decimal & Percentage Representation

Dividing the numerator 350 by denominator 299 produces a repeating decimal (approximately 1.170569, or 117.0569%).

350 ÷ 299 = 1.170569 (117.0569%)

Visual Representation

The diagram below illustrates 22/46 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`350/299`
Mixed Number Form	`1 51/299`
Decimal Form	`1.170569`
Percentage	`117.0569%`

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Frequently Asked Questions

What is 22/46 plus 9/13 as a fraction?

22/46 + 9/13 in simplest fraction form is 350/299 (or 1 51/299 as a mixed number).

What is 22/46 plus 9/13 as a decimal?

22/46 + 9/13 converted to a decimal is 1.170569.

What is 22/46 plus 9/13 as a percentage?

22/46 + 9/13 expressed as a percentage is 117.0569%.

How do you write 22/46 plus 9/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 350/299 can be written as the mixed number 1 51/299.

Does 22/46 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.170569...) because the denominator contains prime factors other than 2 and 5.