What is 22/40 plus 9/13? (Answer: 323/260)

Exact Answer

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Problem: What is 22/40 plus 9/13?
Formula / Expression: 22/40 + 9/13
Final Answer: 1 63/260 (323/260)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 40 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 40 × 13 = 520.
Working: LCD(40, 13) = 520

Step 2: Convert to Equivalent Fractions with Common Denominator 520
Multiply the numerator and denominator of 22/40 by 13, and multiply the numerator and denominator of 9/13 by 40 so both fractions share the common base 520.
Working: 22 × 13/40 × 13 = 286/520 and 9 × 40/13 × 40 = 360/520

Step 3: Add the Numerators
Now add the numerators (286 + 360 = 646) and keep the common denominator 520 unchanged.
Working: 286 + 360/520 = 646/520

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 646 and 520, which is 2. Divide both the numerator and denominator by 2.
Working: 646 ÷ 2/520 ÷ 2 = 323/260

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (323) is greater than the denominator (260), divide 323 by 260: it goes in 1 whole time(s) with a remainder of 63, giving the mixed number 1 63/260.
Working: 323/260 = 1 63/260

Step 6: Decimal & Percentage Representation
Dividing the numerator 323 by denominator 260 produces a repeating decimal (approximately 1.242308, or 124.2308%).
Working: 323 ÷ 260 = 1.242308 (124.2308%)

Key Values:
- Simplified Fraction: 323/260
- Mixed Number Form: 1 63/260
- Decimal Value: 1.242308
- Percentage: 124.2308%

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Solved with FractionsCalc:
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22/40 + 9/13 = 323/260

Simplified Fraction

323/260

Mixed Number

1 63/260

Decimal Value

1.242308

Percentage

124.2308%

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Step-by-Step Solution: 22/40 + 9/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 40 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 40 × 13 = 520.

LCD(40, 13) = 520

Step 2

Convert to Equivalent Fractions with Common Denominator 520

Multiply the numerator and denominator of 22/40 by 13, and multiply the numerator and denominator of 9/13 by 40 so both fractions share the common base 520.

22 × 13/40 × 13 = 286/520 and 9 × 40/13 × 40 = 360/520

Step 3

Add the Numerators

Now add the numerators (286 + 360 = 646) and keep the common denominator 520 unchanged.

286 + 360/520 = 646/520

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 646 and 520, which is 2. Divide both the numerator and denominator by 2.

646 ÷ 2/520 ÷ 2 = 323/260

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (323) is greater than the denominator (260), divide 323 by 260: it goes in 1 whole time(s) with a remainder of 63, giving the mixed number 1 63/260.

323/260 = 163/260

Step 6

Decimal & Percentage Representation

Dividing the numerator 323 by denominator 260 produces a repeating decimal (approximately 1.242308, or 124.2308%).

323 ÷ 260 = 1.242308 (124.2308%)

Visual Representation

The diagram below illustrates 22/40 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`323/260`
Mixed Number Form	`1 63/260`
Decimal Form	`1.242308`
Percentage	`124.2308%`

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Frequently Asked Questions

What is 22/40 plus 9/13 as a fraction?

22/40 + 9/13 in simplest fraction form is 323/260 (or 1 63/260 as a mixed number).

What is 22/40 plus 9/13 as a decimal?

22/40 + 9/13 converted to a decimal is 1.242308.

What is 22/40 plus 9/13 as a percentage?

22/40 + 9/13 expressed as a percentage is 124.2308%.

How do you write 22/40 plus 9/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 323/260 can be written as the mixed number 1 63/260.

Does 22/40 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.242308...) because the denominator contains prime factors other than 2 and 5.