What is 22/42 plus 9/13? (Answer: 332/273)

Exact Answer

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Problem: What is 22/42 plus 9/13?
Formula / Expression: 22/42 + 9/13
Final Answer: 1 59/273 (332/273)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 42 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 42 × 13 = 546.
Working: LCD(42, 13) = 546

Step 2: Convert to Equivalent Fractions with Common Denominator 546
Multiply the numerator and denominator of 22/42 by 13, and multiply the numerator and denominator of 9/13 by 42 so both fractions share the common base 546.
Working: 22 × 13/42 × 13 = 286/546 and 9 × 42/13 × 42 = 378/546

Step 3: Add the Numerators
Now add the numerators (286 + 378 = 664) and keep the common denominator 546 unchanged.
Working: 286 + 378/546 = 664/546

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 664 and 546, which is 2. Divide both the numerator and denominator by 2.
Working: 664 ÷ 2/546 ÷ 2 = 332/273

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (332) is greater than the denominator (273), divide 332 by 273: it goes in 1 whole time(s) with a remainder of 59, giving the mixed number 1 59/273.
Working: 332/273 = 1 59/273

Step 6: Decimal & Percentage Representation
Dividing the numerator 332 by denominator 273 produces a repeating decimal (approximately 1.216117, or 121.6117%).
Working: 332 ÷ 273 = 1.216117 (121.6117%)

Key Values:
- Simplified Fraction: 332/273
- Mixed Number Form: 1 59/273
- Decimal Value: 1.216117
- Percentage: 121.6117%

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Solved with FractionsCalc:
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22/42 + 9/13 = 332/273

Simplified Fraction

332/273

Mixed Number

1 59/273

Decimal Value

1.216117

Percentage

121.6117%

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Step-by-Step Solution: 22/42 + 9/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 42 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 42 × 13 = 546.

LCD(42, 13) = 546

Step 2

Convert to Equivalent Fractions with Common Denominator 546

Multiply the numerator and denominator of 22/42 by 13, and multiply the numerator and denominator of 9/13 by 42 so both fractions share the common base 546.

22 × 13/42 × 13 = 286/546 and 9 × 42/13 × 42 = 378/546

Step 3

Add the Numerators

Now add the numerators (286 + 378 = 664) and keep the common denominator 546 unchanged.

286 + 378/546 = 664/546

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 664 and 546, which is 2. Divide both the numerator and denominator by 2.

664 ÷ 2/546 ÷ 2 = 332/273

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (332) is greater than the denominator (273), divide 332 by 273: it goes in 1 whole time(s) with a remainder of 59, giving the mixed number 1 59/273.

332/273 = 159/273

Step 6

Decimal & Percentage Representation

Dividing the numerator 332 by denominator 273 produces a repeating decimal (approximately 1.216117, or 121.6117%).

332 ÷ 273 = 1.216117 (121.6117%)

Visual Representation

The diagram below illustrates 22/42 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`332/273`
Mixed Number Form	`1 59/273`
Decimal Form	`1.216117`
Percentage	`121.6117%`

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Frequently Asked Questions

What is 22/42 plus 9/13 as a fraction?

22/42 + 9/13 in simplest fraction form is 332/273 (or 1 59/273 as a mixed number).

What is 22/42 plus 9/13 as a decimal?

22/42 + 9/13 converted to a decimal is 1.216117.

What is 22/42 plus 9/13 as a percentage?

22/42 + 9/13 expressed as a percentage is 121.6117%.

How do you write 22/42 plus 9/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 332/273 can be written as the mixed number 1 59/273.

Does 22/42 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.216117...) because the denominator contains prime factors other than 2 and 5.