What is 7/13 plus 12/22? (Answer: 155/143)

Exact Answer

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Problem: What is 7/13 plus 12/22?
Formula / Expression: 7/13 + 12/22
Final Answer: 1 12/143 (155/143)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 13 and 22 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 22 = 286.
Working: LCD(13, 22) = 286

Step 2: Convert to Equivalent Fractions with Common Denominator 286
Multiply the numerator and denominator of 7/13 by 22, and multiply the numerator and denominator of 12/22 by 13 so both fractions share the common base 286.
Working: 7 × 22/13 × 22 = 154/286 and 12 × 13/22 × 13 = 156/286

Step 3: Add the Numerators
Now add the numerators (154 + 156 = 310) and keep the common denominator 286 unchanged.
Working: 154 + 156/286 = 310/286

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 310 and 286, which is 2. Divide both the numerator and denominator by 2.
Working: 310 ÷ 2/286 ÷ 2 = 155/143

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (155) is greater than the denominator (143), divide 155 by 143: it goes in 1 whole time(s) with a remainder of 12, giving the mixed number 1 12/143.
Working: 155/143 = 1 12/143

Step 6: Decimal & Percentage Representation
Dividing the numerator 155 by denominator 143 produces a repeating decimal (approximately 1.083916, or 108.3916%).
Working: 155 ÷ 143 = 1.083916 (108.3916%)

Key Values:
- Simplified Fraction: 155/143
- Mixed Number Form: 1 12/143
- Decimal Value: 1.083916
- Percentage: 108.3916%

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Solved with FractionsCalc:
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7/13 + 12/22 = 155/143

Simplified Fraction

155/143

Mixed Number

1 12/143

Decimal Value

1.083916

Percentage

108.3916%

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Step-by-Step Solution: 7/13 + 12/22

Step 1

Find the Least Common Denominator (LCD)

The denominators 13 and 22 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 22 = 286.

LCD(13, 22) = 286

Step 2

Convert to Equivalent Fractions with Common Denominator 286

Multiply the numerator and denominator of 7/13 by 22, and multiply the numerator and denominator of 12/22 by 13 so both fractions share the common base 286.

7 × 22/13 × 22 = 154/286 and 12 × 13/22 × 13 = 156/286

Step 3

Add the Numerators

Now add the numerators (154 + 156 = 310) and keep the common denominator 286 unchanged.

154 + 156/286 = 310/286

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 310 and 286, which is 2. Divide both the numerator and denominator by 2.

310 ÷ 2/286 ÷ 2 = 155/143

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (155) is greater than the denominator (143), divide 155 by 143: it goes in 1 whole time(s) with a remainder of 12, giving the mixed number 1 12/143.

155/143 = 112/143

Step 6

Decimal & Percentage Representation

Dividing the numerator 155 by denominator 143 produces a repeating decimal (approximately 1.083916, or 108.3916%).

155 ÷ 143 = 1.083916 (108.3916%)

Visual Representation

The diagram below illustrates 7/13 plus 12/22 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`155/143`
Mixed Number Form	`1 12/143`
Decimal Form	`1.083916`
Percentage	`108.3916%`

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Frequently Asked Questions

What is 7/13 plus 12/22 as a fraction?

7/13 + 12/22 in simplest fraction form is 155/143 (or 1 12/143 as a mixed number).

What is 7/13 plus 12/22 as a decimal?

7/13 + 12/22 converted to a decimal is 1.083916.

What is 7/13 plus 12/22 as a percentage?

7/13 + 12/22 expressed as a percentage is 108.3916%.

How do you write 7/13 plus 12/22 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 155/143 can be written as the mixed number 1 12/143.

Does 7/13 plus 12/22 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.083916...) because the denominator contains prime factors other than 2 and 5.