What is 12/21 plus 13/22? (Answer: 179/154)

Exact Answer

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Problem: What is 12/21 plus 13/22?
Formula / Expression: 12/21 + 13/22
Final Answer: 1 25/154 (179/154)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 21 and 22 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 21 × 22 = 462.
Working: LCD(21, 22) = 462

Step 2: Convert to Equivalent Fractions with Common Denominator 462
Multiply the numerator and denominator of 12/21 by 22, and multiply the numerator and denominator of 13/22 by 21 so both fractions share the common base 462.
Working: 12 × 22/21 × 22 = 264/462 and 13 × 21/22 × 21 = 273/462

Step 3: Add the Numerators
Now add the numerators (264 + 273 = 537) and keep the common denominator 462 unchanged.
Working: 264 + 273/462 = 537/462

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 537 and 462, which is 3. Divide both the numerator and denominator by 3.
Working: 537 ÷ 3/462 ÷ 3 = 179/154

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (179) is greater than the denominator (154), divide 179 by 154: it goes in 1 whole time(s) with a remainder of 25, giving the mixed number 1 25/154.
Working: 179/154 = 1 25/154

Step 6: Decimal & Percentage Representation
Dividing the numerator 179 by denominator 154 produces a repeating decimal (approximately 1.162338, or 116.2338%).
Working: 179 ÷ 154 = 1.162338 (116.2338%)

Key Values:
- Simplified Fraction: 179/154
- Mixed Number Form: 1 25/154
- Decimal Value: 1.162338
- Percentage: 116.2338%

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Solved with FractionsCalc:
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12/21 + 13/22 = 179/154

Simplified Fraction

179/154

Mixed Number

1 25/154

Decimal Value

1.162338

Percentage

116.2338%

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Step-by-Step Solution: 12/21 + 13/22

Step 1

Find the Least Common Denominator (LCD)

The denominators 21 and 22 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 21 × 22 = 462.

LCD(21, 22) = 462

Step 2

Convert to Equivalent Fractions with Common Denominator 462

Multiply the numerator and denominator of 12/21 by 22, and multiply the numerator and denominator of 13/22 by 21 so both fractions share the common base 462.

12 × 22/21 × 22 = 264/462 and 13 × 21/22 × 21 = 273/462

Step 3

Add the Numerators

Now add the numerators (264 + 273 = 537) and keep the common denominator 462 unchanged.

264 + 273/462 = 537/462

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 537 and 462, which is 3. Divide both the numerator and denominator by 3.

537 ÷ 3/462 ÷ 3 = 179/154

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (179) is greater than the denominator (154), divide 179 by 154: it goes in 1 whole time(s) with a remainder of 25, giving the mixed number 1 25/154.

179/154 = 125/154

Step 6

Decimal & Percentage Representation

Dividing the numerator 179 by denominator 154 produces a repeating decimal (approximately 1.162338, or 116.2338%).

179 ÷ 154 = 1.162338 (116.2338%)

Visual Representation

The diagram below illustrates 12/21 plus 13/22 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`179/154`
Mixed Number Form	`1 25/154`
Decimal Form	`1.162338`
Percentage	`116.2338%`

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Frequently Asked Questions

What is 12/21 plus 13/22 as a fraction?

12/21 + 13/22 in simplest fraction form is 179/154 (or 1 25/154 as a mixed number).

What is 12/21 plus 13/22 as a decimal?

12/21 + 13/22 converted to a decimal is 1.162338.

What is 12/21 plus 13/22 as a percentage?

12/21 + 13/22 expressed as a percentage is 116.2338%.

How do you write 12/21 plus 13/22 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 179/154 can be written as the mixed number 1 25/154.

Does 12/21 plus 13/22 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.162338...) because the denominator contains prime factors other than 2 and 5.