What is 12/21 plus 15/26? (Answer: 209/182)

Exact Answer

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Problem: What is 12/21 plus 15/26?
Formula / Expression: 12/21 + 15/26
Final Answer: 1 27/182 (209/182)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 21 and 26 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 21 × 26 = 546.
Working: LCD(21, 26) = 546

Step 2: Convert to Equivalent Fractions with Common Denominator 546
Multiply the numerator and denominator of 12/21 by 26, and multiply the numerator and denominator of 15/26 by 21 so both fractions share the common base 546.
Working: 12 × 26/21 × 26 = 312/546 and 15 × 21/26 × 21 = 315/546

Step 3: Add the Numerators
Now add the numerators (312 + 315 = 627) and keep the common denominator 546 unchanged.
Working: 312 + 315/546 = 627/546

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 627 and 546, which is 3. Divide both the numerator and denominator by 3.
Working: 627 ÷ 3/546 ÷ 3 = 209/182

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (209) is greater than the denominator (182), divide 209 by 182: it goes in 1 whole time(s) with a remainder of 27, giving the mixed number 1 27/182.
Working: 209/182 = 1 27/182

Step 6: Decimal & Percentage Representation
Dividing the numerator 209 by denominator 182 produces a repeating decimal (approximately 1.148352, or 114.8352%).
Working: 209 ÷ 182 = 1.148352 (114.8352%)

Key Values:
- Simplified Fraction: 209/182
- Mixed Number Form: 1 27/182
- Decimal Value: 1.148352
- Percentage: 114.8352%

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12/21 + 15/26 = 209/182

Simplified Fraction

209/182

Mixed Number

1 27/182

Decimal Value

1.148352

Percentage

114.8352%

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Step-by-Step Solution: 12/21 + 15/26

Step 1

Find the Least Common Denominator (LCD)

The denominators 21 and 26 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 21 × 26 = 546.

LCD(21, 26) = 546

Step 2

Convert to Equivalent Fractions with Common Denominator 546

Multiply the numerator and denominator of 12/21 by 26, and multiply the numerator and denominator of 15/26 by 21 so both fractions share the common base 546.

12 × 26/21 × 26 = 312/546 and 15 × 21/26 × 21 = 315/546

Step 3

Add the Numerators

Now add the numerators (312 + 315 = 627) and keep the common denominator 546 unchanged.

312 + 315/546 = 627/546

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 627 and 546, which is 3. Divide both the numerator and denominator by 3.

627 ÷ 3/546 ÷ 3 = 209/182

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (209) is greater than the denominator (182), divide 209 by 182: it goes in 1 whole time(s) with a remainder of 27, giving the mixed number 1 27/182.

209/182 = 127/182

Step 6

Decimal & Percentage Representation

Dividing the numerator 209 by denominator 182 produces a repeating decimal (approximately 1.148352, or 114.8352%).

209 ÷ 182 = 1.148352 (114.8352%)

Visual Representation

The diagram below illustrates 12/21 plus 15/26 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`209/182`
Mixed Number Form	`1 27/182`
Decimal Form	`1.148352`
Percentage	`114.8352%`

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Frequently Asked Questions

What is 12/21 plus 15/26 as a fraction?

12/21 + 15/26 in simplest fraction form is 209/182 (or 1 27/182 as a mixed number).

What is 12/21 plus 15/26 as a decimal?

12/21 + 15/26 converted to a decimal is 1.148352.

What is 12/21 plus 15/26 as a percentage?

12/21 + 15/26 expressed as a percentage is 114.8352%.

How do you write 12/21 plus 15/26 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 209/182 can be written as the mixed number 1 27/182.

Does 12/21 plus 15/26 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.148352...) because the denominator contains prime factors other than 2 and 5.