What is 12/17 plus 15/21? (Answer: 169/119)

Exact Answer

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Problem: What is 12/17 plus 15/21?
Formula / Expression: 12/17 + 15/21
Final Answer: 1 50/119 (169/119)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 17 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 17 × 21 = 357.
Working: LCD(17, 21) = 357

Step 2: Convert to Equivalent Fractions with Common Denominator 357
Multiply the numerator and denominator of 12/17 by 21, and multiply the numerator and denominator of 15/21 by 17 so both fractions share the common base 357.
Working: 12 × 21/17 × 21 = 252/357 and 15 × 17/21 × 17 = 255/357

Step 3: Add the Numerators
Now add the numerators (252 + 255 = 507) and keep the common denominator 357 unchanged.
Working: 252 + 255/357 = 507/357

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 507 and 357, which is 3. Divide both the numerator and denominator by 3.
Working: 507 ÷ 3/357 ÷ 3 = 169/119

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (169) is greater than the denominator (119), divide 169 by 119: it goes in 1 whole time(s) with a remainder of 50, giving the mixed number 1 50/119.
Working: 169/119 = 1 50/119

Step 6: Decimal & Percentage Representation
Dividing the numerator 169 by denominator 119 produces a repeating decimal (approximately 1.420168, or 142.0168%).
Working: 169 ÷ 119 = 1.420168 (142.0168%)

Key Values:
- Simplified Fraction: 169/119
- Mixed Number Form: 1 50/119
- Decimal Value: 1.420168
- Percentage: 142.0168%

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Solved with FractionsCalc:
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12/17 + 15/21 = 169/119

Simplified Fraction

169/119

Mixed Number

1 50/119

Decimal Value

1.420168

Percentage

142.0168%

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Step-by-Step Solution: 12/17 + 15/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 17 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 17 × 21 = 357.

LCD(17, 21) = 357

Step 2

Convert to Equivalent Fractions with Common Denominator 357

Multiply the numerator and denominator of 12/17 by 21, and multiply the numerator and denominator of 15/21 by 17 so both fractions share the common base 357.

12 × 21/17 × 21 = 252/357 and 15 × 17/21 × 17 = 255/357

Step 3

Add the Numerators

Now add the numerators (252 + 255 = 507) and keep the common denominator 357 unchanged.

252 + 255/357 = 507/357

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 507 and 357, which is 3. Divide both the numerator and denominator by 3.

507 ÷ 3/357 ÷ 3 = 169/119

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (169) is greater than the denominator (119), divide 169 by 119: it goes in 1 whole time(s) with a remainder of 50, giving the mixed number 1 50/119.

169/119 = 150/119

Step 6

Decimal & Percentage Representation

Dividing the numerator 169 by denominator 119 produces a repeating decimal (approximately 1.420168, or 142.0168%).

169 ÷ 119 = 1.420168 (142.0168%)

Visual Representation

The diagram below illustrates 12/17 plus 15/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`169/119`
Mixed Number Form	`1 50/119`
Decimal Form	`1.420168`
Percentage	`142.0168%`

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Frequently Asked Questions

What is 12/17 plus 15/21 as a fraction?

12/17 + 15/21 in simplest fraction form is 169/119 (or 1 50/119 as a mixed number).

What is 12/17 plus 15/21 as a decimal?

12/17 + 15/21 converted to a decimal is 1.420168.

What is 12/17 plus 15/21 as a percentage?

12/17 + 15/21 expressed as a percentage is 142.0168%.

How do you write 12/17 plus 15/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 169/119 can be written as the mixed number 1 50/119.

Does 12/17 plus 15/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.420168...) because the denominator contains prime factors other than 2 and 5.