What is 13/29 plus 12/21? (Answer: 207/203)

Exact Answer

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Problem: What is 13/29 plus 12/21?
Formula / Expression: 13/29 + 12/21
Final Answer: 1 4/203 (207/203)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 29 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 29 × 21 = 609.
Working: LCD(29, 21) = 609

Step 2: Convert to Equivalent Fractions with Common Denominator 609
Multiply the numerator and denominator of 13/29 by 21, and multiply the numerator and denominator of 12/21 by 29 so both fractions share the common base 609.
Working: 13 × 21/29 × 21 = 273/609 and 12 × 29/21 × 29 = 348/609

Step 3: Add the Numerators
Now add the numerators (273 + 348 = 621) and keep the common denominator 609 unchanged.
Working: 273 + 348/609 = 621/609

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 621 and 609, which is 3. Divide both the numerator and denominator by 3.
Working: 621 ÷ 3/609 ÷ 3 = 207/203

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (207) is greater than the denominator (203), divide 207 by 203: it goes in 1 whole time(s) with a remainder of 4, giving the mixed number 1 4/203.
Working: 207/203 = 1 4/203

Step 6: Decimal & Percentage Representation
Dividing the numerator 207 by denominator 203 produces a repeating decimal (approximately 1.019704, or 101.9704%).
Working: 207 ÷ 203 = 1.019704 (101.9704%)

Key Values:
- Simplified Fraction: 207/203
- Mixed Number Form: 1 4/203
- Decimal Value: 1.019704
- Percentage: 101.9704%

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13/29 + 12/21 = 207/203

Simplified Fraction

207/203

Mixed Number

1 4/203

Decimal Value

1.019704

Percentage

101.9704%

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Step-by-Step Solution: 13/29 + 12/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 29 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 29 × 21 = 609.

LCD(29, 21) = 609

Step 2

Convert to Equivalent Fractions with Common Denominator 609

Multiply the numerator and denominator of 13/29 by 21, and multiply the numerator and denominator of 12/21 by 29 so both fractions share the common base 609.

13 × 21/29 × 21 = 273/609 and 12 × 29/21 × 29 = 348/609

Step 3

Add the Numerators

Now add the numerators (273 + 348 = 621) and keep the common denominator 609 unchanged.

273 + 348/609 = 621/609

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 621 and 609, which is 3. Divide both the numerator and denominator by 3.

621 ÷ 3/609 ÷ 3 = 207/203

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (207) is greater than the denominator (203), divide 207 by 203: it goes in 1 whole time(s) with a remainder of 4, giving the mixed number 1 4/203.

207/203 = 14/203

Step 6

Decimal & Percentage Representation

Dividing the numerator 207 by denominator 203 produces a repeating decimal (approximately 1.019704, or 101.9704%).

207 ÷ 203 = 1.019704 (101.9704%)

Visual Representation

The diagram below illustrates 13/29 plus 12/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`207/203`
Mixed Number Form	`1 4/203`
Decimal Form	`1.019704`
Percentage	`101.9704%`

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Frequently Asked Questions

What is 13/29 plus 12/21 as a fraction?

13/29 + 12/21 in simplest fraction form is 207/203 (or 1 4/203 as a mixed number).

What is 13/29 plus 12/21 as a decimal?

13/29 + 12/21 converted to a decimal is 1.019704.

What is 13/29 plus 12/21 as a percentage?

13/29 + 12/21 expressed as a percentage is 101.9704%.

How do you write 13/29 plus 12/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 207/203 can be written as the mixed number 1 4/203.

Does 13/29 plus 12/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.019704...) because the denominator contains prime factors other than 2 and 5.