What is 13/39 plus 9/21? (Answer: 16/21)

Exact Answer

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Problem: What is 13/39 plus 9/21?
Formula / Expression: 13/39 + 9/21
Final Answer: 16/21
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 39 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 273 (which is smaller than their product 39 × 21 = 819, keeping the calculation simpler).
Working: LCD(39, 21) = 273

Step 2: Convert to Equivalent Fractions with Common Denominator 273
Multiply the numerator and denominator of 13/39 by 7, and multiply the numerator and denominator of 9/21 by 13 so both fractions share the common base 273.
Working: 13 × 7/39 × 7 = 91/273 and 9 × 13/21 × 13 = 117/273

Step 3: Add the Numerators
Now add the numerators (91 + 117 = 208) and keep the common denominator 273 unchanged.
Working: 91 + 117/273 = 208/273

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 208 and 273, which is 13. Divide both the numerator and denominator by 13.
Working: 208 ÷ 13/273 ÷ 13 = 16/21

Step 5: Decimal & Percentage Representation
Dividing the numerator 16 by denominator 21 produces a repeating decimal (approximately 0.761905, or 76.1905%).
Working: 16 ÷ 21 = 0.761905 (76.1905%)

Key Values:
- Simplified Fraction: 16/21
- Mixed Number Form: 16/21
- Decimal Value: 0.761905
- Percentage: 76.1905%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-13-39-plus-9-21/
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13/39 + 9/21 = 16/21

Simplified Fraction

16/21

Mixed Number

Proper (16/21)

Decimal Value

0.761905

Percentage

76.1905%

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Step-by-Step Solution: 13/39 + 9/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 39 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 273 (which is smaller than their product 39 × 21 = 819, keeping the calculation simpler).

LCD(39, 21) = 273

Step 2

Convert to Equivalent Fractions with Common Denominator 273

Multiply the numerator and denominator of 13/39 by 7, and multiply the numerator and denominator of 9/21 by 13 so both fractions share the common base 273.

13 × 7/39 × 7 = 91/273 and 9 × 13/21 × 13 = 117/273

Step 3

Add the Numerators

Now add the numerators (91 + 117 = 208) and keep the common denominator 273 unchanged.

91 + 117/273 = 208/273

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 208 and 273, which is 13. Divide both the numerator and denominator by 13.

208 ÷ 13/273 ÷ 13 = 16/21

Step 5

Decimal & Percentage Representation

Dividing the numerator 16 by denominator 21 produces a repeating decimal (approximately 0.761905, or 76.1905%).

16 ÷ 21 = 0.761905 (76.1905%)

Visual Representation

The diagram below illustrates 13/39 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`16/21`
Mixed Number Form	`16/21`
Decimal Form	`0.761905`
Percentage	`76.1905%`

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Frequently Asked Questions

What is 13/39 plus 9/21 as a fraction?

13/39 + 9/21 in simplest fraction form is 16/21.

What is 13/39 plus 9/21 as a decimal?

13/39 + 9/21 converted to a decimal is 0.761905.

What is 13/39 plus 9/21 as a percentage?

13/39 + 9/21 expressed as a percentage is 76.1905%.

Does 13/39 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.761905...) because the denominator contains prime factors other than 2 and 5.