What is 13/39 plus 10/21? (Answer: 17/21)

Exact Answer

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Problem: What is 13/39 plus 10/21?
Formula / Expression: 13/39 + 10/21
Final Answer: 17/21
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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 10/21 by 13 so both fractions share the common base 273.
Working: 13 × 7/39 × 7 = 91/273 and 10 × 13/21 × 13 = 130/273

Step 3: Add the Numerators
Now add the numerators (91 + 130 = 221) and keep the common denominator 273 unchanged.
Working: 91 + 130/273 = 221/273

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 221 and 273, which is 13. Divide both the numerator and denominator by 13.
Working: 221 ÷ 13/273 ÷ 13 = 17/21

Step 5: Decimal & Percentage Representation
Dividing the numerator 17 by denominator 21 produces a repeating decimal (approximately 0.809524, or 80.9524%).
Working: 17 ÷ 21 = 0.809524 (80.9524%)

Key Values:
- Simplified Fraction: 17/21
- Mixed Number Form: 17/21
- Decimal Value: 0.809524
- Percentage: 80.9524%

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Solved with FractionsCalc:
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13/39 + 10/21 = 17/21

Simplified Fraction

17/21

Mixed Number

Proper (17/21)

Decimal Value

0.809524

Percentage

80.9524%

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Step-by-Step Solution: 13/39 + 10/21

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 10/21 by 13 so both fractions share the common base 273.

13 × 7/39 × 7 = 91/273 and 10 × 13/21 × 13 = 130/273

Step 3

Add the Numerators

Now add the numerators (91 + 130 = 221) and keep the common denominator 273 unchanged.

91 + 130/273 = 221/273

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 221 and 273, which is 13. Divide both the numerator and denominator by 13.

221 ÷ 13/273 ÷ 13 = 17/21

Step 5

Decimal & Percentage Representation

Dividing the numerator 17 by denominator 21 produces a repeating decimal (approximately 0.809524, or 80.9524%).

17 ÷ 21 = 0.809524 (80.9524%)

Visual Representation

The diagram below illustrates 13/39 plus 10/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`17/21`
Mixed Number Form	`17/21`
Decimal Form	`0.809524`
Percentage	`80.9524%`

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Frequently Asked Questions

What is 13/39 plus 10/21 as a fraction?

13/39 + 10/21 in simplest fraction form is 17/21.

What is 13/39 plus 10/21 as a decimal?

13/39 + 10/21 converted to a decimal is 0.809524.

What is 13/39 plus 10/21 as a percentage?

13/39 + 10/21 expressed as a percentage is 80.9524%.

Does 13/39 plus 10/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.809524...) because the denominator contains prime factors other than 2 and 5.