What is 13/39 plus 15/21? (Answer: 22/21)

Exact Answer

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Problem: What is 13/39 plus 15/21?
Formula / Expression: 13/39 + 15/21
Final Answer: 1 1/21 (22/21)
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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 15/21 by 13 so both fractions share the common base 273.
Working: 13 × 7/39 × 7 = 91/273 and 15 × 13/21 × 13 = 195/273

Step 3: Add the Numerators
Now add the numerators (91 + 195 = 286) and keep the common denominator 273 unchanged.
Working: 91 + 195/273 = 286/273

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 286 and 273, which is 13. Divide both the numerator and denominator by 13.
Working: 286 ÷ 13/273 ÷ 13 = 22/21

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (22) is greater than the denominator (21), divide 22 by 21: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/21.
Working: 22/21 = 1 1/21

Step 6: Decimal & Percentage Representation
Dividing the numerator 22 by denominator 21 produces a repeating decimal (approximately 1.047619, or 104.7619%).
Working: 22 ÷ 21 = 1.047619 (104.7619%)

Key Values:
- Simplified Fraction: 22/21
- Mixed Number Form: 1 1/21
- Decimal Value: 1.047619
- Percentage: 104.7619%

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13/39 + 15/21 = 22/21

Simplified Fraction

22/21

Mixed Number

1 1/21

Decimal Value

1.047619

Percentage

104.7619%

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Step-by-Step Solution: 13/39 + 15/21

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 15/21 by 13 so both fractions share the common base 273.

13 × 7/39 × 7 = 91/273 and 15 × 13/21 × 13 = 195/273

Step 3

Add the Numerators

Now add the numerators (91 + 195 = 286) and keep the common denominator 273 unchanged.

91 + 195/273 = 286/273

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 286 and 273, which is 13. Divide both the numerator and denominator by 13.

286 ÷ 13/273 ÷ 13 = 22/21

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (22) is greater than the denominator (21), divide 22 by 21: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/21.

22/21 = 11/21

Step 6

Decimal & Percentage Representation

Dividing the numerator 22 by denominator 21 produces a repeating decimal (approximately 1.047619, or 104.7619%).

22 ÷ 21 = 1.047619 (104.7619%)

Visual Representation

The diagram below illustrates 13/39 plus 15/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`22/21`
Mixed Number Form	`1 1/21`
Decimal Form	`1.047619`
Percentage	`104.7619%`

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Frequently Asked Questions

What is 13/39 plus 15/21 as a fraction?

13/39 + 15/21 in simplest fraction form is 22/21 (or 1 1/21 as a mixed number).

What is 13/39 plus 15/21 as a decimal?

13/39 + 15/21 converted to a decimal is 1.047619.

What is 13/39 plus 15/21 as a percentage?

13/39 + 15/21 expressed as a percentage is 104.7619%.

How do you write 13/39 plus 15/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 22/21 can be written as the mixed number 1 1/21.

Does 13/39 plus 15/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.047619...) because the denominator contains prime factors other than 2 and 5.