What is 6/39 plus 15/21? (Answer: 79/91)

Exact Answer

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Problem: What is 6/39 plus 15/21?
Formula / Expression: 6/39 + 15/21
Final Answer: 79/91
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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 6/39 by 7, and multiply the numerator and denominator of 15/21 by 13 so both fractions share the common base 273.
Working: 6 × 7/39 × 7 = 42/273 and 15 × 13/21 × 13 = 195/273

Step 3: Add the Numerators
Now add the numerators (42 + 195 = 237) and keep the common denominator 273 unchanged.
Working: 42 + 195/273 = 237/273

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 237 and 273, which is 3. Divide both the numerator and denominator by 3.
Working: 237 ÷ 3/273 ÷ 3 = 79/91

Step 5: Decimal & Percentage Representation
Dividing the numerator 79 by denominator 91 produces a repeating decimal (approximately 0.868132, or 86.8132%).
Working: 79 ÷ 91 = 0.868132 (86.8132%)

Key Values:
- Simplified Fraction: 79/91
- Mixed Number Form: 79/91
- Decimal Value: 0.868132
- Percentage: 86.8132%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-6-39-plus-15-21/
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6/39 + 15/21 = 79/91

Simplified Fraction

79/91

Mixed Number

Proper (79/91)

Decimal Value

0.868132

Percentage

86.8132%

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Step-by-Step Solution: 6/39 + 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 6/39 by 7, and multiply the numerator and denominator of 15/21 by 13 so both fractions share the common base 273.

6 × 7/39 × 7 = 42/273 and 15 × 13/21 × 13 = 195/273

Step 3

Add the Numerators

Now add the numerators (42 + 195 = 237) and keep the common denominator 273 unchanged.

42 + 195/273 = 237/273

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 237 and 273, which is 3. Divide both the numerator and denominator by 3.

237 ÷ 3/273 ÷ 3 = 79/91

Step 5

Decimal & Percentage Representation

Dividing the numerator 79 by denominator 91 produces a repeating decimal (approximately 0.868132, or 86.8132%).

79 ÷ 91 = 0.868132 (86.8132%)

Visual Representation

The diagram below illustrates 6/39 plus 15/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`79/91`
Mixed Number Form	`79/91`
Decimal Form	`0.868132`
Percentage	`86.8132%`

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Frequently Asked Questions

What is 6/39 plus 15/21 as a fraction?

6/39 + 15/21 in simplest fraction form is 79/91.

What is 6/39 plus 15/21 as a decimal?

6/39 + 15/21 converted to a decimal is 0.868132.

What is 6/39 plus 15/21 as a percentage?

6/39 + 15/21 expressed as a percentage is 86.8132%.

Does 6/39 plus 15/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.868132...) because the denominator contains prime factors other than 2 and 5.