What is 15/39 plus 15/21? (Answer: 100/91)

Exact Answer

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Problem: What is 15/39 plus 15/21?
Formula / Expression: 15/39 + 15/21
Final Answer: 1 9/91 (100/91)
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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 15/39 by 7, and multiply the numerator and denominator of 15/21 by 13 so both fractions share the common base 273.
Working: 15 × 7/39 × 7 = 105/273 and 15 × 13/21 × 13 = 195/273

Step 3: Add the Numerators
Now add the numerators (105 + 195 = 300) and keep the common denominator 273 unchanged.
Working: 105 + 195/273 = 300/273

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 300 and 273, which is 3. Divide both the numerator and denominator by 3.
Working: 300 ÷ 3/273 ÷ 3 = 100/91

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (100) is greater than the denominator (91), divide 100 by 91: it goes in 1 whole time(s) with a remainder of 9, giving the mixed number 1 9/91.
Working: 100/91 = 1 9/91

Step 6: Decimal & Percentage Representation
Dividing the numerator 100 by denominator 91 produces a repeating decimal (approximately 1.098901, or 109.8901%).
Working: 100 ÷ 91 = 1.098901 (109.8901%)

Key Values:
- Simplified Fraction: 100/91
- Mixed Number Form: 1 9/91
- Decimal Value: 1.098901
- Percentage: 109.8901%

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15/39 + 15/21 = 100/91

Simplified Fraction

100/91

Mixed Number

1 9/91

Decimal Value

1.098901

Percentage

109.8901%

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

15 × 7/39 × 7 = 105/273 and 15 × 13/21 × 13 = 195/273

Step 3

Add the Numerators

Now add the numerators (105 + 195 = 300) and keep the common denominator 273 unchanged.

105 + 195/273 = 300/273

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 300 and 273, which is 3. Divide both the numerator and denominator by 3.

300 ÷ 3/273 ÷ 3 = 100/91

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (100) is greater than the denominator (91), divide 100 by 91: it goes in 1 whole time(s) with a remainder of 9, giving the mixed number 1 9/91.

100/91 = 19/91

Step 6

Decimal & Percentage Representation

Dividing the numerator 100 by denominator 91 produces a repeating decimal (approximately 1.098901, or 109.8901%).

100 ÷ 91 = 1.098901 (109.8901%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`100/91`
Mixed Number Form	`1 9/91`
Decimal Form	`1.098901`
Percentage	`109.8901%`

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Frequently Asked Questions

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

15/39 + 15/21 in simplest fraction form is 100/91 (or 1 9/91 as a mixed number).

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

15/39 + 15/21 converted to a decimal is 1.098901.

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

15/39 + 15/21 expressed as a percentage is 109.8901%.

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

Because the numerator is greater than the denominator, the improper fraction 100/91 can be written as the mixed number 1 9/91.

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

It results in a repeating decimal (approximately 1.098901...) because the denominator contains prime factors other than 2 and 5.