What is 23/39 plus 15/21? (Answer: 356/273)

Exact Answer

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Problem: What is 23/39 plus 15/21?
Formula / Expression: 23/39 + 15/21
Final Answer: 1 83/273 (356/273)
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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 23/39 by 7, and multiply the numerator and denominator of 15/21 by 13 so both fractions share the common base 273.
Working: 23 × 7/39 × 7 = 161/273 and 15 × 13/21 × 13 = 195/273

Step 3: Add the Numerators
Now add the numerators (161 + 195 = 356) and keep the common denominator 273 unchanged.
Working: 161 + 195/273 = 356/273

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 356 and 273 is 1, confirming that 356/273 cannot be reduced further—it is already in its simplest irreducible form.
Working: 356/273

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (356) is greater than the denominator (273), divide 356 by 273: it goes in 1 whole time(s) with a remainder of 83, giving the mixed number 1 83/273.
Working: 356/273 = 1 83/273

Step 6: Decimal & Percentage Representation
Dividing the numerator 356 by denominator 273 produces a repeating decimal (approximately 1.304029, or 130.4029%).
Working: 356 ÷ 273 = 1.304029 (130.4029%)

Key Values:
- Simplified Fraction: 356/273
- Mixed Number Form: 1 83/273
- Decimal Value: 1.304029
- Percentage: 130.4029%

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23/39 + 15/21 = 356/273

Simplified Fraction

356/273

Mixed Number

1 83/273

Decimal Value

1.304029

Percentage

130.4029%

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Step-by-Step Solution: 23/39 + 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 23/39 by 7, and multiply the numerator and denominator of 15/21 by 13 so both fractions share the common base 273.

23 × 7/39 × 7 = 161/273 and 15 × 13/21 × 13 = 195/273

Step 3

Add the Numerators

Now add the numerators (161 + 195 = 356) and keep the common denominator 273 unchanged.

161 + 195/273 = 356/273

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 356 and 273 is 1, confirming that 356/273 cannot be reduced further—it is already in its simplest irreducible form.

356/273

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (356) is greater than the denominator (273), divide 356 by 273: it goes in 1 whole time(s) with a remainder of 83, giving the mixed number 1 83/273.

356/273 = 183/273

Step 6

Decimal & Percentage Representation

Dividing the numerator 356 by denominator 273 produces a repeating decimal (approximately 1.304029, or 130.4029%).

356 ÷ 273 = 1.304029 (130.4029%)

Visual Representation

The diagram below illustrates 23/39 plus 15/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`356/273`
Mixed Number Form	`1 83/273`
Decimal Form	`1.304029`
Percentage	`130.4029%`

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Frequently Asked Questions

What is 23/39 plus 15/21 as a fraction?

23/39 + 15/21 in simplest fraction form is 356/273 (or 1 83/273 as a mixed number).

What is 23/39 plus 15/21 as a decimal?

23/39 + 15/21 converted to a decimal is 1.304029.

What is 23/39 plus 15/21 as a percentage?

23/39 + 15/21 expressed as a percentage is 130.4029%.

How do you write 23/39 plus 15/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 356/273 can be written as the mixed number 1 83/273.

Does 23/39 plus 15/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.304029...) because the denominator contains prime factors other than 2 and 5.