What is 27/39 plus 15/21? (Answer: 128/91)

Exact Answer

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Problem: What is 27/39 plus 15/21?
Formula / Expression: 27/39 + 15/21
Final Answer: 1 37/91 (128/91)
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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 27/39 by 7, and multiply the numerator and denominator of 15/21 by 13 so both fractions share the common base 273.
Working: 27 × 7/39 × 7 = 189/273 and 15 × 13/21 × 13 = 195/273

Step 3: Add the Numerators
Now add the numerators (189 + 195 = 384) and keep the common denominator 273 unchanged.
Working: 189 + 195/273 = 384/273

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 384 and 273, which is 3. Divide both the numerator and denominator by 3.
Working: 384 ÷ 3/273 ÷ 3 = 128/91

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (128) is greater than the denominator (91), divide 128 by 91: it goes in 1 whole time(s) with a remainder of 37, giving the mixed number 1 37/91.
Working: 128/91 = 1 37/91

Step 6: Decimal & Percentage Representation
Dividing the numerator 128 by denominator 91 produces a repeating decimal (approximately 1.406593, or 140.6593%).
Working: 128 ÷ 91 = 1.406593 (140.6593%)

Key Values:
- Simplified Fraction: 128/91
- Mixed Number Form: 1 37/91
- Decimal Value: 1.406593
- Percentage: 140.6593%

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27/39 + 15/21 = 128/91

Simplified Fraction

128/91

Mixed Number

1 37/91

Decimal Value

1.406593

Percentage

140.6593%

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Step-by-Step Solution: 27/39 + 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 27/39 by 7, and multiply the numerator and denominator of 15/21 by 13 so both fractions share the common base 273.

27 × 7/39 × 7 = 189/273 and 15 × 13/21 × 13 = 195/273

Step 3

Add the Numerators

Now add the numerators (189 + 195 = 384) and keep the common denominator 273 unchanged.

189 + 195/273 = 384/273

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 384 and 273, which is 3. Divide both the numerator and denominator by 3.

384 ÷ 3/273 ÷ 3 = 128/91

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (128) is greater than the denominator (91), divide 128 by 91: it goes in 1 whole time(s) with a remainder of 37, giving the mixed number 1 37/91.

128/91 = 137/91

Step 6

Decimal & Percentage Representation

Dividing the numerator 128 by denominator 91 produces a repeating decimal (approximately 1.406593, or 140.6593%).

128 ÷ 91 = 1.406593 (140.6593%)

Visual Representation

The diagram below illustrates 27/39 plus 15/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`128/91`
Mixed Number Form	`1 37/91`
Decimal Form	`1.406593`
Percentage	`140.6593%`

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Frequently Asked Questions

What is 27/39 plus 15/21 as a fraction?

27/39 + 15/21 in simplest fraction form is 128/91 (or 1 37/91 as a mixed number).

What is 27/39 plus 15/21 as a decimal?

27/39 + 15/21 converted to a decimal is 1.406593.

What is 27/39 plus 15/21 as a percentage?

27/39 + 15/21 expressed as a percentage is 140.6593%.

How do you write 27/39 plus 15/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 128/91 can be written as the mixed number 1 37/91.

Does 27/39 plus 15/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.406593...) because the denominator contains prime factors other than 2 and 5.