What is 18/39 plus 15/21? (Answer: 107/91)

Exact Answer

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Problem: What is 18/39 plus 15/21?
Formula / Expression: 18/39 + 15/21
Final Answer: 1 16/91 (107/91)
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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 18/39 by 7, and multiply the numerator and denominator of 15/21 by 13 so both fractions share the common base 273.
Working: 18 × 7/39 × 7 = 126/273 and 15 × 13/21 × 13 = 195/273

Step 3: Add the Numerators
Now add the numerators (126 + 195 = 321) and keep the common denominator 273 unchanged.
Working: 126 + 195/273 = 321/273

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 321 and 273, which is 3. Divide both the numerator and denominator by 3.
Working: 321 ÷ 3/273 ÷ 3 = 107/91

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (107) is greater than the denominator (91), divide 107 by 91: it goes in 1 whole time(s) with a remainder of 16, giving the mixed number 1 16/91.
Working: 107/91 = 1 16/91

Step 6: Decimal & Percentage Representation
Dividing the numerator 107 by denominator 91 produces a repeating decimal (approximately 1.175824, or 117.5824%).
Working: 107 ÷ 91 = 1.175824 (117.5824%)

Key Values:
- Simplified Fraction: 107/91
- Mixed Number Form: 1 16/91
- Decimal Value: 1.175824
- Percentage: 117.5824%

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18/39 + 15/21 = 107/91

Simplified Fraction

107/91

Mixed Number

1 16/91

Decimal Value

1.175824

Percentage

117.5824%

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Step-by-Step Solution: 18/39 + 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 18/39 by 7, and multiply the numerator and denominator of 15/21 by 13 so both fractions share the common base 273.

18 × 7/39 × 7 = 126/273 and 15 × 13/21 × 13 = 195/273

Step 3

Add the Numerators

Now add the numerators (126 + 195 = 321) and keep the common denominator 273 unchanged.

126 + 195/273 = 321/273

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 321 and 273, which is 3. Divide both the numerator and denominator by 3.

321 ÷ 3/273 ÷ 3 = 107/91

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (107) is greater than the denominator (91), divide 107 by 91: it goes in 1 whole time(s) with a remainder of 16, giving the mixed number 1 16/91.

107/91 = 116/91

Step 6

Decimal & Percentage Representation

Dividing the numerator 107 by denominator 91 produces a repeating decimal (approximately 1.175824, or 117.5824%).

107 ÷ 91 = 1.175824 (117.5824%)

Visual Representation

The diagram below illustrates 18/39 plus 15/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`107/91`
Mixed Number Form	`1 16/91`
Decimal Form	`1.175824`
Percentage	`117.5824%`

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Frequently Asked Questions

What is 18/39 plus 15/21 as a fraction?

18/39 + 15/21 in simplest fraction form is 107/91 (or 1 16/91 as a mixed number).

What is 18/39 plus 15/21 as a decimal?

18/39 + 15/21 converted to a decimal is 1.175824.

What is 18/39 plus 15/21 as a percentage?

18/39 + 15/21 expressed as a percentage is 117.5824%.

How do you write 18/39 plus 15/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 107/91 can be written as the mixed number 1 16/91.

Does 18/39 plus 15/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.175824...) because the denominator contains prime factors other than 2 and 5.