What is 15/21 plus 13/18? (Answer: 181/126)

Exact Answer

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Problem: What is 15/21 plus 13/18?
Formula / Expression: 15/21 + 13/18
Final Answer: 1 55/126 (181/126)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 21 and 18 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 126 (which is smaller than their product 21 × 18 = 378, keeping the calculation simpler).
Working: LCD(21, 18) = 126

Step 2: Convert to Equivalent Fractions with Common Denominator 126
Multiply the numerator and denominator of 15/21 by 6, and multiply the numerator and denominator of 13/18 by 7 so both fractions share the common base 126.
Working: 15 × 6/21 × 6 = 90/126 and 13 × 7/18 × 7 = 91/126

Step 3: Add the Numerators
Now add the numerators (90 + 91 = 181) and keep the common denominator 126 unchanged.
Working: 90 + 91/126 = 181/126

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 181 and 126 is 1, confirming that 181/126 cannot be reduced further—it is already in its simplest irreducible form.
Working: 181/126

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (181) is greater than the denominator (126), divide 181 by 126: it goes in 1 whole time(s) with a remainder of 55, giving the mixed number 1 55/126.
Working: 181/126 = 1 55/126

Step 6: Decimal & Percentage Representation
Dividing the numerator 181 by denominator 126 produces a repeating decimal (approximately 1.436508, or 143.6508%).
Working: 181 ÷ 126 = 1.436508 (143.6508%)

Key Values:
- Simplified Fraction: 181/126
- Mixed Number Form: 1 55/126
- Decimal Value: 1.436508
- Percentage: 143.6508%

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Solved with FractionsCalc:
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15/21 + 13/18 = 181/126

Simplified Fraction

181/126

Mixed Number

1 55/126

Decimal Value

1.436508

Percentage

143.6508%

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Step-by-Step Solution: 15/21 + 13/18

Step 1

Find the Least Common Denominator (LCD)

The denominators 21 and 18 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 126 (which is smaller than their product 21 × 18 = 378, keeping the calculation simpler).

LCD(21, 18) = 126

Step 2

Convert to Equivalent Fractions with Common Denominator 126

Multiply the numerator and denominator of 15/21 by 6, and multiply the numerator and denominator of 13/18 by 7 so both fractions share the common base 126.

15 × 6/21 × 6 = 90/126 and 13 × 7/18 × 7 = 91/126

Step 3

Add the Numerators

Now add the numerators (90 + 91 = 181) and keep the common denominator 126 unchanged.

90 + 91/126 = 181/126

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 181 and 126 is 1, confirming that 181/126 cannot be reduced further—it is already in its simplest irreducible form.

181/126

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (181) is greater than the denominator (126), divide 181 by 126: it goes in 1 whole time(s) with a remainder of 55, giving the mixed number 1 55/126.

181/126 = 155/126

Step 6

Decimal & Percentage Representation

Dividing the numerator 181 by denominator 126 produces a repeating decimal (approximately 1.436508, or 143.6508%).

181 ÷ 126 = 1.436508 (143.6508%)

Visual Representation

The diagram below illustrates 15/21 plus 13/18 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`181/126`
Mixed Number Form	`1 55/126`
Decimal Form	`1.436508`
Percentage	`143.6508%`

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Frequently Asked Questions

What is 15/21 plus 13/18 as a fraction?

15/21 + 13/18 in simplest fraction form is 181/126 (or 1 55/126 as a mixed number).

What is 15/21 plus 13/18 as a decimal?

15/21 + 13/18 converted to a decimal is 1.436508.

What is 15/21 plus 13/18 as a percentage?

15/21 + 13/18 expressed as a percentage is 143.6508%.

How do you write 15/21 plus 13/18 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 181/126 can be written as the mixed number 1 55/126.

Does 15/21 plus 13/18 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.436508...) because the denominator contains prime factors other than 2 and 5.