What is 11/18 plus 15/21? (Answer: 167/126)

Exact Answer

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Problem: What is 11/18 plus 15/21?
Formula / Expression: 11/18 + 15/21
Final Answer: 1 41/126 (167/126)
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 126
Multiply the numerator and denominator of 11/18 by 7, and multiply the numerator and denominator of 15/21 by 6 so both fractions share the common base 126.
Working: 11 × 7/18 × 7 = 77/126 and 15 × 6/21 × 6 = 90/126

Step 3: Add the Numerators
Now add the numerators (77 + 90 = 167) and keep the common denominator 126 unchanged.
Working: 77 + 90/126 = 167/126

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 167 and 126 is 1, confirming that 167/126 cannot be reduced further—it is already in its simplest irreducible form.
Working: 167/126

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (167) is greater than the denominator (126), divide 167 by 126: it goes in 1 whole time(s) with a remainder of 41, giving the mixed number 1 41/126.
Working: 167/126 = 1 41/126

Step 6: Decimal & Percentage Representation
Dividing the numerator 167 by denominator 126 produces a repeating decimal (approximately 1.325397, or 132.5397%).
Working: 167 ÷ 126 = 1.325397 (132.5397%)

Key Values:
- Simplified Fraction: 167/126
- Mixed Number Form: 1 41/126
- Decimal Value: 1.325397
- Percentage: 132.5397%

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11/18 + 15/21 = 167/126

Simplified Fraction

167/126

Mixed Number

1 41/126

Decimal Value

1.325397

Percentage

132.5397%

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Step-by-Step Solution: 11/18 + 15/21

Step 1

Find the Least Common Denominator (LCD)

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

LCD(18, 21) = 126

Step 2

Convert to Equivalent Fractions with Common Denominator 126

Multiply the numerator and denominator of 11/18 by 7, and multiply the numerator and denominator of 15/21 by 6 so both fractions share the common base 126.

11 × 7/18 × 7 = 77/126 and 15 × 6/21 × 6 = 90/126

Step 3

Add the Numerators

Now add the numerators (77 + 90 = 167) and keep the common denominator 126 unchanged.

77 + 90/126 = 167/126

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 167 and 126 is 1, confirming that 167/126 cannot be reduced further—it is already in its simplest irreducible form.

167/126

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (167) is greater than the denominator (126), divide 167 by 126: it goes in 1 whole time(s) with a remainder of 41, giving the mixed number 1 41/126.

167/126 = 141/126

Step 6

Decimal & Percentage Representation

Dividing the numerator 167 by denominator 126 produces a repeating decimal (approximately 1.325397, or 132.5397%).

167 ÷ 126 = 1.325397 (132.5397%)

Visual Representation

The diagram below illustrates 11/18 plus 15/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`167/126`
Mixed Number Form	`1 41/126`
Decimal Form	`1.325397`
Percentage	`132.5397%`

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Frequently Asked Questions

What is 11/18 plus 15/21 as a fraction?

11/18 + 15/21 in simplest fraction form is 167/126 (or 1 41/126 as a mixed number).

What is 11/18 plus 15/21 as a decimal?

11/18 + 15/21 converted to a decimal is 1.325397.

What is 11/18 plus 15/21 as a percentage?

11/18 + 15/21 expressed as a percentage is 132.5397%.

How do you write 11/18 plus 15/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 167/126 can be written as the mixed number 1 41/126.

Does 11/18 plus 15/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.325397...) because the denominator contains prime factors other than 2 and 5.