What is 18/33 plus 12/21? (Answer: 86/77)

Exact Answer

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Problem: What is 18/33 plus 12/21?
Formula / Expression: 18/33 + 12/21
Final Answer: 1 9/77 (86/77)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 33 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 231 (which is smaller than their product 33 × 21 = 693, keeping the calculation simpler).
Working: LCD(33, 21) = 231

Step 2: Convert to Equivalent Fractions with Common Denominator 231
Multiply the numerator and denominator of 18/33 by 7, and multiply the numerator and denominator of 12/21 by 11 so both fractions share the common base 231.
Working: 18 × 7/33 × 7 = 126/231 and 12 × 11/21 × 11 = 132/231

Step 3: Add the Numerators
Now add the numerators (126 + 132 = 258) and keep the common denominator 231 unchanged.
Working: 126 + 132/231 = 258/231

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 258 and 231, which is 3. Divide both the numerator and denominator by 3.
Working: 258 ÷ 3/231 ÷ 3 = 86/77

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (86) is greater than the denominator (77), divide 86 by 77: it goes in 1 whole time(s) with a remainder of 9, giving the mixed number 1 9/77.
Working: 86/77 = 1 9/77

Step 6: Decimal & Percentage Representation
Dividing the numerator 86 by denominator 77 produces a repeating decimal (approximately 1.116883, or 111.6883%).
Working: 86 ÷ 77 = 1.116883 (111.6883%)

Key Values:
- Simplified Fraction: 86/77
- Mixed Number Form: 1 9/77
- Decimal Value: 1.116883
- Percentage: 111.6883%

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Solved with FractionsCalc:
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18/33 + 12/21 = 86/77

Simplified Fraction

86/77

Mixed Number

1 9/77

Decimal Value

1.116883

Percentage

111.6883%

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Step-by-Step Solution: 18/33 + 12/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 33 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 231 (which is smaller than their product 33 × 21 = 693, keeping the calculation simpler).

LCD(33, 21) = 231

Step 2

Convert to Equivalent Fractions with Common Denominator 231

Multiply the numerator and denominator of 18/33 by 7, and multiply the numerator and denominator of 12/21 by 11 so both fractions share the common base 231.

18 × 7/33 × 7 = 126/231 and 12 × 11/21 × 11 = 132/231

Step 3

Add the Numerators

Now add the numerators (126 + 132 = 258) and keep the common denominator 231 unchanged.

126 + 132/231 = 258/231

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 258 and 231, which is 3. Divide both the numerator and denominator by 3.

258 ÷ 3/231 ÷ 3 = 86/77

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (86) is greater than the denominator (77), divide 86 by 77: it goes in 1 whole time(s) with a remainder of 9, giving the mixed number 1 9/77.

86/77 = 19/77

Step 6

Decimal & Percentage Representation

Dividing the numerator 86 by denominator 77 produces a repeating decimal (approximately 1.116883, or 111.6883%).

86 ÷ 77 = 1.116883 (111.6883%)

Visual Representation

The diagram below illustrates 18/33 plus 12/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`86/77`
Mixed Number Form	`1 9/77`
Decimal Form	`1.116883`
Percentage	`111.6883%`

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Frequently Asked Questions

What is 18/33 plus 12/21 as a fraction?

18/33 + 12/21 in simplest fraction form is 86/77 (or 1 9/77 as a mixed number).

What is 18/33 plus 12/21 as a decimal?

18/33 + 12/21 converted to a decimal is 1.116883.

What is 18/33 plus 12/21 as a percentage?

18/33 + 12/21 expressed as a percentage is 111.6883%.

How do you write 18/33 plus 12/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 86/77 can be written as the mixed number 1 9/77.

Does 18/33 plus 12/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.116883...) because the denominator contains prime factors other than 2 and 5.