What is 12/33 plus 15/21? (Answer: 83/77)

Exact Answer

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Problem: What is 12/33 plus 15/21?
Formula / Expression: 12/33 + 15/21
Final Answer: 1 6/77 (83/77)
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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 12/33 by 7, and multiply the numerator and denominator of 15/21 by 11 so both fractions share the common base 231.
Working: 12 × 7/33 × 7 = 84/231 and 15 × 11/21 × 11 = 165/231

Step 3: Add the Numerators
Now add the numerators (84 + 165 = 249) and keep the common denominator 231 unchanged.
Working: 84 + 165/231 = 249/231

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 249 and 231, which is 3. Divide both the numerator and denominator by 3.
Working: 249 ÷ 3/231 ÷ 3 = 83/77

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (83) is greater than the denominator (77), divide 83 by 77: it goes in 1 whole time(s) with a remainder of 6, giving the mixed number 1 6/77.
Working: 83/77 = 1 6/77

Step 6: Decimal & Percentage Representation
Dividing the numerator 83 by denominator 77 produces a repeating decimal (approximately 1.077922, or 107.7922%).
Working: 83 ÷ 77 = 1.077922 (107.7922%)

Key Values:
- Simplified Fraction: 83/77
- Mixed Number Form: 1 6/77
- Decimal Value: 1.077922
- Percentage: 107.7922%

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Solved with FractionsCalc:
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12/33 + 15/21 = 83/77

Simplified Fraction

83/77

Mixed Number

1 6/77

Decimal Value

1.077922

Percentage

107.7922%

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Step-by-Step Solution: 12/33 + 15/21

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 12/33 by 7, and multiply the numerator and denominator of 15/21 by 11 so both fractions share the common base 231.

12 × 7/33 × 7 = 84/231 and 15 × 11/21 × 11 = 165/231

Step 3

Add the Numerators

Now add the numerators (84 + 165 = 249) and keep the common denominator 231 unchanged.

84 + 165/231 = 249/231

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 249 and 231, which is 3. Divide both the numerator and denominator by 3.

249 ÷ 3/231 ÷ 3 = 83/77

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (83) is greater than the denominator (77), divide 83 by 77: it goes in 1 whole time(s) with a remainder of 6, giving the mixed number 1 6/77.

83/77 = 16/77

Step 6

Decimal & Percentage Representation

Dividing the numerator 83 by denominator 77 produces a repeating decimal (approximately 1.077922, or 107.7922%).

83 ÷ 77 = 1.077922 (107.7922%)

Visual Representation

The diagram below illustrates 12/33 plus 15/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`83/77`
Mixed Number Form	`1 6/77`
Decimal Form	`1.077922`
Percentage	`107.7922%`

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Frequently Asked Questions

What is 12/33 plus 15/21 as a fraction?

12/33 + 15/21 in simplest fraction form is 83/77 (or 1 6/77 as a mixed number).

What is 12/33 plus 15/21 as a decimal?

12/33 + 15/21 converted to a decimal is 1.077922.

What is 12/33 plus 15/21 as a percentage?

12/33 + 15/21 expressed as a percentage is 107.7922%.

How do you write 12/33 plus 15/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 83/77 can be written as the mixed number 1 6/77.

Does 12/33 plus 15/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.077922...) because the denominator contains prime factors other than 2 and 5.