What is 9/33 plus 12/21? (Answer: 65/77)

Exact Answer

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Problem: What is 9/33 plus 12/21?
Formula / Expression: 9/33 + 12/21
Final Answer: 65/77
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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 9/33 by 7, and multiply the numerator and denominator of 12/21 by 11 so both fractions share the common base 231.
Working: 9 × 7/33 × 7 = 63/231 and 12 × 11/21 × 11 = 132/231

Step 3: Add the Numerators
Now add the numerators (63 + 132 = 195) and keep the common denominator 231 unchanged.
Working: 63 + 132/231 = 195/231

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 195 and 231, which is 3. Divide both the numerator and denominator by 3.
Working: 195 ÷ 3/231 ÷ 3 = 65/77

Step 5: Decimal & Percentage Representation
Dividing the numerator 65 by denominator 77 produces a repeating decimal (approximately 0.844156, or 84.4156%).
Working: 65 ÷ 77 = 0.844156 (84.4156%)

Key Values:
- Simplified Fraction: 65/77
- Mixed Number Form: 65/77
- Decimal Value: 0.844156
- Percentage: 84.4156%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-9-33-plus-12-21/
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9/33 + 12/21 = 65/77

Simplified Fraction

65/77

Mixed Number

Proper (65/77)

Decimal Value

0.844156

Percentage

84.4156%

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Step-by-Step Solution: 9/33 + 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 9/33 by 7, and multiply the numerator and denominator of 12/21 by 11 so both fractions share the common base 231.

9 × 7/33 × 7 = 63/231 and 12 × 11/21 × 11 = 132/231

Step 3

Add the Numerators

Now add the numerators (63 + 132 = 195) and keep the common denominator 231 unchanged.

63 + 132/231 = 195/231

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 195 and 231, which is 3. Divide both the numerator and denominator by 3.

195 ÷ 3/231 ÷ 3 = 65/77

Step 5

Decimal & Percentage Representation

Dividing the numerator 65 by denominator 77 produces a repeating decimal (approximately 0.844156, or 84.4156%).

65 ÷ 77 = 0.844156 (84.4156%)

Visual Representation

The diagram below illustrates 9/33 plus 12/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`65/77`
Mixed Number Form	`65/77`
Decimal Form	`0.844156`
Percentage	`84.4156%`

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Frequently Asked Questions

What is 9/33 plus 12/21 as a fraction?

9/33 + 12/21 in simplest fraction form is 65/77.

What is 9/33 plus 12/21 as a decimal?

9/33 + 12/21 converted to a decimal is 0.844156.

What is 9/33 plus 12/21 as a percentage?

9/33 + 12/21 expressed as a percentage is 84.4156%.

Does 9/33 plus 12/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.844156...) because the denominator contains prime factors other than 2 and 5.