What is 13/33 plus 9/21? (Answer: 190/231)

Exact Answer

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Problem: What is 13/33 plus 9/21?
Formula / Expression: 13/33 + 9/21
Final Answer: 190/231
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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 13/33 by 7, and multiply the numerator and denominator of 9/21 by 11 so both fractions share the common base 231.
Working: 13 × 7/33 × 7 = 91/231 and 9 × 11/21 × 11 = 99/231

Step 3: Add the Numerators
Now add the numerators (91 + 99 = 190) and keep the common denominator 231 unchanged.
Working: 91 + 99/231 = 190/231

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 190 and 231 is 1, confirming that 190/231 cannot be reduced further—it is already in its simplest irreducible form.
Working: 190/231

Step 5: Decimal & Percentage Representation
Dividing the numerator 190 by denominator 231 produces a repeating decimal (approximately 0.822511, or 82.2511%).
Working: 190 ÷ 231 = 0.822511 (82.2511%)

Key Values:
- Simplified Fraction: 190/231
- Mixed Number Form: 190/231
- Decimal Value: 0.822511
- Percentage: 82.2511%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-13-33-plus-9-21/
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13/33 + 9/21 = 190/231

Simplified Fraction

190/231

Mixed Number

Proper (190/231)

Decimal Value

0.822511

Percentage

82.2511%

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Step-by-Step Solution: 13/33 + 9/21

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 13/33 by 7, and multiply the numerator and denominator of 9/21 by 11 so both fractions share the common base 231.

13 × 7/33 × 7 = 91/231 and 9 × 11/21 × 11 = 99/231

Step 3

Add the Numerators

Now add the numerators (91 + 99 = 190) and keep the common denominator 231 unchanged.

91 + 99/231 = 190/231

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 190 and 231 is 1, confirming that 190/231 cannot be reduced further—it is already in its simplest irreducible form.

190/231

Step 5

Decimal & Percentage Representation

Dividing the numerator 190 by denominator 231 produces a repeating decimal (approximately 0.822511, or 82.2511%).

190 ÷ 231 = 0.822511 (82.2511%)

Visual Representation

The diagram below illustrates 13/33 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`190/231`
Mixed Number Form	`190/231`
Decimal Form	`0.822511`
Percentage	`82.2511%`

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Frequently Asked Questions

What is 13/33 plus 9/21 as a fraction?

13/33 + 9/21 in simplest fraction form is 190/231.

What is 13/33 plus 9/21 as a decimal?

13/33 + 9/21 converted to a decimal is 0.822511.

What is 13/33 plus 9/21 as a percentage?

13/33 + 9/21 expressed as a percentage is 82.2511%.

Does 13/33 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.822511...) because the denominator contains prime factors other than 2 and 5.