What is 13/33 plus 15/21? (Answer: 256/231)

Exact Answer

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Problem: What is 13/33 plus 15/21?
Formula / Expression: 13/33 + 15/21
Final Answer: 1 25/231 (256/231)
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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 15/21 by 11 so both fractions share the common base 231.
Working: 13 × 7/33 × 7 = 91/231 and 15 × 11/21 × 11 = 165/231

Step 3: Add the Numerators
Now add the numerators (91 + 165 = 256) and keep the common denominator 231 unchanged.
Working: 91 + 165/231 = 256/231

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 256 and 231 is 1, confirming that 256/231 cannot be reduced further—it is already in its simplest irreducible form.
Working: 256/231

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (256) is greater than the denominator (231), divide 256 by 231: it goes in 1 whole time(s) with a remainder of 25, giving the mixed number 1 25/231.
Working: 256/231 = 1 25/231

Step 6: Decimal & Percentage Representation
Dividing the numerator 256 by denominator 231 produces a repeating decimal (approximately 1.108225, or 110.8225%).
Working: 256 ÷ 231 = 1.108225 (110.8225%)

Key Values:
- Simplified Fraction: 256/231
- Mixed Number Form: 1 25/231
- Decimal Value: 1.108225
- Percentage: 110.8225%

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Solved with FractionsCalc:
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13/33 + 15/21 = 256/231

Simplified Fraction

256/231

Mixed Number

1 25/231

Decimal Value

1.108225

Percentage

110.8225%

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Step-by-Step Solution: 13/33 + 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 13/33 by 7, and multiply the numerator and denominator of 15/21 by 11 so both fractions share the common base 231.

13 × 7/33 × 7 = 91/231 and 15 × 11/21 × 11 = 165/231

Step 3

Add the Numerators

Now add the numerators (91 + 165 = 256) and keep the common denominator 231 unchanged.

91 + 165/231 = 256/231

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 256 and 231 is 1, confirming that 256/231 cannot be reduced further—it is already in its simplest irreducible form.

256/231

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (256) is greater than the denominator (231), divide 256 by 231: it goes in 1 whole time(s) with a remainder of 25, giving the mixed number 1 25/231.

256/231 = 125/231

Step 6

Decimal & Percentage Representation

Dividing the numerator 256 by denominator 231 produces a repeating decimal (approximately 1.108225, or 110.8225%).

256 ÷ 231 = 1.108225 (110.8225%)

Visual Representation

The diagram below illustrates 13/33 plus 15/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`256/231`
Mixed Number Form	`1 25/231`
Decimal Form	`1.108225`
Percentage	`110.8225%`

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Frequently Asked Questions

What is 13/33 plus 15/21 as a fraction?

13/33 + 15/21 in simplest fraction form is 256/231 (or 1 25/231 as a mixed number).

What is 13/33 plus 15/21 as a decimal?

13/33 + 15/21 converted to a decimal is 1.108225.

What is 13/33 plus 15/21 as a percentage?

13/33 + 15/21 expressed as a percentage is 110.8225%.

How do you write 13/33 plus 15/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 256/231 can be written as the mixed number 1 25/231.

Does 13/33 plus 15/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.108225...) because the denominator contains prime factors other than 2 and 5.