What is 8/21 plus 13/33? (Answer: 179/231)

Exact Answer

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Problem: What is 8/21 plus 13/33?
Formula / Expression: 8/21 + 13/33
Final Answer: 179/231
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 231
Multiply the numerator and denominator of 8/21 by 11, and multiply the numerator and denominator of 13/33 by 7 so both fractions share the common base 231.
Working: 8 × 11/21 × 11 = 88/231 and 13 × 7/33 × 7 = 91/231

Step 3: Add the Numerators
Now add the numerators (88 + 91 = 179) and keep the common denominator 231 unchanged.
Working: 88 + 91/231 = 179/231

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 179 and 231 is 1, confirming that 179/231 cannot be reduced further—it is already in its simplest irreducible form.
Working: 179/231

Step 5: Decimal & Percentage Representation
Dividing the numerator 179 by denominator 231 produces a repeating decimal (approximately 0.774892, or 77.4892%).
Working: 179 ÷ 231 = 0.774892 (77.4892%)

Key Values:
- Simplified Fraction: 179/231
- Mixed Number Form: 179/231
- Decimal Value: 0.774892
- Percentage: 77.4892%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-8-21-plus-13-33/
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8/21 + 13/33 = 179/231

Simplified Fraction

179/231

Mixed Number

Proper (179/231)

Decimal Value

0.774892

Percentage

77.4892%

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Step-by-Step Solution: 8/21 + 13/33

Step 1

Find the Least Common Denominator (LCD)

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

LCD(21, 33) = 231

Step 2

Convert to Equivalent Fractions with Common Denominator 231

Multiply the numerator and denominator of 8/21 by 11, and multiply the numerator and denominator of 13/33 by 7 so both fractions share the common base 231.

8 × 11/21 × 11 = 88/231 and 13 × 7/33 × 7 = 91/231

Step 3

Add the Numerators

Now add the numerators (88 + 91 = 179) and keep the common denominator 231 unchanged.

88 + 91/231 = 179/231

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 179 and 231 is 1, confirming that 179/231 cannot be reduced further—it is already in its simplest irreducible form.

179/231

Step 5

Decimal & Percentage Representation

Dividing the numerator 179 by denominator 231 produces a repeating decimal (approximately 0.774892, or 77.4892%).

179 ÷ 231 = 0.774892 (77.4892%)

Visual Representation

The diagram below illustrates 8/21 plus 13/33 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`179/231`
Mixed Number Form	`179/231`
Decimal Form	`0.774892`
Percentage	`77.4892%`

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Frequently Asked Questions

What is 8/21 plus 13/33 as a fraction?

8/21 + 13/33 in simplest fraction form is 179/231.

What is 8/21 plus 13/33 as a decimal?

8/21 + 13/33 converted to a decimal is 0.774892.

What is 8/21 plus 13/33 as a percentage?

8/21 + 13/33 expressed as a percentage is 77.4892%.

Does 8/21 plus 13/33 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.774892...) because the denominator contains prime factors other than 2 and 5.