What is 8/33 plus 11/21? (Answer: 59/77)

Exact Answer

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Problem: What is 8/33 plus 11/21?
Formula / Expression: 8/33 + 11/21
Final Answer: 59/77
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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 8/33 by 7, and multiply the numerator and denominator of 11/21 by 11 so both fractions share the common base 231.
Working: 8 × 7/33 × 7 = 56/231 and 11 × 11/21 × 11 = 121/231

Step 3: Add the Numerators
Now add the numerators (56 + 121 = 177) and keep the common denominator 231 unchanged.
Working: 56 + 121/231 = 177/231

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 177 and 231, which is 3. Divide both the numerator and denominator by 3.
Working: 177 ÷ 3/231 ÷ 3 = 59/77

Step 5: Decimal & Percentage Representation
Dividing the numerator 59 by denominator 77 produces a repeating decimal (approximately 0.766234, or 76.6234%).
Working: 59 ÷ 77 = 0.766234 (76.6234%)

Key Values:
- Simplified Fraction: 59/77
- Mixed Number Form: 59/77
- Decimal Value: 0.766234
- Percentage: 76.6234%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-8-33-plus-11-21/
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8/33 + 11/21 = 59/77

Simplified Fraction

59/77

Mixed Number

Proper (59/77)

Decimal Value

0.766234

Percentage

76.6234%

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Step-by-Step Solution: 8/33 + 11/21

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

8 × 7/33 × 7 = 56/231 and 11 × 11/21 × 11 = 121/231

Step 3

Add the Numerators

Now add the numerators (56 + 121 = 177) and keep the common denominator 231 unchanged.

56 + 121/231 = 177/231

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 177 and 231, which is 3. Divide both the numerator and denominator by 3.

177 ÷ 3/231 ÷ 3 = 59/77

Step 5

Decimal & Percentage Representation

Dividing the numerator 59 by denominator 77 produces a repeating decimal (approximately 0.766234, or 76.6234%).

59 ÷ 77 = 0.766234 (76.6234%)

Visual Representation

The diagram below illustrates 8/33 plus 11/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`59/77`
Mixed Number Form	`59/77`
Decimal Form	`0.766234`
Percentage	`76.6234%`

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Frequently Asked Questions

What is 8/33 plus 11/21 as a fraction?

8/33 + 11/21 in simplest fraction form is 59/77.

What is 8/33 plus 11/21 as a decimal?

8/33 + 11/21 converted to a decimal is 0.766234.

What is 8/33 plus 11/21 as a percentage?

8/33 + 11/21 expressed as a percentage is 76.6234%.

Does 8/33 plus 11/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.766234...) because the denominator contains prime factors other than 2 and 5.