What is 5/33 plus 11/21? (Answer: 52/77)

Exact Answer

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Problem: What is 5/33 plus 11/21?
Formula / Expression: 5/33 + 11/21
Final Answer: 52/77
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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 5/33 by 7, and multiply the numerator and denominator of 11/21 by 11 so both fractions share the common base 231.
Working: 5 × 7/33 × 7 = 35/231 and 11 × 11/21 × 11 = 121/231

Step 3: Add the Numerators
Now add the numerators (35 + 121 = 156) and keep the common denominator 231 unchanged.
Working: 35 + 121/231 = 156/231

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 156 and 231, which is 3. Divide both the numerator and denominator by 3.
Working: 156 ÷ 3/231 ÷ 3 = 52/77

Step 5: Decimal & Percentage Representation
Dividing the numerator 52 by denominator 77 produces a repeating decimal (approximately 0.675325, or 67.5325%).
Working: 52 ÷ 77 = 0.675325 (67.5325%)

Key Values:
- Simplified Fraction: 52/77
- Mixed Number Form: 52/77
- Decimal Value: 0.675325
- Percentage: 67.5325%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-5-33-plus-11-21/
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5/33 + 11/21 = 52/77

Simplified Fraction

52/77

Mixed Number

Proper (52/77)

Decimal Value

0.675325

Percentage

67.5325%

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Step-by-Step Solution: 5/33 + 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 5/33 by 7, and multiply the numerator and denominator of 11/21 by 11 so both fractions share the common base 231.

5 × 7/33 × 7 = 35/231 and 11 × 11/21 × 11 = 121/231

Step 3

Add the Numerators

Now add the numerators (35 + 121 = 156) and keep the common denominator 231 unchanged.

35 + 121/231 = 156/231

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 156 and 231, which is 3. Divide both the numerator and denominator by 3.

156 ÷ 3/231 ÷ 3 = 52/77

Step 5

Decimal & Percentage Representation

Dividing the numerator 52 by denominator 77 produces a repeating decimal (approximately 0.675325, or 67.5325%).

52 ÷ 77 = 0.675325 (67.5325%)

Visual Representation

The diagram below illustrates 5/33 plus 11/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`52/77`
Mixed Number Form	`52/77`
Decimal Form	`0.675325`
Percentage	`67.5325%`

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Frequently Asked Questions

What is 5/33 plus 11/21 as a fraction?

5/33 + 11/21 in simplest fraction form is 52/77.

What is 5/33 plus 11/21 as a decimal?

5/33 + 11/21 converted to a decimal is 0.675325.

What is 5/33 plus 11/21 as a percentage?

5/33 + 11/21 expressed as a percentage is 67.5325%.

Does 5/33 plus 11/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.675325...) because the denominator contains prime factors other than 2 and 5.