What is 5/33 plus 8/21? (Answer: 41/77)

Exact Answer

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Problem: What is 5/33 plus 8/21?
Formula / Expression: 5/33 + 8/21
Final Answer: 41/77
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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 8/21 by 11 so both fractions share the common base 231.
Working: 5 × 7/33 × 7 = 35/231 and 8 × 11/21 × 11 = 88/231

Step 3: Add the Numerators
Now add the numerators (35 + 88 = 123) and keep the common denominator 231 unchanged.
Working: 35 + 88/231 = 123/231

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 123 and 231, which is 3. Divide both the numerator and denominator by 3.
Working: 123 ÷ 3/231 ÷ 3 = 41/77

Step 5: Decimal & Percentage Representation
Dividing the numerator 41 by denominator 77 produces a repeating decimal (approximately 0.532468, or 53.2468%).
Working: 41 ÷ 77 = 0.532468 (53.2468%)

Key Values:
- Simplified Fraction: 41/77
- Mixed Number Form: 41/77
- Decimal Value: 0.532468
- Percentage: 53.2468%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-5-33-plus-8-21/
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5/33 + 8/21 = 41/77

Simplified Fraction

41/77

Mixed Number

Proper (41/77)

Decimal Value

0.532468

Percentage

53.2468%

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Step-by-Step Solution: 5/33 + 8/21

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 8/21 by 11 so both fractions share the common base 231.

5 × 7/33 × 7 = 35/231 and 8 × 11/21 × 11 = 88/231

Step 3

Add the Numerators

Now add the numerators (35 + 88 = 123) and keep the common denominator 231 unchanged.

35 + 88/231 = 123/231

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 123 and 231, which is 3. Divide both the numerator and denominator by 3.

123 ÷ 3/231 ÷ 3 = 41/77

Step 5

Decimal & Percentage Representation

Dividing the numerator 41 by denominator 77 produces a repeating decimal (approximately 0.532468, or 53.2468%).

41 ÷ 77 = 0.532468 (53.2468%)

Visual Representation

The diagram below illustrates 5/33 plus 8/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`41/77`
Mixed Number Form	`41/77`
Decimal Form	`0.532468`
Percentage	`53.2468%`

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Frequently Asked Questions

What is 5/33 plus 8/21 as a fraction?

5/33 + 8/21 in simplest fraction form is 41/77.

What is 5/33 plus 8/21 as a decimal?

5/33 + 8/21 converted to a decimal is 0.532468.

What is 5/33 plus 8/21 as a percentage?

5/33 + 8/21 expressed as a percentage is 53.2468%.

Does 5/33 plus 8/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.532468...) because the denominator contains prime factors other than 2 and 5.