What is 5/33 plus 4/21? (Answer: 79/231)

Exact Answer

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Problem: What is 5/33 plus 4/21?
Formula / Expression: 5/33 + 4/21
Final Answer: 79/231
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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 5/33 by 7, and multiply the numerator and denominator of 4/21 by 11 so both fractions share the common base 231.
Working: 5 × 7/33 × 7 = 35/231 and 4 × 11/21 × 11 = 44/231

Step 3: Add the Numerators
Now add the numerators (35 + 44 = 79) and keep the common denominator 231 unchanged.
Working: 35 + 44/231 = 79/231

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 79 and 231 is 1, confirming that 79/231 cannot be reduced further—it is already in its simplest irreducible form.
Working: 79/231

Step 5: Decimal & Percentage Representation
Dividing the numerator 79 by denominator 231 produces a repeating decimal (approximately 0.341991, or 34.1991%).
Working: 79 ÷ 231 = 0.341991 (34.1991%)

Key Values:
- Simplified Fraction: 79/231
- Mixed Number Form: 79/231
- Decimal Value: 0.341991
- Percentage: 34.1991%

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5/33 + 4/21 = 79/231

Simplified Fraction

79/231

Mixed Number

Proper (79/231)

Decimal Value

0.341991

Percentage

34.1991%

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Step-by-Step Solution: 5/33 + 4/21

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 4/21 by 11 so both fractions share the common base 231.

5 × 7/33 × 7 = 35/231 and 4 × 11/21 × 11 = 44/231

Step 3

Add the Numerators

Now add the numerators (35 + 44 = 79) and keep the common denominator 231 unchanged.

35 + 44/231 = 79/231

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 79 and 231 is 1, confirming that 79/231 cannot be reduced further—it is already in its simplest irreducible form.

79/231

Step 5

Decimal & Percentage Representation

Dividing the numerator 79 by denominator 231 produces a repeating decimal (approximately 0.341991, or 34.1991%).

79 ÷ 231 = 0.341991 (34.1991%)

Visual Representation

The diagram below illustrates 5/33 plus 4/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`79/231`
Mixed Number Form	`79/231`
Decimal Form	`0.341991`
Percentage	`34.1991%`

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Frequently Asked Questions

What is 5/33 plus 4/21 as a fraction?

5/33 + 4/21 in simplest fraction form is 79/231.

What is 5/33 plus 4/21 as a decimal?

5/33 + 4/21 converted to a decimal is 0.341991.

What is 5/33 plus 4/21 as a percentage?

5/33 + 4/21 expressed as a percentage is 34.1991%.

Does 5/33 plus 4/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.341991...) because the denominator contains prime factors other than 2 and 5.