What is 1/33 plus 3/21? (Answer: 40/231)

Exact Answer

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Problem: What is 1/33 plus 3/21?
Formula / Expression: 1/33 + 3/21
Final Answer: 40/231
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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 1/33 by 7, and multiply the numerator and denominator of 3/21 by 11 so both fractions share the common base 231.
Working: 1 × 7/33 × 7 = 7/231 and 3 × 11/21 × 11 = 33/231

Step 3: Add the Numerators
Now add the numerators (7 + 33 = 40) and keep the common denominator 231 unchanged.
Working: 7 + 33/231 = 40/231

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 40 and 231 is 1, confirming that 40/231 cannot be reduced further—it is already in its simplest irreducible form.
Working: 40/231

Step 5: Decimal & Percentage Representation
Dividing the numerator 40 by denominator 231 produces a repeating decimal (approximately 0.17316, or 17.316%).
Working: 40 ÷ 231 = 0.17316 (17.316%)

Key Values:
- Simplified Fraction: 40/231
- Mixed Number Form: 40/231
- Decimal Value: 0.17316
- Percentage: 17.316%

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1/33 + 3/21 = 40/231

Simplified Fraction

40/231

Mixed Number

Proper (40/231)

Decimal Value

0.17316

Percentage

17.316%

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Step-by-Step Solution: 1/33 + 3/21

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 1/33 by 7, and multiply the numerator and denominator of 3/21 by 11 so both fractions share the common base 231.

1 × 7/33 × 7 = 7/231 and 3 × 11/21 × 11 = 33/231

Step 3

Add the Numerators

Now add the numerators (7 + 33 = 40) and keep the common denominator 231 unchanged.

7 + 33/231 = 40/231

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 40 and 231 is 1, confirming that 40/231 cannot be reduced further—it is already in its simplest irreducible form.

40/231

Step 5

Decimal & Percentage Representation

Dividing the numerator 40 by denominator 231 produces a repeating decimal (approximately 0.17316, or 17.316%).

40 ÷ 231 = 0.17316 (17.316%)

Visual Representation

The diagram below illustrates 1/33 plus 3/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`40/231`
Mixed Number Form	`40/231`
Decimal Form	`0.17316`
Percentage	`17.316%`

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Frequently Asked Questions

What is 1/33 plus 3/21 as a fraction?

1/33 + 3/21 in simplest fraction form is 40/231.

What is 1/33 plus 3/21 as a decimal?

1/33 + 3/21 converted to a decimal is 0.17316.

What is 1/33 plus 3/21 as a percentage?

1/33 + 3/21 expressed as a percentage is 17.316%.

Does 1/33 plus 3/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.17316...) because the denominator contains prime factors other than 2 and 5.