What is 9/33 plus 8/21? (Answer: 151/231)

Exact Answer

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Problem: What is 9/33 plus 8/21?
Formula / Expression: 9/33 + 8/21
Final Answer: 151/231
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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 9/33 by 7, and multiply the numerator and denominator of 8/21 by 11 so both fractions share the common base 231.
Working: 9 × 7/33 × 7 = 63/231 and 8 × 11/21 × 11 = 88/231

Step 3: Add the Numerators
Now add the numerators (63 + 88 = 151) and keep the common denominator 231 unchanged.
Working: 63 + 88/231 = 151/231

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 151 and 231 is 1, confirming that 151/231 cannot be reduced further—it is already in its simplest irreducible form.
Working: 151/231

Step 5: Decimal & Percentage Representation
Dividing the numerator 151 by denominator 231 produces a repeating decimal (approximately 0.65368, or 65.368%).
Working: 151 ÷ 231 = 0.65368 (65.368%)

Key Values:
- Simplified Fraction: 151/231
- Mixed Number Form: 151/231
- Decimal Value: 0.65368
- Percentage: 65.368%

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Solved with FractionsCalc:
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9/33 + 8/21 = 151/231

Simplified Fraction

151/231

Mixed Number

Proper (151/231)

Decimal Value

0.65368

Percentage

65.368%

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Step-by-Step Solution: 9/33 + 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 9/33 by 7, and multiply the numerator and denominator of 8/21 by 11 so both fractions share the common base 231.

9 × 7/33 × 7 = 63/231 and 8 × 11/21 × 11 = 88/231

Step 3

Add the Numerators

Now add the numerators (63 + 88 = 151) and keep the common denominator 231 unchanged.

63 + 88/231 = 151/231

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 151 and 231 is 1, confirming that 151/231 cannot be reduced further—it is already in its simplest irreducible form.

151/231

Step 5

Decimal & Percentage Representation

Dividing the numerator 151 by denominator 231 produces a repeating decimal (approximately 0.65368, or 65.368%).

151 ÷ 231 = 0.65368 (65.368%)

Visual Representation

The diagram below illustrates 9/33 plus 8/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`151/231`
Mixed Number Form	`151/231`
Decimal Form	`0.65368`
Percentage	`65.368%`

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Frequently Asked Questions

What is 9/33 plus 8/21 as a fraction?

9/33 + 8/21 in simplest fraction form is 151/231.

What is 9/33 plus 8/21 as a decimal?

9/33 + 8/21 converted to a decimal is 0.65368.

What is 9/33 plus 8/21 as a percentage?

9/33 + 8/21 expressed as a percentage is 65.368%.

Does 9/33 plus 8/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.65368...) because the denominator contains prime factors other than 2 and 5.