What is 3/33 plus 9/21? (Answer: 40/77)

Exact Answer

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Problem: What is 3/33 plus 9/21?
Formula / Expression: 3/33 + 9/21
Final Answer: 40/77
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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 3/33 by 7, and multiply the numerator and denominator of 9/21 by 11 so both fractions share the common base 231.
Working: 3 × 7/33 × 7 = 21/231 and 9 × 11/21 × 11 = 99/231

Step 3: Add the Numerators
Now add the numerators (21 + 99 = 120) and keep the common denominator 231 unchanged.
Working: 21 + 99/231 = 120/231

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 120 and 231, which is 3. Divide both the numerator and denominator by 3.
Working: 120 ÷ 3/231 ÷ 3 = 40/77

Step 5: Decimal & Percentage Representation
Dividing the numerator 40 by denominator 77 produces a repeating decimal (approximately 0.519481, or 51.9481%).
Working: 40 ÷ 77 = 0.519481 (51.9481%)

Key Values:
- Simplified Fraction: 40/77
- Mixed Number Form: 40/77
- Decimal Value: 0.519481
- Percentage: 51.9481%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-33-plus-9-21/
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3/33 + 9/21 = 40/77

Simplified Fraction

40/77

Mixed Number

Proper (40/77)

Decimal Value

0.519481

Percentage

51.9481%

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Step-by-Step Solution: 3/33 + 9/21

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 3/33 by 7, and multiply the numerator and denominator of 9/21 by 11 so both fractions share the common base 231.

3 × 7/33 × 7 = 21/231 and 9 × 11/21 × 11 = 99/231

Step 3

Add the Numerators

Now add the numerators (21 + 99 = 120) and keep the common denominator 231 unchanged.

21 + 99/231 = 120/231

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 120 and 231, which is 3. Divide both the numerator and denominator by 3.

120 ÷ 3/231 ÷ 3 = 40/77

Step 5

Decimal & Percentage Representation

Dividing the numerator 40 by denominator 77 produces a repeating decimal (approximately 0.519481, or 51.9481%).

40 ÷ 77 = 0.519481 (51.9481%)

Visual Representation

The diagram below illustrates 3/33 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`40/77`
Mixed Number Form	`40/77`
Decimal Form	`0.519481`
Percentage	`51.9481%`

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Frequently Asked Questions

What is 3/33 plus 9/21 as a fraction?

3/33 + 9/21 in simplest fraction form is 40/77.

What is 3/33 plus 9/21 as a decimal?

3/33 + 9/21 converted to a decimal is 0.519481.

What is 3/33 plus 9/21 as a percentage?

3/33 + 9/21 expressed as a percentage is 51.9481%.

Does 3/33 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.519481...) because the denominator contains prime factors other than 2 and 5.