What is 3/33 plus 9/39? (Answer: 46/143)

Exact Answer

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Problem: What is 3/33 plus 9/39?
Formula / Expression: 3/33 + 9/39
Final Answer: 46/143
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 33 and 39 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 429 (which is smaller than their product 33 × 39 = 1287, keeping the calculation simpler).
Working: LCD(33, 39) = 429

Step 2: Convert to Equivalent Fractions with Common Denominator 429
Multiply the numerator and denominator of 3/33 by 13, and multiply the numerator and denominator of 9/39 by 11 so both fractions share the common base 429.
Working: 3 × 13/33 × 13 = 39/429 and 9 × 11/39 × 11 = 99/429

Step 3: Add the Numerators
Now add the numerators (39 + 99 = 138) and keep the common denominator 429 unchanged.
Working: 39 + 99/429 = 138/429

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 138 and 429, which is 3. Divide both the numerator and denominator by 3.
Working: 138 ÷ 3/429 ÷ 3 = 46/143

Step 5: Decimal & Percentage Representation
Dividing the numerator 46 by denominator 143 produces a repeating decimal (approximately 0.321678, or 32.1678%).
Working: 46 ÷ 143 = 0.321678 (32.1678%)

Key Values:
- Simplified Fraction: 46/143
- Mixed Number Form: 46/143
- Decimal Value: 0.321678
- Percentage: 32.1678%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-33-plus-9-39/
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3/33 + 9/39 = 46/143

Simplified Fraction

46/143

Mixed Number

Proper (46/143)

Decimal Value

0.321678

Percentage

32.1678%

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Step-by-Step Solution: 3/33 + 9/39

Step 1

Find the Least Common Denominator (LCD)

The denominators 33 and 39 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 429 (which is smaller than their product 33 × 39 = 1287, keeping the calculation simpler).

LCD(33, 39) = 429

Step 2

Convert to Equivalent Fractions with Common Denominator 429

Multiply the numerator and denominator of 3/33 by 13, and multiply the numerator and denominator of 9/39 by 11 so both fractions share the common base 429.

3 × 13/33 × 13 = 39/429 and 9 × 11/39 × 11 = 99/429

Step 3

Add the Numerators

Now add the numerators (39 + 99 = 138) and keep the common denominator 429 unchanged.

39 + 99/429 = 138/429

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 138 and 429, which is 3. Divide both the numerator and denominator by 3.

138 ÷ 3/429 ÷ 3 = 46/143

Step 5

Decimal & Percentage Representation

Dividing the numerator 46 by denominator 143 produces a repeating decimal (approximately 0.321678, or 32.1678%).

46 ÷ 143 = 0.321678 (32.1678%)

Visual Representation

The diagram below illustrates 3/33 plus 9/39 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`46/143`
Mixed Number Form	`46/143`
Decimal Form	`0.321678`
Percentage	`32.1678%`

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Frequently Asked Questions

What is 3/33 plus 9/39 as a fraction?

3/33 + 9/39 in simplest fraction form is 46/143.

What is 3/33 plus 9/39 as a decimal?

3/33 + 9/39 converted to a decimal is 0.321678.

What is 3/33 plus 9/39 as a percentage?

3/33 + 9/39 expressed as a percentage is 32.1678%.

Does 3/33 plus 9/39 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.321678...) because the denominator contains prime factors other than 2 and 5.