What is 18/33 plus 9/13? (Answer: 177/143)

Exact Answer

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Problem: What is 18/33 plus 9/13?
Formula / Expression: 18/33 + 9/13
Final Answer: 1 34/143 (177/143)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 33 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 33 × 13 = 429.
Working: LCD(33, 13) = 429

Step 2: Convert to Equivalent Fractions with Common Denominator 429
Multiply the numerator and denominator of 18/33 by 13, and multiply the numerator and denominator of 9/13 by 33 so both fractions share the common base 429.
Working: 18 × 13/33 × 13 = 234/429 and 9 × 33/13 × 33 = 297/429

Step 3: Add the Numerators
Now add the numerators (234 + 297 = 531) and keep the common denominator 429 unchanged.
Working: 234 + 297/429 = 531/429

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 531 and 429, which is 3. Divide both the numerator and denominator by 3.
Working: 531 ÷ 3/429 ÷ 3 = 177/143

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (177) is greater than the denominator (143), divide 177 by 143: it goes in 1 whole time(s) with a remainder of 34, giving the mixed number 1 34/143.
Working: 177/143 = 1 34/143

Step 6: Decimal & Percentage Representation
Dividing the numerator 177 by denominator 143 produces a repeating decimal (approximately 1.237762, or 123.7762%).
Working: 177 ÷ 143 = 1.237762 (123.7762%)

Key Values:
- Simplified Fraction: 177/143
- Mixed Number Form: 1 34/143
- Decimal Value: 1.237762
- Percentage: 123.7762%

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18/33 + 9/13 = 177/143

Simplified Fraction

177/143

Mixed Number

1 34/143

Decimal Value

1.237762

Percentage

123.7762%

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Step-by-Step Solution: 18/33 + 9/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 33 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 33 × 13 = 429.

LCD(33, 13) = 429

Step 2

Convert to Equivalent Fractions with Common Denominator 429

Multiply the numerator and denominator of 18/33 by 13, and multiply the numerator and denominator of 9/13 by 33 so both fractions share the common base 429.

18 × 13/33 × 13 = 234/429 and 9 × 33/13 × 33 = 297/429

Step 3

Add the Numerators

Now add the numerators (234 + 297 = 531) and keep the common denominator 429 unchanged.

234 + 297/429 = 531/429

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 531 and 429, which is 3. Divide both the numerator and denominator by 3.

531 ÷ 3/429 ÷ 3 = 177/143

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (177) is greater than the denominator (143), divide 177 by 143: it goes in 1 whole time(s) with a remainder of 34, giving the mixed number 1 34/143.

177/143 = 134/143

Step 6

Decimal & Percentage Representation

Dividing the numerator 177 by denominator 143 produces a repeating decimal (approximately 1.237762, or 123.7762%).

177 ÷ 143 = 1.237762 (123.7762%)

Visual Representation

The diagram below illustrates 18/33 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`177/143`
Mixed Number Form	`1 34/143`
Decimal Form	`1.237762`
Percentage	`123.7762%`

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Frequently Asked Questions

What is 18/33 plus 9/13 as a fraction?

18/33 + 9/13 in simplest fraction form is 177/143 (or 1 34/143 as a mixed number).

What is 18/33 plus 9/13 as a decimal?

18/33 + 9/13 converted to a decimal is 1.237762.

What is 18/33 plus 9/13 as a percentage?

18/33 + 9/13 expressed as a percentage is 123.7762%.

How do you write 18/33 plus 9/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 177/143 can be written as the mixed number 1 34/143.

Does 18/33 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.237762...) because the denominator contains prime factors other than 2 and 5.