What is 9/33 plus 2/4? (Answer: 17/22)

Exact Answer

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Problem: What is 9/33 plus 2/4?
Formula / Expression: 9/33 + 2/4
Final Answer: 17/22
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 33 and 4 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 33 × 4 = 132.
Working: LCD(33, 4) = 132

Step 2: Convert to Equivalent Fractions with Common Denominator 132
Multiply the numerator and denominator of 9/33 by 4, and multiply the numerator and denominator of 2/4 by 33 so both fractions share the common base 132.
Working: 9 × 4/33 × 4 = 36/132 and 2 × 33/4 × 33 = 66/132

Step 3: Add the Numerators
Now add the numerators (36 + 66 = 102) and keep the common denominator 132 unchanged.
Working: 36 + 66/132 = 102/132

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 102 and 132, which is 6. Divide both the numerator and denominator by 6.
Working: 102 ÷ 6/132 ÷ 6 = 17/22

Step 5: Decimal & Percentage Representation
Dividing the numerator 17 by denominator 22 produces a repeating decimal (approximately 0.772727, or 77.2727%).
Working: 17 ÷ 22 = 0.772727 (77.2727%)

Key Values:
- Simplified Fraction: 17/22
- Mixed Number Form: 17/22
- Decimal Value: 0.772727
- Percentage: 77.2727%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-9-33-plus-2-4/
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9/33 + 2/4 = 17/22

Simplified Fraction

17/22

Mixed Number

Proper (17/22)

Decimal Value

0.772727

Percentage

77.2727%

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Step-by-Step Solution: 9/33 + 2/4

Step 1

Find the Least Common Denominator (LCD)

The denominators 33 and 4 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 33 × 4 = 132.

LCD(33, 4) = 132

Step 2

Convert to Equivalent Fractions with Common Denominator 132

Multiply the numerator and denominator of 9/33 by 4, and multiply the numerator and denominator of 2/4 by 33 so both fractions share the common base 132.

9 × 4/33 × 4 = 36/132 and 2 × 33/4 × 33 = 66/132

Step 3

Add the Numerators

Now add the numerators (36 + 66 = 102) and keep the common denominator 132 unchanged.

36 + 66/132 = 102/132

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 102 and 132, which is 6. Divide both the numerator and denominator by 6.

102 ÷ 6/132 ÷ 6 = 17/22

Step 5

Decimal & Percentage Representation

Dividing the numerator 17 by denominator 22 produces a repeating decimal (approximately 0.772727, or 77.2727%).

17 ÷ 22 = 0.772727 (77.2727%)

Visual Representation

The diagram below illustrates 9/33 plus 2/4 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`17/22`
Mixed Number Form	`17/22`
Decimal Form	`0.772727`
Percentage	`77.2727%`

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Frequently Asked Questions

What is 9/33 plus 2/4 as a fraction?

9/33 + 2/4 in simplest fraction form is 17/22.

What is 9/33 plus 2/4 as a decimal?

9/33 + 2/4 converted to a decimal is 0.772727.

What is 9/33 plus 2/4 as a percentage?

9/33 + 2/4 expressed as a percentage is 77.2727%.

Does 9/33 plus 2/4 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.772727...) because the denominator contains prime factors other than 2 and 5.