What is 7/33 plus 2/9? (Answer: 43/99)

Exact Answer

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Problem: What is 7/33 plus 2/9?
Formula / Expression: 7/33 + 2/9
Final Answer: 43/99
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 33 and 9 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 99 (which is smaller than their product 33 × 9 = 297, keeping the calculation simpler).
Working: LCD(33, 9) = 99

Step 2: Convert to Equivalent Fractions with Common Denominator 99
Multiply the numerator and denominator of 7/33 by 3, and multiply the numerator and denominator of 2/9 by 11 so both fractions share the common base 99.
Working: 7 × 3/33 × 3 = 21/99 and 2 × 11/9 × 11 = 22/99

Step 3: Add the Numerators
Now add the numerators (21 + 22 = 43) and keep the common denominator 99 unchanged.
Working: 21 + 22/99 = 43/99

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 43 and 99 is 1, confirming that 43/99 cannot be reduced further—it is already in its simplest irreducible form.
Working: 43/99

Step 5: Decimal & Percentage Representation
Dividing the numerator 43 by denominator 99 produces a repeating decimal (approximately 0.434343, or 43.4343%).
Working: 43 ÷ 99 = 0.434343 (43.4343%)

Key Values:
- Simplified Fraction: 43/99
- Mixed Number Form: 43/99
- Decimal Value: 0.434343
- Percentage: 43.4343%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-7-33-plus-2-9/
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7/33 + 2/9 = 43/99

Simplified Fraction

43/99

Mixed Number

Proper (43/99)

Decimal Value

0.434343

Percentage

43.4343%

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Step-by-Step Solution: 7/33 + 2/9

Step 1

Find the Least Common Denominator (LCD)

The denominators 33 and 9 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 99 (which is smaller than their product 33 × 9 = 297, keeping the calculation simpler).

LCD(33, 9) = 99

Step 2

Convert to Equivalent Fractions with Common Denominator 99

Multiply the numerator and denominator of 7/33 by 3, and multiply the numerator and denominator of 2/9 by 11 so both fractions share the common base 99.

7 × 3/33 × 3 = 21/99 and 2 × 11/9 × 11 = 22/99

Step 3

Add the Numerators

Now add the numerators (21 + 22 = 43) and keep the common denominator 99 unchanged.

21 + 22/99 = 43/99

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 43 and 99 is 1, confirming that 43/99 cannot be reduced further—it is already in its simplest irreducible form.

43/99

Step 5

Decimal & Percentage Representation

Dividing the numerator 43 by denominator 99 produces a repeating decimal (approximately 0.434343, or 43.4343%).

43 ÷ 99 = 0.434343 (43.4343%)

Visual Representation

The diagram below illustrates 7/33 plus 2/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`43/99`
Mixed Number Form	`43/99`
Decimal Form	`0.434343`
Percentage	`43.4343%`

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Frequently Asked Questions

What is 7/33 plus 2/9 as a fraction?

7/33 + 2/9 in simplest fraction form is 43/99.

What is 7/33 plus 2/9 as a decimal?

7/33 + 2/9 converted to a decimal is 0.434343.

What is 7/33 plus 2/9 as a percentage?

7/33 + 2/9 expressed as a percentage is 43.4343%.

Does 7/33 plus 2/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.434343...) because the denominator contains prime factors other than 2 and 5.