What is 7/33 plus 2/7? (Answer: 115/231)

Exact Answer

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Problem: What is 7/33 plus 2/7?
Formula / Expression: 7/33 + 2/7
Final Answer: 115/231
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 33 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 33 × 7 = 231.
Working: LCD(33, 7) = 231

Step 2: Convert to Equivalent Fractions with Common Denominator 231
Multiply the numerator and denominator of 7/33 by 7, and multiply the numerator and denominator of 2/7 by 33 so both fractions share the common base 231.
Working: 7 × 7/33 × 7 = 49/231 and 2 × 33/7 × 33 = 66/231

Step 3: Add the Numerators
Now add the numerators (49 + 66 = 115) and keep the common denominator 231 unchanged.
Working: 49 + 66/231 = 115/231

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 115 and 231 is 1, confirming that 115/231 cannot be reduced further—it is already in its simplest irreducible form.
Working: 115/231

Step 5: Decimal & Percentage Representation
Dividing the numerator 115 by denominator 231 produces a repeating decimal (approximately 0.497835, or 49.7835%).
Working: 115 ÷ 231 = 0.497835 (49.7835%)

Key Values:
- Simplified Fraction: 115/231
- Mixed Number Form: 115/231
- Decimal Value: 0.497835
- Percentage: 49.7835%

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Solved with FractionsCalc:
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7/33 + 2/7 = 115/231

Simplified Fraction

115/231

Mixed Number

Proper (115/231)

Decimal Value

0.497835

Percentage

49.7835%

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

Step 1

Find the Least Common Denominator (LCD)

The denominators 33 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 33 × 7 = 231.

LCD(33, 7) = 231

Step 2

Convert to Equivalent Fractions with Common Denominator 231

Multiply the numerator and denominator of 7/33 by 7, and multiply the numerator and denominator of 2/7 by 33 so both fractions share the common base 231.

7 × 7/33 × 7 = 49/231 and 2 × 33/7 × 33 = 66/231

Step 3

Add the Numerators

Now add the numerators (49 + 66 = 115) and keep the common denominator 231 unchanged.

49 + 66/231 = 115/231

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 115 and 231 is 1, confirming that 115/231 cannot be reduced further—it is already in its simplest irreducible form.

115/231

Step 5

Decimal & Percentage Representation

Dividing the numerator 115 by denominator 231 produces a repeating decimal (approximately 0.497835, or 49.7835%).

115 ÷ 231 = 0.497835 (49.7835%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`115/231`
Mixed Number Form	`115/231`
Decimal Form	`0.497835`
Percentage	`49.7835%`

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Frequently Asked Questions

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

7/33 + 2/7 in simplest fraction form is 115/231.

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

7/33 + 2/7 converted to a decimal is 0.497835.

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

7/33 + 2/7 expressed as a percentage is 49.7835%.

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

It results in a repeating decimal (approximately 0.497835...) because the denominator contains prime factors other than 2 and 5.