What is 7/33 plus 2/8? (Answer: 61/132)

Exact Answer

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Problem: What is 7/33 plus 2/8?
Formula / Expression: 7/33 + 2/8
Final Answer: 61/132
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 33 and 8 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 33 × 8 = 264.
Working: LCD(33, 8) = 264

Step 2: Convert to Equivalent Fractions with Common Denominator 264
Multiply the numerator and denominator of 7/33 by 8, and multiply the numerator and denominator of 2/8 by 33 so both fractions share the common base 264.
Working: 7 × 8/33 × 8 = 56/264 and 2 × 33/8 × 33 = 66/264

Step 3: Add the Numerators
Now add the numerators (56 + 66 = 122) and keep the common denominator 264 unchanged.
Working: 56 + 66/264 = 122/264

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 122 and 264, which is 2. Divide both the numerator and denominator by 2.
Working: 122 ÷ 2/264 ÷ 2 = 61/132

Step 5: Decimal & Percentage Representation
Dividing the numerator 61 by denominator 132 produces a repeating decimal (approximately 0.462121, or 46.2121%).
Working: 61 ÷ 132 = 0.462121 (46.2121%)

Key Values:
- Simplified Fraction: 61/132
- Mixed Number Form: 61/132
- Decimal Value: 0.462121
- Percentage: 46.2121%

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Solved with FractionsCalc:
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7/33 + 2/8 = 61/132

Simplified Fraction

61/132

Mixed Number

Proper (61/132)

Decimal Value

0.462121

Percentage

46.2121%

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Step-by-Step Solution: 7/33 + 2/8

Step 1

Find the Least Common Denominator (LCD)

The denominators 33 and 8 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 33 × 8 = 264.

LCD(33, 8) = 264

Step 2

Convert to Equivalent Fractions with Common Denominator 264

Multiply the numerator and denominator of 7/33 by 8, and multiply the numerator and denominator of 2/8 by 33 so both fractions share the common base 264.

7 × 8/33 × 8 = 56/264 and 2 × 33/8 × 33 = 66/264

Step 3

Add the Numerators

Now add the numerators (56 + 66 = 122) and keep the common denominator 264 unchanged.

56 + 66/264 = 122/264

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 122 and 264, which is 2. Divide both the numerator and denominator by 2.

122 ÷ 2/264 ÷ 2 = 61/132

Step 5

Decimal & Percentage Representation

Dividing the numerator 61 by denominator 132 produces a repeating decimal (approximately 0.462121, or 46.2121%).

61 ÷ 132 = 0.462121 (46.2121%)

Visual Representation

The diagram below illustrates 7/33 plus 2/8 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`61/132`
Mixed Number Form	`61/132`
Decimal Form	`0.462121`
Percentage	`46.2121%`

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Frequently Asked Questions

What is 7/33 plus 2/8 as a fraction?

7/33 + 2/8 in simplest fraction form is 61/132.

What is 7/33 plus 2/8 as a decimal?

7/33 + 2/8 converted to a decimal is 0.462121.

What is 7/33 plus 2/8 as a percentage?

7/33 + 2/8 expressed as a percentage is 46.2121%.

Does 7/33 plus 2/8 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.462121...) because the denominator contains prime factors other than 2 and 5.