What is 7/33 plus 2/4? (Answer: 47/66)

Exact Answer

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Problem: What is 7/33 plus 2/4?
Formula / Expression: 7/33 + 2/4
Final Answer: 47/66
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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 7/33 by 4, and multiply the numerator and denominator of 2/4 by 33 so both fractions share the common base 132.
Working: 7 × 4/33 × 4 = 28/132 and 2 × 33/4 × 33 = 66/132

Step 3: Add the Numerators
Now add the numerators (28 + 66 = 94) and keep the common denominator 132 unchanged.
Working: 28 + 66/132 = 94/132

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 94 and 132, which is 2. Divide both the numerator and denominator by 2.
Working: 94 ÷ 2/132 ÷ 2 = 47/66

Step 5: Decimal & Percentage Representation
Dividing the numerator 47 by denominator 66 produces a repeating decimal (approximately 0.712121, or 71.2121%).
Working: 47 ÷ 66 = 0.712121 (71.2121%)

Key Values:
- Simplified Fraction: 47/66
- Mixed Number Form: 47/66
- Decimal Value: 0.712121
- Percentage: 71.2121%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-7-33-plus-2-4/
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7/33 + 2/4 = 47/66

Simplified Fraction

47/66

Mixed Number

Proper (47/66)

Decimal Value

0.712121

Percentage

71.2121%

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Step-by-Step Solution: 7/33 + 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 7/33 by 4, and multiply the numerator and denominator of 2/4 by 33 so both fractions share the common base 132.

7 × 4/33 × 4 = 28/132 and 2 × 33/4 × 33 = 66/132

Step 3

Add the Numerators

Now add the numerators (28 + 66 = 94) and keep the common denominator 132 unchanged.

28 + 66/132 = 94/132

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 94 and 132, which is 2. Divide both the numerator and denominator by 2.

94 ÷ 2/132 ÷ 2 = 47/66

Step 5

Decimal & Percentage Representation

Dividing the numerator 47 by denominator 66 produces a repeating decimal (approximately 0.712121, or 71.2121%).

47 ÷ 66 = 0.712121 (71.2121%)

Visual Representation

The diagram below illustrates 7/33 plus 2/4 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`47/66`
Mixed Number Form	`47/66`
Decimal Form	`0.712121`
Percentage	`71.2121%`

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Frequently Asked Questions

What is 7/33 plus 2/4 as a fraction?

7/33 + 2/4 in simplest fraction form is 47/66.

What is 7/33 plus 2/4 as a decimal?

7/33 + 2/4 converted to a decimal is 0.712121.

What is 7/33 plus 2/4 as a percentage?

7/33 + 2/4 expressed as a percentage is 71.2121%.

Does 7/33 plus 2/4 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.712121...) because the denominator contains prime factors other than 2 and 5.