What is 7/33 plus 2/3? (Answer: 29/33)

Exact Answer

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Problem: What is 7/33 plus 2/3?
Formula / Expression: 7/33 + 2/3
Final Answer: 29/33
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 33 is an exact multiple of 3 (3 × 11 = 33). The Least Common Denominator (LCD) is simply 33, meaning we only need to scale one fraction.
Working: LCD(33, 3) = 33

Step 2: Convert to Equivalent Fractions with Common Denominator 33
Multiply the numerator and denominator of 7/33 by 1, and multiply the numerator and denominator of 2/3 by 11 so both fractions share the common base 33.
Working: 7 × 1/33 × 1 = 7/33 and 2 × 11/3 × 11 = 22/33

Step 3: Add the Numerators
Now add the numerators (7 + 22 = 29) and keep the common denominator 33 unchanged.
Working: 7 + 22/33 = 29/33

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 29 and 33 is 1, confirming that 29/33 cannot be reduced further—it is already in its simplest irreducible form.
Working: 29/33

Step 5: Decimal & Percentage Representation
Dividing the numerator 29 by denominator 33 produces a repeating decimal (approximately 0.878788, or 87.8788%).
Working: 29 ÷ 33 = 0.878788 (87.8788%)

Key Values:
- Simplified Fraction: 29/33
- Mixed Number Form: 29/33
- Decimal Value: 0.878788
- Percentage: 87.8788%

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Solved with FractionsCalc:
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7/33 + 2/3 = 29/33

Simplified Fraction

29/33

Mixed Number

Proper (29/33)

Decimal Value

0.878788

Percentage

87.8788%

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Step-by-Step Solution: 7/33 + 2/3

Step 1

Find the Least Common Denominator (LCD)

Notice that 33 is an exact multiple of 3 (3 × 11 = 33). The Least Common Denominator (LCD) is simply 33, meaning we only need to scale one fraction.

LCD(33, 3) = 33

Step 2

Convert to Equivalent Fractions with Common Denominator 33

Multiply the numerator and denominator of 7/33 by 1, and multiply the numerator and denominator of 2/3 by 11 so both fractions share the common base 33.

7 × 1/33 × 1 = 7/33 and 2 × 11/3 × 11 = 22/33

Step 3

Add the Numerators

Now add the numerators (7 + 22 = 29) and keep the common denominator 33 unchanged.

7 + 22/33 = 29/33

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 29 and 33 is 1, confirming that 29/33 cannot be reduced further—it is already in its simplest irreducible form.

29/33

Step 5

Decimal & Percentage Representation

Dividing the numerator 29 by denominator 33 produces a repeating decimal (approximately 0.878788, or 87.8788%).

29 ÷ 33 = 0.878788 (87.8788%)

Visual Representation

The diagram below illustrates 7/33 plus 2/3 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`29/33`
Mixed Number Form	`29/33`
Decimal Form	`0.878788`
Percentage	`87.8788%`

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Frequently Asked Questions

What is 7/33 plus 2/3 as a fraction?

7/33 + 2/3 in simplest fraction form is 29/33.

What is 7/33 plus 2/3 as a decimal?

7/33 + 2/3 converted to a decimal is 0.878788.

What is 7/33 plus 2/3 as a percentage?

7/33 + 2/3 expressed as a percentage is 87.8788%.

Does 7/33 plus 2/3 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.878788...) because the denominator contains prime factors other than 2 and 5.