What is 7/21 plus 11/33? (Answer: 2/3)

Exact Answer

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Problem: What is 7/21 plus 11/33?
Formula / Expression: 7/21 + 11/33
Final Answer: 2/3
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 21 and 33 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 231 (which is smaller than their product 21 × 33 = 693, keeping the calculation simpler).
Working: LCD(21, 33) = 231

Step 2: Convert to Equivalent Fractions with Common Denominator 231
Multiply the numerator and denominator of 7/21 by 11, and multiply the numerator and denominator of 11/33 by 7 so both fractions share the common base 231.
Working: 7 × 11/21 × 11 = 77/231 and 11 × 7/33 × 7 = 77/231

Step 3: Add the Numerators
Now add the numerators (77 + 77 = 154) and keep the common denominator 231 unchanged.
Working: 77 + 77/231 = 154/231

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 154 and 231, which is 77. Divide both the numerator and denominator by 77.
Working: 154 ÷ 77/231 ÷ 77 = 2/3

Step 5: Decimal & Percentage Representation
Dividing the numerator 2 by denominator 3 produces a repeating decimal (approximately 0.666667, or 66.6667%).
Working: 2 ÷ 3 = 0.666667 (66.6667%)

Key Values:
- Simplified Fraction: 2/3
- Mixed Number Form: 2/3
- Decimal Value: 0.666667
- Percentage: 66.6667%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-7-21-plus-11-33/
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7/21 + 11/33 = 2/3

Simplified Fraction

2/3

Mixed Number

Proper (2/3)

Decimal Value

0.666667

Percentage

66.6667%

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Step-by-Step Solution: 7/21 + 11/33

Step 1

Find the Least Common Denominator (LCD)

The denominators 21 and 33 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 231 (which is smaller than their product 21 × 33 = 693, keeping the calculation simpler).

LCD(21, 33) = 231

Step 2

Convert to Equivalent Fractions with Common Denominator 231

Multiply the numerator and denominator of 7/21 by 11, and multiply the numerator and denominator of 11/33 by 7 so both fractions share the common base 231.

7 × 11/21 × 11 = 77/231 and 11 × 7/33 × 7 = 77/231

Step 3

Add the Numerators

Now add the numerators (77 + 77 = 154) and keep the common denominator 231 unchanged.

77 + 77/231 = 154/231

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 154 and 231, which is 77. Divide both the numerator and denominator by 77.

154 ÷ 77/231 ÷ 77 = 2/3

Step 5

Decimal & Percentage Representation

Dividing the numerator 2 by denominator 3 produces a repeating decimal (approximately 0.666667, or 66.6667%).

2 ÷ 3 = 0.666667 (66.6667%)

Visual Representation

The diagram below illustrates 7/21 plus 11/33 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`2/3`
Mixed Number Form	`2/3`
Decimal Form	`0.666667`
Percentage	`66.6667%`

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Frequently Asked Questions

What is 7/21 plus 11/33 as a fraction?

7/21 + 11/33 in simplest fraction form is 2/3.

What is 7/21 plus 11/33 as a decimal?

7/21 + 11/33 converted to a decimal is 0.666667.

What is 7/21 plus 11/33 as a percentage?

7/21 + 11/33 expressed as a percentage is 66.6667%.

Does 7/21 plus 11/33 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.666667...) because the denominator contains prime factors other than 2 and 5.