What is 2/33 plus 2/21? (Answer: 12/77)

Exact Answer

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Problem: What is 2/33 plus 2/21?
Formula / Expression: 2/33 + 2/21
Final Answer: 12/77
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 231
Multiply the numerator and denominator of 2/33 by 7, and multiply the numerator and denominator of 2/21 by 11 so both fractions share the common base 231.
Working: 2 × 7/33 × 7 = 14/231 and 2 × 11/21 × 11 = 22/231

Step 3: Add the Numerators
Now add the numerators (14 + 22 = 36) and keep the common denominator 231 unchanged.
Working: 14 + 22/231 = 36/231

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 36 and 231, which is 3. Divide both the numerator and denominator by 3.
Working: 36 ÷ 3/231 ÷ 3 = 12/77

Step 5: Decimal & Percentage Representation
Dividing the numerator 12 by denominator 77 produces a repeating decimal (approximately 0.155844, or 15.5844%).
Working: 12 ÷ 77 = 0.155844 (15.5844%)

Key Values:
- Simplified Fraction: 12/77
- Mixed Number Form: 12/77
- Decimal Value: 0.155844
- Percentage: 15.5844%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-33-plus-2-21/
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2/33 + 2/21 = 12/77

Simplified Fraction

12/77

Mixed Number

Proper (12/77)

Decimal Value

0.155844

Percentage

15.5844%

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Step-by-Step Solution: 2/33 + 2/21

Step 1

Find the Least Common Denominator (LCD)

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

LCD(33, 21) = 231

Step 2

Convert to Equivalent Fractions with Common Denominator 231

Multiply the numerator and denominator of 2/33 by 7, and multiply the numerator and denominator of 2/21 by 11 so both fractions share the common base 231.

2 × 7/33 × 7 = 14/231 and 2 × 11/21 × 11 = 22/231

Step 3

Add the Numerators

Now add the numerators (14 + 22 = 36) and keep the common denominator 231 unchanged.

14 + 22/231 = 36/231

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 36 and 231, which is 3. Divide both the numerator and denominator by 3.

36 ÷ 3/231 ÷ 3 = 12/77

Step 5

Decimal & Percentage Representation

Dividing the numerator 12 by denominator 77 produces a repeating decimal (approximately 0.155844, or 15.5844%).

12 ÷ 77 = 0.155844 (15.5844%)

Visual Representation

The diagram below illustrates 2/33 plus 2/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`12/77`
Mixed Number Form	`12/77`
Decimal Form	`0.155844`
Percentage	`15.5844%`

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Frequently Asked Questions

What is 2/33 plus 2/21 as a fraction?

2/33 + 2/21 in simplest fraction form is 12/77.

What is 2/33 plus 2/21 as a decimal?

2/33 + 2/21 converted to a decimal is 0.155844.

What is 2/33 plus 2/21 as a percentage?

2/33 + 2/21 expressed as a percentage is 15.5844%.

Does 2/33 plus 2/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.155844...) because the denominator contains prime factors other than 2 and 5.