What is 2/30 plus 2/22? (Answer: 26/165)

Exact Answer

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Problem: What is 2/30 plus 2/22?
Formula / Expression: 2/30 + 2/22
Final Answer: 26/165
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 30 and 22 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 330 (which is smaller than their product 30 × 22 = 660, keeping the calculation simpler).
Working: LCD(30, 22) = 330

Step 2: Convert to Equivalent Fractions with Common Denominator 330
Multiply the numerator and denominator of 2/30 by 11, and multiply the numerator and denominator of 2/22 by 15 so both fractions share the common base 330.
Working: 2 × 11/30 × 11 = 22/330 and 2 × 15/22 × 15 = 30/330

Step 3: Add the Numerators
Now add the numerators (22 + 30 = 52) and keep the common denominator 330 unchanged.
Working: 22 + 30/330 = 52/330

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 52 and 330, which is 2. Divide both the numerator and denominator by 2.
Working: 52 ÷ 2/330 ÷ 2 = 26/165

Step 5: Decimal & Percentage Representation
Dividing the numerator 26 by denominator 165 produces a repeating decimal (approximately 0.157576, or 15.7576%).
Working: 26 ÷ 165 = 0.157576 (15.7576%)

Key Values:
- Simplified Fraction: 26/165
- Mixed Number Form: 26/165
- Decimal Value: 0.157576
- Percentage: 15.7576%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-30-plus-2-22/
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2/30 + 2/22 = 26/165

Simplified Fraction

26/165

Mixed Number

Proper (26/165)

Decimal Value

0.157576

Percentage

15.7576%

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Step-by-Step Solution: 2/30 + 2/22

Step 1

Find the Least Common Denominator (LCD)

The denominators 30 and 22 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 330 (which is smaller than their product 30 × 22 = 660, keeping the calculation simpler).

LCD(30, 22) = 330

Step 2

Convert to Equivalent Fractions with Common Denominator 330

Multiply the numerator and denominator of 2/30 by 11, and multiply the numerator and denominator of 2/22 by 15 so both fractions share the common base 330.

2 × 11/30 × 11 = 22/330 and 2 × 15/22 × 15 = 30/330

Step 3

Add the Numerators

Now add the numerators (22 + 30 = 52) and keep the common denominator 330 unchanged.

22 + 30/330 = 52/330

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 52 and 330, which is 2. Divide both the numerator and denominator by 2.

52 ÷ 2/330 ÷ 2 = 26/165

Step 5

Decimal & Percentage Representation

Dividing the numerator 26 by denominator 165 produces a repeating decimal (approximately 0.157576, or 15.7576%).

26 ÷ 165 = 0.157576 (15.7576%)

Visual Representation

The diagram below illustrates 2/30 plus 2/22 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`26/165`
Mixed Number Form	`26/165`
Decimal Form	`0.157576`
Percentage	`15.7576%`

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Frequently Asked Questions

What is 2/30 plus 2/22 as a fraction?

2/30 + 2/22 in simplest fraction form is 26/165.

What is 2/30 plus 2/22 as a decimal?

2/30 + 2/22 converted to a decimal is 0.157576.

What is 2/30 plus 2/22 as a percentage?

2/30 + 2/22 expressed as a percentage is 15.7576%.

Does 2/30 plus 2/22 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.157576...) because the denominator contains prime factors other than 2 and 5.