What is 2/46 plus 2/22? (Answer: 34/253)

Exact Answer

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Problem: What is 2/46 plus 2/22?
Formula / Expression: 2/46 + 2/22
Final Answer: 34/253
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 46 and 22 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 506 (which is smaller than their product 46 × 22 = 1012, keeping the calculation simpler).
Working: LCD(46, 22) = 506

Step 2: Convert to Equivalent Fractions with Common Denominator 506
Multiply the numerator and denominator of 2/46 by 11, and multiply the numerator and denominator of 2/22 by 23 so both fractions share the common base 506.
Working: 2 × 11/46 × 11 = 22/506 and 2 × 23/22 × 23 = 46/506

Step 3: Add the Numerators
Now add the numerators (22 + 46 = 68) and keep the common denominator 506 unchanged.
Working: 22 + 46/506 = 68/506

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 68 and 506, which is 2. Divide both the numerator and denominator by 2.
Working: 68 ÷ 2/506 ÷ 2 = 34/253

Step 5: Decimal & Percentage Representation
Dividing the numerator 34 by denominator 253 produces a repeating decimal (approximately 0.134387, or 13.4387%).
Working: 34 ÷ 253 = 0.134387 (13.4387%)

Key Values:
- Simplified Fraction: 34/253
- Mixed Number Form: 34/253
- Decimal Value: 0.134387
- Percentage: 13.4387%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-46-plus-2-22/
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2/46 + 2/22 = 34/253

Simplified Fraction

34/253

Mixed Number

Proper (34/253)

Decimal Value

0.134387

Percentage

13.4387%

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Step-by-Step Solution: 2/46 + 2/22

Step 1

Find the Least Common Denominator (LCD)

The denominators 46 and 22 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 506 (which is smaller than their product 46 × 22 = 1012, keeping the calculation simpler).

LCD(46, 22) = 506

Step 2

Convert to Equivalent Fractions with Common Denominator 506

Multiply the numerator and denominator of 2/46 by 11, and multiply the numerator and denominator of 2/22 by 23 so both fractions share the common base 506.

2 × 11/46 × 11 = 22/506 and 2 × 23/22 × 23 = 46/506

Step 3

Add the Numerators

Now add the numerators (22 + 46 = 68) and keep the common denominator 506 unchanged.

22 + 46/506 = 68/506

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 68 and 506, which is 2. Divide both the numerator and denominator by 2.

68 ÷ 2/506 ÷ 2 = 34/253

Step 5

Decimal & Percentage Representation

Dividing the numerator 34 by denominator 253 produces a repeating decimal (approximately 0.134387, or 13.4387%).

34 ÷ 253 = 0.134387 (13.4387%)

Visual Representation

The diagram below illustrates 2/46 plus 2/22 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`34/253`
Mixed Number Form	`34/253`
Decimal Form	`0.134387`
Percentage	`13.4387%`

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Frequently Asked Questions

What is 2/46 plus 2/22 as a fraction?

2/46 + 2/22 in simplest fraction form is 34/253.

What is 2/46 plus 2/22 as a decimal?

2/46 + 2/22 converted to a decimal is 0.134387.

What is 2/46 plus 2/22 as a percentage?

2/46 + 2/22 expressed as a percentage is 13.4387%.

Does 2/46 plus 2/22 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.134387...) because the denominator contains prime factors other than 2 and 5.