What is 2/40 plus 2/22? (Answer: 31/220)

Exact Answer

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Problem: What is 2/40 plus 2/22?
Formula / Expression: 2/40 + 2/22
Final Answer: 31/220
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 40 and 22 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 440 (which is smaller than their product 40 × 22 = 880, keeping the calculation simpler).
Working: LCD(40, 22) = 440

Step 2: Convert to Equivalent Fractions with Common Denominator 440
Multiply the numerator and denominator of 2/40 by 11, and multiply the numerator and denominator of 2/22 by 20 so both fractions share the common base 440.
Working: 2 × 11/40 × 11 = 22/440 and 2 × 20/22 × 20 = 40/440

Step 3: Add the Numerators
Now add the numerators (22 + 40 = 62) and keep the common denominator 440 unchanged.
Working: 22 + 40/440 = 62/440

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 62 and 440, which is 2. Divide both the numerator and denominator by 2.
Working: 62 ÷ 2/440 ÷ 2 = 31/220

Step 5: Decimal & Percentage Representation
Dividing the numerator 31 by denominator 220 produces a repeating decimal (approximately 0.140909, or 14.0909%).
Working: 31 ÷ 220 = 0.140909 (14.0909%)

Key Values:
- Simplified Fraction: 31/220
- Mixed Number Form: 31/220
- Decimal Value: 0.140909
- Percentage: 14.0909%

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Solved with FractionsCalc:
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2/40 + 2/22 = 31/220

Simplified Fraction

31/220

Mixed Number

Proper (31/220)

Decimal Value

0.140909

Percentage

14.0909%

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Step-by-Step Solution: 2/40 + 2/22

Step 1

Find the Least Common Denominator (LCD)

The denominators 40 and 22 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 440 (which is smaller than their product 40 × 22 = 880, keeping the calculation simpler).

LCD(40, 22) = 440

Step 2

Convert to Equivalent Fractions with Common Denominator 440

Multiply the numerator and denominator of 2/40 by 11, and multiply the numerator and denominator of 2/22 by 20 so both fractions share the common base 440.

2 × 11/40 × 11 = 22/440 and 2 × 20/22 × 20 = 40/440

Step 3

Add the Numerators

Now add the numerators (22 + 40 = 62) and keep the common denominator 440 unchanged.

22 + 40/440 = 62/440

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 62 and 440, which is 2. Divide both the numerator and denominator by 2.

62 ÷ 2/440 ÷ 2 = 31/220

Step 5

Decimal & Percentage Representation

Dividing the numerator 31 by denominator 220 produces a repeating decimal (approximately 0.140909, or 14.0909%).

31 ÷ 220 = 0.140909 (14.0909%)

Visual Representation

The diagram below illustrates 2/40 plus 2/22 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`31/220`
Mixed Number Form	`31/220`
Decimal Form	`0.140909`
Percentage	`14.0909%`

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Frequently Asked Questions

What is 2/40 plus 2/22 as a fraction?

2/40 + 2/22 in simplest fraction form is 31/220.

What is 2/40 plus 2/22 as a decimal?

2/40 + 2/22 converted to a decimal is 0.140909.

What is 2/40 plus 2/22 as a percentage?

2/40 + 2/22 expressed as a percentage is 14.0909%.

Does 2/40 plus 2/22 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.140909...) because the denominator contains prime factors other than 2 and 5.