What is 2/40 plus 2/18? (Answer: 29/180)

Exact Answer

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Problem: What is 2/40 plus 2/18?
Formula / Expression: 2/40 + 2/18
Final Answer: 29/180
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 40 and 18 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 360 (which is smaller than their product 40 × 18 = 720, keeping the calculation simpler).
Working: LCD(40, 18) = 360

Step 2: Convert to Equivalent Fractions with Common Denominator 360
Multiply the numerator and denominator of 2/40 by 9, and multiply the numerator and denominator of 2/18 by 20 so both fractions share the common base 360.
Working: 2 × 9/40 × 9 = 18/360 and 2 × 20/18 × 20 = 40/360

Step 3: Add the Numerators
Now add the numerators (18 + 40 = 58) and keep the common denominator 360 unchanged.
Working: 18 + 40/360 = 58/360

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 58 and 360, which is 2. Divide both the numerator and denominator by 2.
Working: 58 ÷ 2/360 ÷ 2 = 29/180

Step 5: Decimal & Percentage Representation
Dividing the numerator 29 by denominator 180 produces a repeating decimal (approximately 0.161111, or 16.1111%).
Working: 29 ÷ 180 = 0.161111 (16.1111%)

Key Values:
- Simplified Fraction: 29/180
- Mixed Number Form: 29/180
- Decimal Value: 0.161111
- Percentage: 16.1111%

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Solved with FractionsCalc:
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2/40 + 2/18 = 29/180

Simplified Fraction

29/180

Mixed Number

Proper (29/180)

Decimal Value

0.161111

Percentage

16.1111%

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Step-by-Step Solution: 2/40 + 2/18

Step 1

Find the Least Common Denominator (LCD)

The denominators 40 and 18 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 360 (which is smaller than their product 40 × 18 = 720, keeping the calculation simpler).

LCD(40, 18) = 360

Step 2

Convert to Equivalent Fractions with Common Denominator 360

Multiply the numerator and denominator of 2/40 by 9, and multiply the numerator and denominator of 2/18 by 20 so both fractions share the common base 360.

2 × 9/40 × 9 = 18/360 and 2 × 20/18 × 20 = 40/360

Step 3

Add the Numerators

Now add the numerators (18 + 40 = 58) and keep the common denominator 360 unchanged.

18 + 40/360 = 58/360

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 58 and 360, which is 2. Divide both the numerator and denominator by 2.

58 ÷ 2/360 ÷ 2 = 29/180

Step 5

Decimal & Percentage Representation

Dividing the numerator 29 by denominator 180 produces a repeating decimal (approximately 0.161111, or 16.1111%).

29 ÷ 180 = 0.161111 (16.1111%)

Visual Representation

The diagram below illustrates 2/40 plus 2/18 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`29/180`
Mixed Number Form	`29/180`
Decimal Form	`0.161111`
Percentage	`16.1111%`

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Frequently Asked Questions

What is 2/40 plus 2/18 as a fraction?

2/40 + 2/18 in simplest fraction form is 29/180.

What is 2/40 plus 2/18 as a decimal?

2/40 + 2/18 converted to a decimal is 0.161111.

What is 2/40 plus 2/18 as a percentage?

2/40 + 2/18 expressed as a percentage is 16.1111%.

Does 2/40 plus 2/18 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.161111...) because the denominator contains prime factors other than 2 and 5.