What is 2/40 plus 5/9? (Answer: 109/180)

Exact Answer

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Problem: What is 2/40 plus 5/9?
Formula / Expression: 2/40 + 5/9
Final Answer: 109/180
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 40 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 40 × 9 = 360.
Working: LCD(40, 9) = 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 5/9 by 40 so both fractions share the common base 360.
Working: 2 × 9/40 × 9 = 18/360 and 5 × 40/9 × 40 = 200/360

Step 3: Add the Numerators
Now add the numerators (18 + 200 = 218) and keep the common denominator 360 unchanged.
Working: 18 + 200/360 = 218/360

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 218 and 360, which is 2. Divide both the numerator and denominator by 2.
Working: 218 ÷ 2/360 ÷ 2 = 109/180

Step 5: Decimal & Percentage Representation
Dividing the numerator 109 by denominator 180 produces a repeating decimal (approximately 0.605556, or 60.5556%).
Working: 109 ÷ 180 = 0.605556 (60.5556%)

Key Values:
- Simplified Fraction: 109/180
- Mixed Number Form: 109/180
- Decimal Value: 0.605556
- Percentage: 60.5556%

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Solved with FractionsCalc:
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2/40 + 5/9 = 109/180

Simplified Fraction

109/180

Mixed Number

Proper (109/180)

Decimal Value

0.605556

Percentage

60.5556%

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Step-by-Step Solution: 2/40 + 5/9

Step 1

Find the Least Common Denominator (LCD)

The denominators 40 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 40 × 9 = 360.

LCD(40, 9) = 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 5/9 by 40 so both fractions share the common base 360.

2 × 9/40 × 9 = 18/360 and 5 × 40/9 × 40 = 200/360

Step 3

Add the Numerators

Now add the numerators (18 + 200 = 218) and keep the common denominator 360 unchanged.

18 + 200/360 = 218/360

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 218 and 360, which is 2. Divide both the numerator and denominator by 2.

218 ÷ 2/360 ÷ 2 = 109/180

Step 5

Decimal & Percentage Representation

Dividing the numerator 109 by denominator 180 produces a repeating decimal (approximately 0.605556, or 60.5556%).

109 ÷ 180 = 0.605556 (60.5556%)

Visual Representation

The diagram below illustrates 2/40 plus 5/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`109/180`
Mixed Number Form	`109/180`
Decimal Form	`0.605556`
Percentage	`60.5556%`

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Frequently Asked Questions

What is 2/40 plus 5/9 as a fraction?

2/40 + 5/9 in simplest fraction form is 109/180.

What is 2/40 plus 5/9 as a decimal?

2/40 + 5/9 converted to a decimal is 0.605556.

What is 2/40 plus 5/9 as a percentage?

2/40 + 5/9 expressed as a percentage is 60.5556%.

Does 2/40 plus 5/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.605556...) because the denominator contains prime factors other than 2 and 5.