What is 1/40 plus 2/9? (Answer: 89/360)

Exact Answer

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Problem: What is 1/40 plus 2/9?
Formula / Expression: 1/40 + 2/9
Final Answer: 89/360
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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 1/40 by 9, and multiply the numerator and denominator of 2/9 by 40 so both fractions share the common base 360.
Working: 1 × 9/40 × 9 = 9/360 and 2 × 40/9 × 40 = 80/360

Step 3: Add the Numerators
Now add the numerators (9 + 80 = 89) and keep the common denominator 360 unchanged.
Working: 9 + 80/360 = 89/360

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 89 and 360 is 1, confirming that 89/360 cannot be reduced further—it is already in its simplest irreducible form.
Working: 89/360

Step 5: Decimal & Percentage Representation
Dividing the numerator 89 by denominator 360 produces a repeating decimal (approximately 0.247222, or 24.7222%).
Working: 89 ÷ 360 = 0.247222 (24.7222%)

Key Values:
- Simplified Fraction: 89/360
- Mixed Number Form: 89/360
- Decimal Value: 0.247222
- Percentage: 24.7222%

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Solved with FractionsCalc:
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1/40 + 2/9 = 89/360

Simplified Fraction

89/360

Mixed Number

Proper (89/360)

Decimal Value

0.247222

Percentage

24.7222%

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Step-by-Step Solution: 1/40 + 2/9

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 1/40 by 9, and multiply the numerator and denominator of 2/9 by 40 so both fractions share the common base 360.

1 × 9/40 × 9 = 9/360 and 2 × 40/9 × 40 = 80/360

Step 3

Add the Numerators

Now add the numerators (9 + 80 = 89) and keep the common denominator 360 unchanged.

9 + 80/360 = 89/360

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 89 and 360 is 1, confirming that 89/360 cannot be reduced further—it is already in its simplest irreducible form.

89/360

Step 5

Decimal & Percentage Representation

Dividing the numerator 89 by denominator 360 produces a repeating decimal (approximately 0.247222, or 24.7222%).

89 ÷ 360 = 0.247222 (24.7222%)

Visual Representation

The diagram below illustrates 1/40 plus 2/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`89/360`
Mixed Number Form	`89/360`
Decimal Form	`0.247222`
Percentage	`24.7222%`

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Frequently Asked Questions

What is 1/40 plus 2/9 as a fraction?

1/40 + 2/9 in simplest fraction form is 89/360.

What is 1/40 plus 2/9 as a decimal?

1/40 + 2/9 converted to a decimal is 0.247222.

What is 1/40 plus 2/9 as a percentage?

1/40 + 2/9 expressed as a percentage is 24.7222%.

Does 1/40 plus 2/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.247222...) because the denominator contains prime factors other than 2 and 5.