What is 2/9 plus 9/40? (Answer: 161/360)

Exact Answer

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Problem: What is 2/9 plus 9/40?
Formula / Expression: 2/9 + 9/40
Final Answer: 161/360
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 360
Multiply the numerator and denominator of 2/9 by 40, and multiply the numerator and denominator of 9/40 by 9 so both fractions share the common base 360.
Working: 2 × 40/9 × 40 = 80/360 and 9 × 9/40 × 9 = 81/360

Step 3: Add the Numerators
Now add the numerators (80 + 81 = 161) and keep the common denominator 360 unchanged.
Working: 80 + 81/360 = 161/360

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 161 and 360 is 1, confirming that 161/360 cannot be reduced further—it is already in its simplest irreducible form.
Working: 161/360

Step 5: Decimal & Percentage Representation
Dividing the numerator 161 by denominator 360 produces a repeating decimal (approximately 0.447222, or 44.7222%).
Working: 161 ÷ 360 = 0.447222 (44.7222%)

Key Values:
- Simplified Fraction: 161/360
- Mixed Number Form: 161/360
- Decimal Value: 0.447222
- Percentage: 44.7222%

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Solved with FractionsCalc:
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2/9 + 9/40 = 161/360

Simplified Fraction

161/360

Mixed Number

Proper (161/360)

Decimal Value

0.447222

Percentage

44.7222%

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

Step 1

Find the Least Common Denominator (LCD)

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

LCD(9, 40) = 360

Step 2

Convert to Equivalent Fractions with Common Denominator 360

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

2 × 40/9 × 40 = 80/360 and 9 × 9/40 × 9 = 81/360

Step 3

Add the Numerators

Now add the numerators (80 + 81 = 161) and keep the common denominator 360 unchanged.

80 + 81/360 = 161/360

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 161 and 360 is 1, confirming that 161/360 cannot be reduced further—it is already in its simplest irreducible form.

161/360

Step 5

Decimal & Percentage Representation

Dividing the numerator 161 by denominator 360 produces a repeating decimal (approximately 0.447222, or 44.7222%).

161 ÷ 360 = 0.447222 (44.7222%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`161/360`
Mixed Number Form	`161/360`
Decimal Form	`0.447222`
Percentage	`44.7222%`

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Frequently Asked Questions

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

2/9 + 9/40 in simplest fraction form is 161/360.

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

2/9 + 9/40 converted to a decimal is 0.447222.

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

2/9 + 9/40 expressed as a percentage is 44.7222%.

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

It results in a repeating decimal (approximately 0.447222...) because the denominator contains prime factors other than 2 and 5.