What is 3/40 plus 2/9? (Answer: 107/360)

Exact Answer

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Problem: What is 3/40 plus 2/9?
Formula / Expression: 3/40 + 2/9
Final Answer: 107/360
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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 3/40 by 9, and multiply the numerator and denominator of 2/9 by 40 so both fractions share the common base 360.
Working: 3 × 9/40 × 9 = 27/360 and 2 × 40/9 × 40 = 80/360

Step 3: Add the Numerators
Now add the numerators (27 + 80 = 107) and keep the common denominator 360 unchanged.
Working: 27 + 80/360 = 107/360

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 107 and 360 is 1, confirming that 107/360 cannot be reduced further—it is already in its simplest irreducible form.
Working: 107/360

Step 5: Decimal & Percentage Representation
Dividing the numerator 107 by denominator 360 produces a repeating decimal (approximately 0.297222, or 29.7222%).
Working: 107 ÷ 360 = 0.297222 (29.7222%)

Key Values:
- Simplified Fraction: 107/360
- Mixed Number Form: 107/360
- Decimal Value: 0.297222
- Percentage: 29.7222%

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3/40 + 2/9 = 107/360

Simplified Fraction

107/360

Mixed Number

Proper (107/360)

Decimal Value

0.297222

Percentage

29.7222%

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Step-by-Step Solution: 3/40 + 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 3/40 by 9, and multiply the numerator and denominator of 2/9 by 40 so both fractions share the common base 360.

3 × 9/40 × 9 = 27/360 and 2 × 40/9 × 40 = 80/360

Step 3

Add the Numerators

Now add the numerators (27 + 80 = 107) and keep the common denominator 360 unchanged.

27 + 80/360 = 107/360

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 107 and 360 is 1, confirming that 107/360 cannot be reduced further—it is already in its simplest irreducible form.

107/360

Step 5

Decimal & Percentage Representation

Dividing the numerator 107 by denominator 360 produces a repeating decimal (approximately 0.297222, or 29.7222%).

107 ÷ 360 = 0.297222 (29.7222%)

Visual Representation

The diagram below illustrates 3/40 plus 2/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`107/360`
Mixed Number Form	`107/360`
Decimal Form	`0.297222`
Percentage	`29.7222%`

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Frequently Asked Questions

What is 3/40 plus 2/9 as a fraction?

3/40 + 2/9 in simplest fraction form is 107/360.

What is 3/40 plus 2/9 as a decimal?

3/40 + 2/9 converted to a decimal is 0.297222.

What is 3/40 plus 2/9 as a percentage?

3/40 + 2/9 expressed as a percentage is 29.7222%.

Does 3/40 plus 2/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.297222...) because the denominator contains prime factors other than 2 and 5.