What is 2/40 plus 3/9? (Answer: 23/60)

Exact Answer

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Problem: What is 2/40 plus 3/9?
Formula / Expression: 2/40 + 3/9
Final Answer: 23/60
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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 3/9 by 40 so both fractions share the common base 360.
Working: 2 × 9/40 × 9 = 18/360 and 3 × 40/9 × 40 = 120/360

Step 3: Add the Numerators
Now add the numerators (18 + 120 = 138) and keep the common denominator 360 unchanged.
Working: 18 + 120/360 = 138/360

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 138 and 360, which is 6. Divide both the numerator and denominator by 6.
Working: 138 ÷ 6/360 ÷ 6 = 23/60

Step 5: Decimal & Percentage Representation
Dividing the numerator 23 by denominator 60 produces a repeating decimal (approximately 0.383333, or 38.3333%).
Working: 23 ÷ 60 = 0.383333 (38.3333%)

Key Values:
- Simplified Fraction: 23/60
- Mixed Number Form: 23/60
- Decimal Value: 0.383333
- Percentage: 38.3333%

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Solved with FractionsCalc:
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2/40 + 3/9 = 23/60

Simplified Fraction

23/60

Mixed Number

Proper (23/60)

Decimal Value

0.383333

Percentage

38.3333%

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Step-by-Step Solution: 2/40 + 3/9

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 3/9 by 40 so both fractions share the common base 360.

2 × 9/40 × 9 = 18/360 and 3 × 40/9 × 40 = 120/360

Step 3

Add the Numerators

Now add the numerators (18 + 120 = 138) and keep the common denominator 360 unchanged.

18 + 120/360 = 138/360

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 138 and 360, which is 6. Divide both the numerator and denominator by 6.

138 ÷ 6/360 ÷ 6 = 23/60

Step 5

Decimal & Percentage Representation

Dividing the numerator 23 by denominator 60 produces a repeating decimal (approximately 0.383333, or 38.3333%).

23 ÷ 60 = 0.383333 (38.3333%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`23/60`
Mixed Number Form	`23/60`
Decimal Form	`0.383333`
Percentage	`38.3333%`

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Frequently Asked Questions

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

2/40 + 3/9 in simplest fraction form is 23/60.

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

2/40 + 3/9 converted to a decimal is 0.383333.

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

2/40 + 3/9 expressed as a percentage is 38.3333%.

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

It results in a repeating decimal (approximately 0.383333...) because the denominator contains prime factors other than 2 and 5.