What is 5/40 plus 2/9? (Answer: 25/72)

Exact Answer

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Problem: What is 5/40 plus 2/9?
Formula / Expression: 5/40 + 2/9
Final Answer: 25/72
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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 5/40 by 9, and multiply the numerator and denominator of 2/9 by 40 so both fractions share the common base 360.
Working: 5 × 9/40 × 9 = 45/360 and 2 × 40/9 × 40 = 80/360

Step 3: Add the Numerators
Now add the numerators (45 + 80 = 125) and keep the common denominator 360 unchanged.
Working: 45 + 80/360 = 125/360

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 125 and 360, which is 5. Divide both the numerator and denominator by 5.
Working: 125 ÷ 5/360 ÷ 5 = 25/72

Step 5: Decimal & Percentage Representation
Dividing the numerator 25 by denominator 72 produces a repeating decimal (approximately 0.347222, or 34.7222%).
Working: 25 ÷ 72 = 0.347222 (34.7222%)

Key Values:
- Simplified Fraction: 25/72
- Mixed Number Form: 25/72
- Decimal Value: 0.347222
- Percentage: 34.7222%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-5-40-plus-2-9/
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5/40 + 2/9 = 25/72

Simplified Fraction

25/72

Mixed Number

Proper (25/72)

Decimal Value

0.347222

Percentage

34.7222%

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Step-by-Step Solution: 5/40 + 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 5/40 by 9, and multiply the numerator and denominator of 2/9 by 40 so both fractions share the common base 360.

5 × 9/40 × 9 = 45/360 and 2 × 40/9 × 40 = 80/360

Step 3

Add the Numerators

Now add the numerators (45 + 80 = 125) and keep the common denominator 360 unchanged.

45 + 80/360 = 125/360

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 125 and 360, which is 5. Divide both the numerator and denominator by 5.

125 ÷ 5/360 ÷ 5 = 25/72

Step 5

Decimal & Percentage Representation

Dividing the numerator 25 by denominator 72 produces a repeating decimal (approximately 0.347222, or 34.7222%).

25 ÷ 72 = 0.347222 (34.7222%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`25/72`
Mixed Number Form	`25/72`
Decimal Form	`0.347222`
Percentage	`34.7222%`

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Frequently Asked Questions

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

5/40 + 2/9 in simplest fraction form is 25/72.

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

5/40 + 2/9 converted to a decimal is 0.347222.

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

5/40 + 2/9 expressed as a percentage is 34.7222%.

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

It results in a repeating decimal (approximately 0.347222...) because the denominator contains prime factors other than 2 and 5.