What is 6/40 plus 2/9? (Answer: 67/180)

Exact Answer

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Problem: What is 6/40 plus 2/9?
Formula / Expression: 6/40 + 2/9
Final Answer: 67/180
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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 6/40 by 9, and multiply the numerator and denominator of 2/9 by 40 so both fractions share the common base 360.
Working: 6 × 9/40 × 9 = 54/360 and 2 × 40/9 × 40 = 80/360

Step 3: Add the Numerators
Now add the numerators (54 + 80 = 134) and keep the common denominator 360 unchanged.
Working: 54 + 80/360 = 134/360

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 134 and 360, which is 2. Divide both the numerator and denominator by 2.
Working: 134 ÷ 2/360 ÷ 2 = 67/180

Step 5: Decimal & Percentage Representation
Dividing the numerator 67 by denominator 180 produces a repeating decimal (approximately 0.372222, or 37.2222%).
Working: 67 ÷ 180 = 0.372222 (37.2222%)

Key Values:
- Simplified Fraction: 67/180
- Mixed Number Form: 67/180
- Decimal Value: 0.372222
- Percentage: 37.2222%

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Solved with FractionsCalc:
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6/40 + 2/9 = 67/180

Simplified Fraction

67/180

Mixed Number

Proper (67/180)

Decimal Value

0.372222

Percentage

37.2222%

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Step-by-Step Solution: 6/40 + 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 6/40 by 9, and multiply the numerator and denominator of 2/9 by 40 so both fractions share the common base 360.

6 × 9/40 × 9 = 54/360 and 2 × 40/9 × 40 = 80/360

Step 3

Add the Numerators

Now add the numerators (54 + 80 = 134) and keep the common denominator 360 unchanged.

54 + 80/360 = 134/360

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 134 and 360, which is 2. Divide both the numerator and denominator by 2.

134 ÷ 2/360 ÷ 2 = 67/180

Step 5

Decimal & Percentage Representation

Dividing the numerator 67 by denominator 180 produces a repeating decimal (approximately 0.372222, or 37.2222%).

67 ÷ 180 = 0.372222 (37.2222%)

Visual Representation

The diagram below illustrates 6/40 plus 2/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`67/180`
Mixed Number Form	`67/180`
Decimal Form	`0.372222`
Percentage	`37.2222%`

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Frequently Asked Questions

What is 6/40 plus 2/9 as a fraction?

6/40 + 2/9 in simplest fraction form is 67/180.

What is 6/40 plus 2/9 as a decimal?

6/40 + 2/9 converted to a decimal is 0.372222.

What is 6/40 plus 2/9 as a percentage?

6/40 + 2/9 expressed as a percentage is 37.2222%.

Does 6/40 plus 2/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.372222...) because the denominator contains prime factors other than 2 and 5.