What is 7/40 plus 2/9? (Answer: 143/360)

Exact Answer

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Problem: What is 7/40 plus 2/9?
Formula / Expression: 7/40 + 2/9
Final Answer: 143/360
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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 7/40 by 9, and multiply the numerator and denominator of 2/9 by 40 so both fractions share the common base 360.
Working: 7 × 9/40 × 9 = 63/360 and 2 × 40/9 × 40 = 80/360

Step 3: Add the Numerators
Now add the numerators (63 + 80 = 143) and keep the common denominator 360 unchanged.
Working: 63 + 80/360 = 143/360

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 143 and 360 is 1, confirming that 143/360 cannot be reduced further—it is already in its simplest irreducible form.
Working: 143/360

Step 5: Decimal & Percentage Representation
Dividing the numerator 143 by denominator 360 produces a repeating decimal (approximately 0.397222, or 39.7222%).
Working: 143 ÷ 360 = 0.397222 (39.7222%)

Key Values:
- Simplified Fraction: 143/360
- Mixed Number Form: 143/360
- Decimal Value: 0.397222
- Percentage: 39.7222%

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7/40 + 2/9 = 143/360

Simplified Fraction

143/360

Mixed Number

Proper (143/360)

Decimal Value

0.397222

Percentage

39.7222%

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Step-by-Step Solution: 7/40 + 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 7/40 by 9, and multiply the numerator and denominator of 2/9 by 40 so both fractions share the common base 360.

7 × 9/40 × 9 = 63/360 and 2 × 40/9 × 40 = 80/360

Step 3

Add the Numerators

Now add the numerators (63 + 80 = 143) and keep the common denominator 360 unchanged.

63 + 80/360 = 143/360

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 143 and 360 is 1, confirming that 143/360 cannot be reduced further—it is already in its simplest irreducible form.

143/360

Step 5

Decimal & Percentage Representation

Dividing the numerator 143 by denominator 360 produces a repeating decimal (approximately 0.397222, or 39.7222%).

143 ÷ 360 = 0.397222 (39.7222%)

Visual Representation

The diagram below illustrates 7/40 plus 2/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`143/360`
Mixed Number Form	`143/360`
Decimal Form	`0.397222`
Percentage	`39.7222%`

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Frequently Asked Questions

What is 7/40 plus 2/9 as a fraction?

7/40 + 2/9 in simplest fraction form is 143/360.

What is 7/40 plus 2/9 as a decimal?

7/40 + 2/9 converted to a decimal is 0.397222.

What is 7/40 plus 2/9 as a percentage?

7/40 + 2/9 expressed as a percentage is 39.7222%.

Does 7/40 plus 2/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.397222...) because the denominator contains prime factors other than 2 and 5.