What is 9/40 plus 3/9? (Answer: 67/120)

Exact Answer

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Problem: What is 9/40 plus 3/9?
Formula / Expression: 9/40 + 3/9
Final Answer: 67/120
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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 9/40 by 9, and multiply the numerator and denominator of 3/9 by 40 so both fractions share the common base 360.
Working: 9 × 9/40 × 9 = 81/360 and 3 × 40/9 × 40 = 120/360

Step 3: Add the Numerators
Now add the numerators (81 + 120 = 201) and keep the common denominator 360 unchanged.
Working: 81 + 120/360 = 201/360

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 201 and 360, which is 3. Divide both the numerator and denominator by 3.
Working: 201 ÷ 3/360 ÷ 3 = 67/120

Step 5: Decimal & Percentage Representation
Dividing the numerator 67 by denominator 120 produces a repeating decimal (approximately 0.558333, or 55.8333%).
Working: 67 ÷ 120 = 0.558333 (55.8333%)

Key Values:
- Simplified Fraction: 67/120
- Mixed Number Form: 67/120
- Decimal Value: 0.558333
- Percentage: 55.8333%

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Solved with FractionsCalc:
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9/40 + 3/9 = 67/120

Simplified Fraction

67/120

Mixed Number

Proper (67/120)

Decimal Value

0.558333

Percentage

55.8333%

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

9 × 9/40 × 9 = 81/360 and 3 × 40/9 × 40 = 120/360

Step 3

Add the Numerators

Now add the numerators (81 + 120 = 201) and keep the common denominator 360 unchanged.

81 + 120/360 = 201/360

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 201 and 360, which is 3. Divide both the numerator and denominator by 3.

201 ÷ 3/360 ÷ 3 = 67/120

Step 5

Decimal & Percentage Representation

Dividing the numerator 67 by denominator 120 produces a repeating decimal (approximately 0.558333, or 55.8333%).

67 ÷ 120 = 0.558333 (55.8333%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`67/120`
Mixed Number Form	`67/120`
Decimal Form	`0.558333`
Percentage	`55.8333%`

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Frequently Asked Questions

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

9/40 + 3/9 in simplest fraction form is 67/120.

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

9/40 + 3/9 converted to a decimal is 0.558333.

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

9/40 + 3/9 expressed as a percentage is 55.8333%.

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

It results in a repeating decimal (approximately 0.558333...) because the denominator contains prime factors other than 2 and 5.