What is 3/40 plus 2/3? (Answer: 89/120)

Exact Answer

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Problem: What is 3/40 plus 2/3?
Formula / Expression: 3/40 + 2/3
Final Answer: 89/120
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 40 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 40 × 3 = 120.
Working: LCD(40, 3) = 120

Step 2: Convert to Equivalent Fractions with Common Denominator 120
Multiply the numerator and denominator of 3/40 by 3, and multiply the numerator and denominator of 2/3 by 40 so both fractions share the common base 120.
Working: 3 × 3/40 × 3 = 9/120 and 2 × 40/3 × 40 = 80/120

Step 3: Add the Numerators
Now add the numerators (9 + 80 = 89) and keep the common denominator 120 unchanged.
Working: 9 + 80/120 = 89/120

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 89 and 120 is 1, confirming that 89/120 cannot be reduced further—it is already in its simplest irreducible form.
Working: 89/120

Step 5: Decimal & Percentage Representation
Dividing the numerator 89 by denominator 120 produces a repeating decimal (approximately 0.741667, or 74.1667%).
Working: 89 ÷ 120 = 0.741667 (74.1667%)

Key Values:
- Simplified Fraction: 89/120
- Mixed Number Form: 89/120
- Decimal Value: 0.741667
- Percentage: 74.1667%

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3/40 + 2/3 = 89/120

Simplified Fraction

89/120

Mixed Number

Proper (89/120)

Decimal Value

0.741667

Percentage

74.1667%

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

Step 1

Find the Least Common Denominator (LCD)

The denominators 40 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 40 × 3 = 120.

LCD(40, 3) = 120

Step 2

Convert to Equivalent Fractions with Common Denominator 120

Multiply the numerator and denominator of 3/40 by 3, and multiply the numerator and denominator of 2/3 by 40 so both fractions share the common base 120.

3 × 3/40 × 3 = 9/120 and 2 × 40/3 × 40 = 80/120

Step 3

Add the Numerators

Now add the numerators (9 + 80 = 89) and keep the common denominator 120 unchanged.

9 + 80/120 = 89/120

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 89 and 120 is 1, confirming that 89/120 cannot be reduced further—it is already in its simplest irreducible form.

89/120

Step 5

Decimal & Percentage Representation

Dividing the numerator 89 by denominator 120 produces a repeating decimal (approximately 0.741667, or 74.1667%).

89 ÷ 120 = 0.741667 (74.1667%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`89/120`
Mixed Number Form	`89/120`
Decimal Form	`0.741667`
Percentage	`74.1667%`

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Frequently Asked Questions

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

3/40 + 2/3 in simplest fraction form is 89/120.

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

3/40 + 2/3 converted to a decimal is 0.741667.

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

3/40 + 2/3 expressed as a percentage is 74.1667%.

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

It results in a repeating decimal (approximately 0.741667...) because the denominator contains prime factors other than 2 and 5.