What is 5/40 plus 2/3? (Answer: 19/24)

Exact Answer

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Problem: What is 5/40 plus 2/3?
Formula / Expression: 5/40 + 2/3
Final Answer: 19/24
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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 5/40 by 3, and multiply the numerator and denominator of 2/3 by 40 so both fractions share the common base 120.
Working: 5 × 3/40 × 3 = 15/120 and 2 × 40/3 × 40 = 80/120

Step 3: Add the Numerators
Now add the numerators (15 + 80 = 95) and keep the common denominator 120 unchanged.
Working: 15 + 80/120 = 95/120

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 95 and 120, which is 5. Divide both the numerator and denominator by 5.
Working: 95 ÷ 5/120 ÷ 5 = 19/24

Step 5: Decimal & Percentage Representation
Dividing the numerator 19 by denominator 24 produces a repeating decimal (approximately 0.791667, or 79.1667%).
Working: 19 ÷ 24 = 0.791667 (79.1667%)

Key Values:
- Simplified Fraction: 19/24
- Mixed Number Form: 19/24
- Decimal Value: 0.791667
- Percentage: 79.1667%

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Solved with FractionsCalc:
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5/40 + 2/3 = 19/24

Simplified Fraction

19/24

Mixed Number

Proper (19/24)

Decimal Value

0.791667

Percentage

79.1667%

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Step-by-Step Solution: 5/40 + 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 5/40 by 3, and multiply the numerator and denominator of 2/3 by 40 so both fractions share the common base 120.

5 × 3/40 × 3 = 15/120 and 2 × 40/3 × 40 = 80/120

Step 3

Add the Numerators

Now add the numerators (15 + 80 = 95) and keep the common denominator 120 unchanged.

15 + 80/120 = 95/120

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 95 and 120, which is 5. Divide both the numerator and denominator by 5.

95 ÷ 5/120 ÷ 5 = 19/24

Step 5

Decimal & Percentage Representation

Dividing the numerator 19 by denominator 24 produces a repeating decimal (approximately 0.791667, or 79.1667%).

19 ÷ 24 = 0.791667 (79.1667%)

Visual Representation

The diagram below illustrates 5/40 plus 2/3 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`19/24`
Mixed Number Form	`19/24`
Decimal Form	`0.791667`
Percentage	`79.1667%`

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Frequently Asked Questions

What is 5/40 plus 2/3 as a fraction?

5/40 + 2/3 in simplest fraction form is 19/24.

What is 5/40 plus 2/3 as a decimal?

5/40 + 2/3 converted to a decimal is 0.791667.

What is 5/40 plus 2/3 as a percentage?

5/40 + 2/3 expressed as a percentage is 79.1667%.

Does 5/40 plus 2/3 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.791667...) because the denominator contains prime factors other than 2 and 5.