What is 4/24 plus 2/5? (Answer: 17/30)

Exact Answer

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Problem: What is 4/24 plus 2/5?
Formula / Expression: 4/24 + 2/5
Final Answer: 17/30
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 24 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 24 × 5 = 120.
Working: LCD(24, 5) = 120

Step 2: Convert to Equivalent Fractions with Common Denominator 120
Multiply the numerator and denominator of 4/24 by 5, and multiply the numerator and denominator of 2/5 by 24 so both fractions share the common base 120.
Working: 4 × 5/24 × 5 = 20/120 and 2 × 24/5 × 24 = 48/120

Step 3: Add the Numerators
Now add the numerators (20 + 48 = 68) and keep the common denominator 120 unchanged.
Working: 20 + 48/120 = 68/120

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 68 and 120, which is 4. Divide both the numerator and denominator by 4.
Working: 68 ÷ 4/120 ÷ 4 = 17/30

Step 5: Decimal & Percentage Representation
Dividing the numerator 17 by denominator 30 produces a repeating decimal (approximately 0.566667, or 56.6667%).
Working: 17 ÷ 30 = 0.566667 (56.6667%)

Key Values:
- Simplified Fraction: 17/30
- Mixed Number Form: 17/30
- Decimal Value: 0.566667
- Percentage: 56.6667%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-4-24-plus-2-5/
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4/24 + 2/5 = 17/30

Simplified Fraction

17/30

Mixed Number

Proper (17/30)

Decimal Value

0.566667

Percentage

56.6667%

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Step-by-Step Solution: 4/24 + 2/5

Step 1

Find the Least Common Denominator (LCD)

The denominators 24 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 24 × 5 = 120.

LCD(24, 5) = 120

Step 2

Convert to Equivalent Fractions with Common Denominator 120

Multiply the numerator and denominator of 4/24 by 5, and multiply the numerator and denominator of 2/5 by 24 so both fractions share the common base 120.

4 × 5/24 × 5 = 20/120 and 2 × 24/5 × 24 = 48/120

Step 3

Add the Numerators

Now add the numerators (20 + 48 = 68) and keep the common denominator 120 unchanged.

20 + 48/120 = 68/120

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 68 and 120, which is 4. Divide both the numerator and denominator by 4.

68 ÷ 4/120 ÷ 4 = 17/30

Step 5

Decimal & Percentage Representation

Dividing the numerator 17 by denominator 30 produces a repeating decimal (approximately 0.566667, or 56.6667%).

17 ÷ 30 = 0.566667 (56.6667%)

Visual Representation

The diagram below illustrates 4/24 plus 2/5 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`17/30`
Mixed Number Form	`17/30`
Decimal Form	`0.566667`
Percentage	`56.6667%`

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Frequently Asked Questions

What is 4/24 plus 2/5 as a fraction?

4/24 + 2/5 in simplest fraction form is 17/30.

What is 4/24 plus 2/5 as a decimal?

4/24 + 2/5 converted to a decimal is 0.566667.

What is 4/24 plus 2/5 as a percentage?

4/24 + 2/5 expressed as a percentage is 56.6667%.

Does 4/24 plus 2/5 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.566667...) because the denominator contains prime factors other than 2 and 5.