What is 7/24 plus 2/5? (Answer: 83/120)

Exact Answer

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Problem: What is 7/24 plus 2/5?
Formula / Expression: 7/24 + 2/5
Final Answer: 83/120
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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 7/24 by 5, and multiply the numerator and denominator of 2/5 by 24 so both fractions share the common base 120.
Working: 7 × 5/24 × 5 = 35/120 and 2 × 24/5 × 24 = 48/120

Step 3: Add the Numerators
Now add the numerators (35 + 48 = 83) and keep the common denominator 120 unchanged.
Working: 35 + 48/120 = 83/120

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 83 and 120 is 1, confirming that 83/120 cannot be reduced further—it is already in its simplest irreducible form.
Working: 83/120

Step 5: Decimal & Percentage Representation
Dividing the numerator 83 by denominator 120 produces a repeating decimal (approximately 0.691667, or 69.1667%).
Working: 83 ÷ 120 = 0.691667 (69.1667%)

Key Values:
- Simplified Fraction: 83/120
- Mixed Number Form: 83/120
- Decimal Value: 0.691667
- Percentage: 69.1667%

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Solved with FractionsCalc:
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7/24 + 2/5 = 83/120

Simplified Fraction

83/120

Mixed Number

Proper (83/120)

Decimal Value

0.691667

Percentage

69.1667%

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Step-by-Step Solution: 7/24 + 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 7/24 by 5, and multiply the numerator and denominator of 2/5 by 24 so both fractions share the common base 120.

7 × 5/24 × 5 = 35/120 and 2 × 24/5 × 24 = 48/120

Step 3

Add the Numerators

Now add the numerators (35 + 48 = 83) and keep the common denominator 120 unchanged.

35 + 48/120 = 83/120

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 83 and 120 is 1, confirming that 83/120 cannot be reduced further—it is already in its simplest irreducible form.

83/120

Step 5

Decimal & Percentage Representation

Dividing the numerator 83 by denominator 120 produces a repeating decimal (approximately 0.691667, or 69.1667%).

83 ÷ 120 = 0.691667 (69.1667%)

Visual Representation

The diagram below illustrates 7/24 plus 2/5 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`83/120`
Mixed Number Form	`83/120`
Decimal Form	`0.691667`
Percentage	`69.1667%`

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Frequently Asked Questions

What is 7/24 plus 2/5 as a fraction?

7/24 + 2/5 in simplest fraction form is 83/120.

What is 7/24 plus 2/5 as a decimal?

7/24 + 2/5 converted to a decimal is 0.691667.

What is 7/24 plus 2/5 as a percentage?

7/24 + 2/5 expressed as a percentage is 69.1667%.

Does 7/24 plus 2/5 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.691667...) because the denominator contains prime factors other than 2 and 5.