What is 9/24 plus 2/5? (Answer: 31/40)

Exact Answer

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Problem: What is 9/24 plus 2/5?
Formula / Expression: 9/24 + 2/5
Final Answer: 31/40
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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 9/24 by 5, and multiply the numerator and denominator of 2/5 by 24 so both fractions share the common base 120.
Working: 9 × 5/24 × 5 = 45/120 and 2 × 24/5 × 24 = 48/120

Step 3: Add the Numerators
Now add the numerators (45 + 48 = 93) and keep the common denominator 120 unchanged.
Working: 45 + 48/120 = 93/120

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 93 and 120, which is 3. Divide both the numerator and denominator by 3.
Working: 93 ÷ 3/120 ÷ 3 = 31/40

Step 5: Decimal & Percentage Representation
Dividing the numerator 31 by denominator 40 yields an exact terminating decimal of 0.775 (or 77.5%).
Working: 31 ÷ 40 = 0.775 (77.5%)

Key Values:
- Simplified Fraction: 31/40
- Mixed Number Form: 31/40
- Decimal Value: 0.775
- Percentage: 77.5%

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Solved with FractionsCalc:
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9/24 + 2/5 = 31/40

Simplified Fraction

31/40

Mixed Number

Proper (31/40)

Decimal Value

0.775

Percentage

77.5%

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Step-by-Step Solution: 9/24 + 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 9/24 by 5, and multiply the numerator and denominator of 2/5 by 24 so both fractions share the common base 120.

9 × 5/24 × 5 = 45/120 and 2 × 24/5 × 24 = 48/120

Step 3

Add the Numerators

Now add the numerators (45 + 48 = 93) and keep the common denominator 120 unchanged.

45 + 48/120 = 93/120

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 93 and 120, which is 3. Divide both the numerator and denominator by 3.

93 ÷ 3/120 ÷ 3 = 31/40

Step 5

Decimal & Percentage Representation

Dividing the numerator 31 by denominator 40 yields an exact terminating decimal of 0.775 (or 77.5%).

31 ÷ 40 = 0.775 (77.5%)

Visual Representation

The diagram below illustrates 9/24 plus 2/5 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`31/40`
Mixed Number Form	`31/40`
Decimal Form	`0.775`
Percentage	`77.5%`

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Frequently Asked Questions

What is 9/24 plus 2/5 as a fraction?

9/24 + 2/5 in simplest fraction form is 31/40.

What is 9/24 plus 2/5 as a decimal?

9/24 + 2/5 converted to a decimal is 0.775.

What is 9/24 plus 2/5 as a percentage?

9/24 + 2/5 expressed as a percentage is 77.5%.

Does 9/24 plus 2/5 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.775) because the denominator in simplest terms contains only prime factors 2 and/or 5.