What is 2/24 plus 3/10? (Answer: 23/60)

Exact Answer

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Problem: What is 2/24 plus 3/10?
Formula / Expression: 2/24 + 3/10
Final Answer: 23/60
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 24 and 10 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 120 (which is smaller than their product 24 × 10 = 240, keeping the calculation simpler).
Working: LCD(24, 10) = 120

Step 2: Convert to Equivalent Fractions with Common Denominator 120
Multiply the numerator and denominator of 2/24 by 5, and multiply the numerator and denominator of 3/10 by 12 so both fractions share the common base 120.
Working: 2 × 5/24 × 5 = 10/120 and 3 × 12/10 × 12 = 36/120

Step 3: Add the Numerators
Now add the numerators (10 + 36 = 46) and keep the common denominator 120 unchanged.
Working: 10 + 36/120 = 46/120

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 46 and 120, which is 2. Divide both the numerator and denominator by 2.
Working: 46 ÷ 2/120 ÷ 2 = 23/60

Step 5: Decimal & Percentage Representation
Dividing the numerator 23 by denominator 60 produces a repeating decimal (approximately 0.383333, or 38.3333%).
Working: 23 ÷ 60 = 0.383333 (38.3333%)

Key Values:
- Simplified Fraction: 23/60
- Mixed Number Form: 23/60
- Decimal Value: 0.383333
- Percentage: 38.3333%

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Solved with FractionsCalc:
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2/24 + 3/10 = 23/60

Simplified Fraction

23/60

Mixed Number

Proper (23/60)

Decimal Value

0.383333

Percentage

38.3333%

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Step-by-Step Solution: 2/24 + 3/10

Step 1

Find the Least Common Denominator (LCD)

The denominators 24 and 10 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 120 (which is smaller than their product 24 × 10 = 240, keeping the calculation simpler).

LCD(24, 10) = 120

Step 2

Convert to Equivalent Fractions with Common Denominator 120

Multiply the numerator and denominator of 2/24 by 5, and multiply the numerator and denominator of 3/10 by 12 so both fractions share the common base 120.

2 × 5/24 × 5 = 10/120 and 3 × 12/10 × 12 = 36/120

Step 3

Add the Numerators

Now add the numerators (10 + 36 = 46) and keep the common denominator 120 unchanged.

10 + 36/120 = 46/120

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 46 and 120, which is 2. Divide both the numerator and denominator by 2.

46 ÷ 2/120 ÷ 2 = 23/60

Step 5

Decimal & Percentage Representation

Dividing the numerator 23 by denominator 60 produces a repeating decimal (approximately 0.383333, or 38.3333%).

23 ÷ 60 = 0.383333 (38.3333%)

Visual Representation

The diagram below illustrates 2/24 plus 3/10 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`23/60`
Mixed Number Form	`23/60`
Decimal Form	`0.383333`
Percentage	`38.3333%`

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Frequently Asked Questions

What is 2/24 plus 3/10 as a fraction?

2/24 + 3/10 in simplest fraction form is 23/60.

What is 2/24 plus 3/10 as a decimal?

2/24 + 3/10 converted to a decimal is 0.383333.

What is 2/24 plus 3/10 as a percentage?

2/24 + 3/10 expressed as a percentage is 38.3333%.

Does 2/24 plus 3/10 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.383333...) because the denominator contains prime factors other than 2 and 5.