What is 2/24 plus 3/7? (Answer: 43/84)

Exact Answer

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Problem: What is 2/24 plus 3/7?
Formula / Expression: 2/24 + 3/7
Final Answer: 43/84
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 24 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 24 × 7 = 168.
Working: LCD(24, 7) = 168

Step 2: Convert to Equivalent Fractions with Common Denominator 168
Multiply the numerator and denominator of 2/24 by 7, and multiply the numerator and denominator of 3/7 by 24 so both fractions share the common base 168.
Working: 2 × 7/24 × 7 = 14/168 and 3 × 24/7 × 24 = 72/168

Step 3: Add the Numerators
Now add the numerators (14 + 72 = 86) and keep the common denominator 168 unchanged.
Working: 14 + 72/168 = 86/168

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 86 and 168, which is 2. Divide both the numerator and denominator by 2.
Working: 86 ÷ 2/168 ÷ 2 = 43/84

Step 5: Decimal & Percentage Representation
Dividing the numerator 43 by denominator 84 produces a repeating decimal (approximately 0.511905, or 51.1905%).
Working: 43 ÷ 84 = 0.511905 (51.1905%)

Key Values:
- Simplified Fraction: 43/84
- Mixed Number Form: 43/84
- Decimal Value: 0.511905
- Percentage: 51.1905%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-24-plus-3-7/
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2/24 + 3/7 = 43/84

Simplified Fraction

43/84

Mixed Number

Proper (43/84)

Decimal Value

0.511905

Percentage

51.1905%

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Step-by-Step Solution: 2/24 + 3/7

Step 1

Find the Least Common Denominator (LCD)

The denominators 24 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 24 × 7 = 168.

LCD(24, 7) = 168

Step 2

Convert to Equivalent Fractions with Common Denominator 168

Multiply the numerator and denominator of 2/24 by 7, and multiply the numerator and denominator of 3/7 by 24 so both fractions share the common base 168.

2 × 7/24 × 7 = 14/168 and 3 × 24/7 × 24 = 72/168

Step 3

Add the Numerators

Now add the numerators (14 + 72 = 86) and keep the common denominator 168 unchanged.

14 + 72/168 = 86/168

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 86 and 168, which is 2. Divide both the numerator and denominator by 2.

86 ÷ 2/168 ÷ 2 = 43/84

Step 5

Decimal & Percentage Representation

Dividing the numerator 43 by denominator 84 produces a repeating decimal (approximately 0.511905, or 51.1905%).

43 ÷ 84 = 0.511905 (51.1905%)

Visual Representation

The diagram below illustrates 2/24 plus 3/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`43/84`
Mixed Number Form	`43/84`
Decimal Form	`0.511905`
Percentage	`51.1905%`

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Frequently Asked Questions

What is 2/24 plus 3/7 as a fraction?

2/24 + 3/7 in simplest fraction form is 43/84.

What is 2/24 plus 3/7 as a decimal?

2/24 + 3/7 converted to a decimal is 0.511905.

What is 2/24 plus 3/7 as a percentage?

2/24 + 3/7 expressed as a percentage is 51.1905%.

Does 2/24 plus 3/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.511905...) because the denominator contains prime factors other than 2 and 5.