What is 2/24 plus 5/7? (Answer: 67/84)

Exact Answer

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Problem: What is 2/24 plus 5/7?
Formula / Expression: 2/24 + 5/7
Final Answer: 67/84
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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 5/7 by 24 so both fractions share the common base 168.
Working: 2 × 7/24 × 7 = 14/168 and 5 × 24/7 × 24 = 120/168

Step 3: Add the Numerators
Now add the numerators (14 + 120 = 134) and keep the common denominator 168 unchanged.
Working: 14 + 120/168 = 134/168

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 134 and 168, which is 2. Divide both the numerator and denominator by 2.
Working: 134 ÷ 2/168 ÷ 2 = 67/84

Step 5: Decimal & Percentage Representation
Dividing the numerator 67 by denominator 84 produces a repeating decimal (approximately 0.797619, or 79.7619%).
Working: 67 ÷ 84 = 0.797619 (79.7619%)

Key Values:
- Simplified Fraction: 67/84
- Mixed Number Form: 67/84
- Decimal Value: 0.797619
- Percentage: 79.7619%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-24-plus-5-7/
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2/24 + 5/7 = 67/84

Simplified Fraction

67/84

Mixed Number

Proper (67/84)

Decimal Value

0.797619

Percentage

79.7619%

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Step-by-Step Solution: 2/24 + 5/7

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 5/7 by 24 so both fractions share the common base 168.

2 × 7/24 × 7 = 14/168 and 5 × 24/7 × 24 = 120/168

Step 3

Add the Numerators

Now add the numerators (14 + 120 = 134) and keep the common denominator 168 unchanged.

14 + 120/168 = 134/168

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 134 and 168, which is 2. Divide both the numerator and denominator by 2.

134 ÷ 2/168 ÷ 2 = 67/84

Step 5

Decimal & Percentage Representation

Dividing the numerator 67 by denominator 84 produces a repeating decimal (approximately 0.797619, or 79.7619%).

67 ÷ 84 = 0.797619 (79.7619%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`67/84`
Mixed Number Form	`67/84`
Decimal Form	`0.797619`
Percentage	`79.7619%`

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Frequently Asked Questions

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

2/24 + 5/7 in simplest fraction form is 67/84.

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

2/24 + 5/7 converted to a decimal is 0.797619.

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

2/24 + 5/7 expressed as a percentage is 79.7619%.

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

It results in a repeating decimal (approximately 0.797619...) because the denominator contains prime factors other than 2 and 5.