What is 7/24 plus 2/3? (Answer: 23/24)

Exact Answer

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Problem: What is 7/24 plus 2/3?
Formula / Expression: 7/24 + 2/3
Final Answer: 23/24
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 24 is an exact multiple of 3 (3 × 8 = 24). The Least Common Denominator (LCD) is simply 24, meaning we only need to scale one fraction.
Working: LCD(24, 3) = 24

Step 2: Convert to Equivalent Fractions with Common Denominator 24
Multiply the numerator and denominator of 7/24 by 1, and multiply the numerator and denominator of 2/3 by 8 so both fractions share the common base 24.
Working: 7 × 1/24 × 1 = 7/24 and 2 × 8/3 × 8 = 16/24

Step 3: Add the Numerators
Now add the numerators (7 + 16 = 23) and keep the common denominator 24 unchanged.
Working: 7 + 16/24 = 23/24

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 23 and 24 is 1, confirming that 23/24 cannot be reduced further—it is already in its simplest irreducible form.
Working: 23/24

Step 5: Decimal & Percentage Representation
Dividing the numerator 23 by denominator 24 produces a repeating decimal (approximately 0.958333, or 95.8333%).
Working: 23 ÷ 24 = 0.958333 (95.8333%)

Key Values:
- Simplified Fraction: 23/24
- Mixed Number Form: 23/24
- Decimal Value: 0.958333
- Percentage: 95.8333%

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Solved with FractionsCalc:
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7/24 + 2/3 = 23/24

Simplified Fraction

23/24

Mixed Number

Proper (23/24)

Decimal Value

0.958333

Percentage

95.8333%

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

Step 1

Find the Least Common Denominator (LCD)

Notice that 24 is an exact multiple of 3 (3 × 8 = 24). The Least Common Denominator (LCD) is simply 24, meaning we only need to scale one fraction.

LCD(24, 3) = 24

Step 2

Convert to Equivalent Fractions with Common Denominator 24

Multiply the numerator and denominator of 7/24 by 1, and multiply the numerator and denominator of 2/3 by 8 so both fractions share the common base 24.

7 × 1/24 × 1 = 7/24 and 2 × 8/3 × 8 = 16/24

Step 3

Add the Numerators

Now add the numerators (7 + 16 = 23) and keep the common denominator 24 unchanged.

7 + 16/24 = 23/24

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 23 and 24 is 1, confirming that 23/24 cannot be reduced further—it is already in its simplest irreducible form.

23/24

Step 5

Decimal & Percentage Representation

Dividing the numerator 23 by denominator 24 produces a repeating decimal (approximately 0.958333, or 95.8333%).

23 ÷ 24 = 0.958333 (95.8333%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`23/24`
Mixed Number Form	`23/24`
Decimal Form	`0.958333`
Percentage	`95.8333%`

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Frequently Asked Questions

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

7/24 + 2/3 in simplest fraction form is 23/24.

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

7/24 + 2/3 converted to a decimal is 0.958333.

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

7/24 + 2/3 expressed as a percentage is 95.8333%.

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

It results in a repeating decimal (approximately 0.958333...) because the denominator contains prime factors other than 2 and 5.