What is 10/24 plus 2/3? (Answer: 13/12)

Exact Answer

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Problem: What is 10/24 plus 2/3?
Formula / Expression: 10/24 + 2/3
Final Answer: 1 1/12 (13/12)
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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 10/24 by 1, and multiply the numerator and denominator of 2/3 by 8 so both fractions share the common base 24.
Working: 10 × 1/24 × 1 = 10/24 and 2 × 8/3 × 8 = 16/24

Step 3: Add the Numerators
Now add the numerators (10 + 16 = 26) and keep the common denominator 24 unchanged.
Working: 10 + 16/24 = 26/24

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 26 and 24, which is 2. Divide both the numerator and denominator by 2.
Working: 26 ÷ 2/24 ÷ 2 = 13/12

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (13) is greater than the denominator (12), divide 13 by 12: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/12.
Working: 13/12 = 1 1/12

Step 6: Decimal & Percentage Representation
Dividing the numerator 13 by denominator 12 produces a repeating decimal (approximately 1.083333, or 108.3333%).
Working: 13 ÷ 12 = 1.083333 (108.3333%)

Key Values:
- Simplified Fraction: 13/12
- Mixed Number Form: 1 1/12
- Decimal Value: 1.083333
- Percentage: 108.3333%

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Solved with FractionsCalc:
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10/24 + 2/3 = 13/12

Simplified Fraction

13/12

Mixed Number

1 1/12

Decimal Value

1.083333

Percentage

108.3333%

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Step-by-Step Solution: 10/24 + 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 10/24 by 1, and multiply the numerator and denominator of 2/3 by 8 so both fractions share the common base 24.

10 × 1/24 × 1 = 10/24 and 2 × 8/3 × 8 = 16/24

Step 3

Add the Numerators

Now add the numerators (10 + 16 = 26) and keep the common denominator 24 unchanged.

10 + 16/24 = 26/24

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 26 and 24, which is 2. Divide both the numerator and denominator by 2.

26 ÷ 2/24 ÷ 2 = 13/12

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (13) is greater than the denominator (12), divide 13 by 12: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/12.

13/12 = 11/12

Step 6

Decimal & Percentage Representation

Dividing the numerator 13 by denominator 12 produces a repeating decimal (approximately 1.083333, or 108.3333%).

13 ÷ 12 = 1.083333 (108.3333%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`13/12`
Mixed Number Form	`1 1/12`
Decimal Form	`1.083333`
Percentage	`108.3333%`

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Frequently Asked Questions

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

10/24 + 2/3 in simplest fraction form is 13/12 (or 1 1/12 as a mixed number).

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

10/24 + 2/3 converted to a decimal is 1.083333.

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

10/24 + 2/3 expressed as a percentage is 108.3333%.

How do you write 10/24 plus 2/3 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 13/12 can be written as the mixed number 1 1/12.

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

It results in a repeating decimal (approximately 1.083333...) because the denominator contains prime factors other than 2 and 5.