What is 3/8 plus 2/3? (Answer: 25/24)

Exact Answer

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Problem: What is 3/8 plus 2/3?
Formula / Expression: 3/8 + 2/3
Final Answer: 1 1/24 (25/24)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 8 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 8 × 3 = 24.
Working: LCD(8, 3) = 24

Step 2: Convert to Equivalent Fractions with Common Denominator 24
Multiply the numerator and denominator of 3/8 by 3, and multiply the numerator and denominator of 2/3 by 8 so both fractions share the common base 24.
Working: 3 × 3/8 × 3 = 9/24 and 2 × 8/3 × 8 = 16/24

Step 3: Add the Numerators
Now add the numerators (9 + 16 = 25) and keep the common denominator 24 unchanged.
Working: 9 + 16/24 = 25/24

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 25 and 24 is 1, confirming that 25/24 cannot be reduced further—it is already in its simplest irreducible form.
Working: 25/24

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (25) is greater than the denominator (24), divide 25 by 24: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/24.
Working: 25/24 = 1 1/24

Step 6: Decimal & Percentage Representation
Dividing the numerator 25 by denominator 24 produces a repeating decimal (approximately 1.041667, or 104.1667%).
Working: 25 ÷ 24 = 1.041667 (104.1667%)

Key Values:
- Simplified Fraction: 25/24
- Mixed Number Form: 1 1/24
- Decimal Value: 1.041667
- Percentage: 104.1667%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-8-plus-2-3/
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3/8 + 2/3 = 25/24

Simplified Fraction

25/24

Mixed Number

1 1/24

Decimal Value

1.041667

Percentage

104.1667%

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Step-by-Step Solution: 3/8 + 2/3

Step 1

Find the Least Common Denominator (LCD)

The denominators 8 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 8 × 3 = 24.

LCD(8, 3) = 24

Step 2

Convert to Equivalent Fractions with Common Denominator 24

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

3 × 3/8 × 3 = 9/24 and 2 × 8/3 × 8 = 16/24

Step 3

Add the Numerators

Now add the numerators (9 + 16 = 25) and keep the common denominator 24 unchanged.

9 + 16/24 = 25/24

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 25 and 24 is 1, confirming that 25/24 cannot be reduced further—it is already in its simplest irreducible form.

25/24

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (25) is greater than the denominator (24), divide 25 by 24: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/24.

25/24 = 11/24

Step 6

Decimal & Percentage Representation

Dividing the numerator 25 by denominator 24 produces a repeating decimal (approximately 1.041667, or 104.1667%).

25 ÷ 24 = 1.041667 (104.1667%)

Visual Representation

The diagram below illustrates 3/8 plus 2/3 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`25/24`
Mixed Number Form	`1 1/24`
Decimal Form	`1.041667`
Percentage	`104.1667%`

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Frequently Asked Questions

What is 3/8 plus 2/3 as a fraction?

3/8 + 2/3 in simplest fraction form is 25/24 (or 1 1/24 as a mixed number).

What is 3/8 plus 2/3 as a decimal?

3/8 + 2/3 converted to a decimal is 1.041667.

What is 3/8 plus 2/3 as a percentage?

3/8 + 2/3 expressed as a percentage is 104.1667%.

How do you write 3/8 plus 2/3 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 25/24 can be written as the mixed number 1 1/24.

Does 3/8 plus 2/3 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.041667...) because the denominator contains prime factors other than 2 and 5.