What is 1/3 plus 3/8? (Answer: 17/24)

Exact Answer

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Problem: What is 1/3 plus 3/8?
Formula / Expression: 1/3 + 3/8
Final Answer: 17/24
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 24
Multiply the numerator and denominator of 1/3 by 8, and multiply the numerator and denominator of 3/8 by 3 so both fractions share the common base 24.
Working: 1 × 8/3 × 8 = 8/24 and 3 × 3/8 × 3 = 9/24

Step 3: Add the Numerators
Now add the numerators (8 + 9 = 17) and keep the common denominator 24 unchanged.
Working: 8 + 9/24 = 17/24

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 17 and 24 is 1, confirming that 17/24 cannot be reduced further—it is already in its simplest irreducible form.
Working: 17/24

Step 5: Decimal & Percentage Representation
Dividing the numerator 17 by denominator 24 produces a repeating decimal (approximately 0.708333, or 70.8333%).
Working: 17 ÷ 24 = 0.708333 (70.8333%)

Key Values:
- Simplified Fraction: 17/24
- Mixed Number Form: 17/24
- Decimal Value: 0.708333
- Percentage: 70.8333%

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Solved with FractionsCalc:
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1/3 + 3/8 = 17/24

Simplified Fraction

17/24

Mixed Number

Proper (17/24)

Decimal Value

0.708333

Percentage

70.8333%

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Step-by-Step Solution: 1/3 + 3/8

Step 1

Find the Least Common Denominator (LCD)

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

LCD(3, 8) = 24

Step 2

Convert to Equivalent Fractions with Common Denominator 24

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

1 × 8/3 × 8 = 8/24 and 3 × 3/8 × 3 = 9/24

Step 3

Add the Numerators

Now add the numerators (8 + 9 = 17) and keep the common denominator 24 unchanged.

8 + 9/24 = 17/24

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 17 and 24 is 1, confirming that 17/24 cannot be reduced further—it is already in its simplest irreducible form.

17/24

Step 5

Decimal & Percentage Representation

Dividing the numerator 17 by denominator 24 produces a repeating decimal (approximately 0.708333, or 70.8333%).

17 ÷ 24 = 0.708333 (70.8333%)

Visual Representation

The diagram below illustrates 1/3 plus 3/8 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`17/24`
Mixed Number Form	`17/24`
Decimal Form	`0.708333`
Percentage	`70.8333%`

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Frequently Asked Questions

What is 1/3 plus 3/8 as a fraction?

1/3 + 3/8 in simplest fraction form is 17/24.

What is 1/3 plus 3/8 as a decimal?

1/3 + 3/8 converted to a decimal is 0.708333.

What is 1/3 plus 3/8 as a percentage?

1/3 + 3/8 expressed as a percentage is 70.8333%.

Does 1/3 plus 3/8 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.708333...) because the denominator contains prime factors other than 2 and 5.