What is 3/8 plus 5/6? (Answer: 29/24)

Exact Answer

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Problem: What is 3/8 plus 5/6?
Formula / Expression: 3/8 + 5/6
Final Answer: 1 5/24 (29/24)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 8 and 6 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 24 (which is smaller than their product 8 × 6 = 48, keeping the calculation simpler).
Working: LCD(8, 6) = 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 5/6 by 4 so both fractions share the common base 24.
Working: 3 × 3/8 × 3 = 9/24 and 5 × 4/6 × 4 = 20/24

Step 3: Add the Numerators
Now add the numerators (9 + 20 = 29) and keep the common denominator 24 unchanged.
Working: 9 + 20/24 = 29/24

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 29 and 24 is 1, confirming that 29/24 cannot be reduced further—it is already in its simplest irreducible form.
Working: 29/24

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (29) is greater than the denominator (24), divide 29 by 24: it goes in 1 whole time(s) with a remainder of 5, giving the mixed number 1 5/24.
Working: 29/24 = 1 5/24

Step 6: Decimal & Percentage Representation
Dividing the numerator 29 by denominator 24 produces a repeating decimal (approximately 1.208333, or 120.8333%).
Working: 29 ÷ 24 = 1.208333 (120.8333%)

Key Values:
- Simplified Fraction: 29/24
- Mixed Number Form: 1 5/24
- Decimal Value: 1.208333
- Percentage: 120.8333%

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Solved with FractionsCalc:
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3/8 + 5/6 = 29/24

Simplified Fraction

29/24

Mixed Number

1 5/24

Decimal Value

1.208333

Percentage

120.8333%

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Step-by-Step Solution: 3/8 + 5/6

Step 1

Find the Least Common Denominator (LCD)

The denominators 8 and 6 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 24 (which is smaller than their product 8 × 6 = 48, keeping the calculation simpler).

LCD(8, 6) = 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 5/6 by 4 so both fractions share the common base 24.

3 × 3/8 × 3 = 9/24 and 5 × 4/6 × 4 = 20/24

Step 3

Add the Numerators

Now add the numerators (9 + 20 = 29) and keep the common denominator 24 unchanged.

9 + 20/24 = 29/24

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 29 and 24 is 1, confirming that 29/24 cannot be reduced further—it is already in its simplest irreducible form.

29/24

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (29) is greater than the denominator (24), divide 29 by 24: it goes in 1 whole time(s) with a remainder of 5, giving the mixed number 1 5/24.

29/24 = 15/24

Step 6

Decimal & Percentage Representation

Dividing the numerator 29 by denominator 24 produces a repeating decimal (approximately 1.208333, or 120.8333%).

29 ÷ 24 = 1.208333 (120.8333%)

Visual Representation

The diagram below illustrates 3/8 plus 5/6 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`29/24`
Mixed Number Form	`1 5/24`
Decimal Form	`1.208333`
Percentage	`120.8333%`

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Frequently Asked Questions

What is 3/8 plus 5/6 as a fraction?

3/8 + 5/6 in simplest fraction form is 29/24 (or 1 5/24 as a mixed number).

What is 3/8 plus 5/6 as a decimal?

3/8 + 5/6 converted to a decimal is 1.208333.

What is 3/8 plus 5/6 as a percentage?

3/8 + 5/6 expressed as a percentage is 120.8333%.

How do you write 3/8 plus 5/6 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 29/24 can be written as the mixed number 1 5/24.

Does 3/8 plus 5/6 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.208333...) because the denominator contains prime factors other than 2 and 5.