What is 5/8 plus 2/3? (Answer: 31/24)

Exact Answer

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Problem: What is 5/8 plus 2/3?
Formula / Expression: 5/8 + 2/3
Final Answer: 1 7/24 (31/24)
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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 5/8 by 3, and multiply the numerator and denominator of 2/3 by 8 so both fractions share the common base 24.
Working: 5 × 3/8 × 3 = 15/24 and 2 × 8/3 × 8 = 16/24

Step 3: Add the Numerators
Now add the numerators (15 + 16 = 31) and keep the common denominator 24 unchanged.
Working: 15 + 16/24 = 31/24

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 31 and 24 is 1, confirming that 31/24 cannot be reduced further—it is already in its simplest irreducible form.
Working: 31/24

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (31) is greater than the denominator (24), divide 31 by 24: it goes in 1 whole time(s) with a remainder of 7, giving the mixed number 1 7/24.
Working: 31/24 = 1 7/24

Step 6: Decimal & Percentage Representation
Dividing the numerator 31 by denominator 24 produces a repeating decimal (approximately 1.291667, or 129.1667%).
Working: 31 ÷ 24 = 1.291667 (129.1667%)

Key Values:
- Simplified Fraction: 31/24
- Mixed Number Form: 1 7/24
- Decimal Value: 1.291667
- Percentage: 129.1667%

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Solved with FractionsCalc:
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5/8 + 2/3 = 31/24

Simplified Fraction

31/24

Mixed Number

1 7/24

Decimal Value

1.291667

Percentage

129.1667%

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Step-by-Step Solution: 5/8 + 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 5/8 by 3, and multiply the numerator and denominator of 2/3 by 8 so both fractions share the common base 24.

5 × 3/8 × 3 = 15/24 and 2 × 8/3 × 8 = 16/24

Step 3

Add the Numerators

Now add the numerators (15 + 16 = 31) and keep the common denominator 24 unchanged.

15 + 16/24 = 31/24

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 31 and 24 is 1, confirming that 31/24 cannot be reduced further—it is already in its simplest irreducible form.

31/24

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (31) is greater than the denominator (24), divide 31 by 24: it goes in 1 whole time(s) with a remainder of 7, giving the mixed number 1 7/24.

31/24 = 17/24

Step 6

Decimal & Percentage Representation

Dividing the numerator 31 by denominator 24 produces a repeating decimal (approximately 1.291667, or 129.1667%).

31 ÷ 24 = 1.291667 (129.1667%)

Visual Representation

The diagram below illustrates 5/8 plus 2/3 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`31/24`
Mixed Number Form	`1 7/24`
Decimal Form	`1.291667`
Percentage	`129.1667%`

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Frequently Asked Questions

What is 5/8 plus 2/3 as a fraction?

5/8 + 2/3 in simplest fraction form is 31/24 (or 1 7/24 as a mixed number).

What is 5/8 plus 2/3 as a decimal?

5/8 + 2/3 converted to a decimal is 1.291667.

What is 5/8 plus 2/3 as a percentage?

5/8 + 2/3 expressed as a percentage is 129.1667%.

How do you write 5/8 plus 2/3 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 31/24 can be written as the mixed number 1 7/24.

Does 5/8 plus 2/3 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.291667...) because the denominator contains prime factors other than 2 and 5.