What is 5/8 plus 6/9? (Answer: 31/24)

Exact Answer

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Problem: What is 5/8 plus 6/9?
Formula / Expression: 5/8 + 6/9
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 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 8 × 9 = 72.
Working: LCD(8, 9) = 72

Step 2: Convert to Equivalent Fractions with Common Denominator 72
Multiply the numerator and denominator of 5/8 by 9, and multiply the numerator and denominator of 6/9 by 8 so both fractions share the common base 72.
Working: 5 × 9/8 × 9 = 45/72 and 6 × 8/9 × 8 = 48/72

Step 3: Add the Numerators
Now add the numerators (45 + 48 = 93) and keep the common denominator 72 unchanged.
Working: 45 + 48/72 = 93/72

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 93 and 72, which is 3. Divide both the numerator and denominator by 3.
Working: 93 ÷ 3/72 ÷ 3 = 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 + 6/9 = 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 + 6/9

Step 1

Find the Least Common Denominator (LCD)

The denominators 8 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 8 × 9 = 72.

LCD(8, 9) = 72

Step 2

Convert to Equivalent Fractions with Common Denominator 72

Multiply the numerator and denominator of 5/8 by 9, and multiply the numerator and denominator of 6/9 by 8 so both fractions share the common base 72.

5 × 9/8 × 9 = 45/72 and 6 × 8/9 × 8 = 48/72

Step 3

Add the Numerators

Now add the numerators (45 + 48 = 93) and keep the common denominator 72 unchanged.

45 + 48/72 = 93/72

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 93 and 72, which is 3. Divide both the numerator and denominator by 3.

93 ÷ 3/72 ÷ 3 = 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 6/9 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 6/9 as a fraction?

5/8 + 6/9 in simplest fraction form is 31/24 (or 1 7/24 as a mixed number).

What is 5/8 plus 6/9 as a decimal?

5/8 + 6/9 converted to a decimal is 1.291667.

What is 5/8 plus 6/9 as a percentage?

5/8 + 6/9 expressed as a percentage is 129.1667%.

How do you write 5/8 plus 6/9 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 6/9 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.