What is 5/8 plus 7/9? (Answer: 101/72)

Exact Answer

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Problem: What is 5/8 plus 7/9?
Formula / Expression: 5/8 + 7/9
Final Answer: 1 29/72 (101/72)
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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 7/9 by 8 so both fractions share the common base 72.
Working: 5 × 9/8 × 9 = 45/72 and 7 × 8/9 × 8 = 56/72

Step 3: Add the Numerators
Now add the numerators (45 + 56 = 101) and keep the common denominator 72 unchanged.
Working: 45 + 56/72 = 101/72

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 101 and 72 is 1, confirming that 101/72 cannot be reduced further—it is already in its simplest irreducible form.
Working: 101/72

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (101) is greater than the denominator (72), divide 101 by 72: it goes in 1 whole time(s) with a remainder of 29, giving the mixed number 1 29/72.
Working: 101/72 = 1 29/72

Step 6: Decimal & Percentage Representation
Dividing the numerator 101 by denominator 72 produces a repeating decimal (approximately 1.402778, or 140.2778%).
Working: 101 ÷ 72 = 1.402778 (140.2778%)

Key Values:
- Simplified Fraction: 101/72
- Mixed Number Form: 1 29/72
- Decimal Value: 1.402778
- Percentage: 140.2778%

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Solved with FractionsCalc:
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5/8 + 7/9 = 101/72

Simplified Fraction

101/72

Mixed Number

1 29/72

Decimal Value

1.402778

Percentage

140.2778%

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Step-by-Step Solution: 5/8 + 7/9

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 7/9 by 8 so both fractions share the common base 72.

5 × 9/8 × 9 = 45/72 and 7 × 8/9 × 8 = 56/72

Step 3

Add the Numerators

Now add the numerators (45 + 56 = 101) and keep the common denominator 72 unchanged.

45 + 56/72 = 101/72

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 101 and 72 is 1, confirming that 101/72 cannot be reduced further—it is already in its simplest irreducible form.

101/72

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (101) is greater than the denominator (72), divide 101 by 72: it goes in 1 whole time(s) with a remainder of 29, giving the mixed number 1 29/72.

101/72 = 129/72

Step 6

Decimal & Percentage Representation

Dividing the numerator 101 by denominator 72 produces a repeating decimal (approximately 1.402778, or 140.2778%).

101 ÷ 72 = 1.402778 (140.2778%)

Visual Representation

The diagram below illustrates 5/8 plus 7/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`101/72`
Mixed Number Form	`1 29/72`
Decimal Form	`1.402778`
Percentage	`140.2778%`

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Frequently Asked Questions

What is 5/8 plus 7/9 as a fraction?

5/8 + 7/9 in simplest fraction form is 101/72 (or 1 29/72 as a mixed number).

What is 5/8 plus 7/9 as a decimal?

5/8 + 7/9 converted to a decimal is 1.402778.

What is 5/8 plus 7/9 as a percentage?

5/8 + 7/9 expressed as a percentage is 140.2778%.

How do you write 5/8 plus 7/9 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 101/72 can be written as the mixed number 1 29/72.

Does 5/8 plus 7/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.402778...) because the denominator contains prime factors other than 2 and 5.