What is 5/7 plus 8/9? (Answer: 101/63)

Exact Answer

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Problem: What is 5/7 plus 8/9?
Formula / Expression: 5/7 + 8/9
Final Answer: 1 38/63 (101/63)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 7 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 7 × 9 = 63.
Working: LCD(7, 9) = 63

Step 2: Convert to Equivalent Fractions with Common Denominator 63
Multiply the numerator and denominator of 5/7 by 9, and multiply the numerator and denominator of 8/9 by 7 so both fractions share the common base 63.
Working: 5 × 9/7 × 9 = 45/63 and 8 × 7/9 × 7 = 56/63

Step 3: Add the Numerators
Now add the numerators (45 + 56 = 101) and keep the common denominator 63 unchanged.
Working: 45 + 56/63 = 101/63

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 101 and 63 is 1, confirming that 101/63 cannot be reduced further—it is already in its simplest irreducible form.
Working: 101/63

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (101) is greater than the denominator (63), divide 101 by 63: it goes in 1 whole time(s) with a remainder of 38, giving the mixed number 1 38/63.
Working: 101/63 = 1 38/63

Step 6: Decimal & Percentage Representation
Dividing the numerator 101 by denominator 63 produces a repeating decimal (approximately 1.603175, or 160.3175%).
Working: 101 ÷ 63 = 1.603175 (160.3175%)

Key Values:
- Simplified Fraction: 101/63
- Mixed Number Form: 1 38/63
- Decimal Value: 1.603175
- Percentage: 160.3175%

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Solved with FractionsCalc:
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5/7 + 8/9 = 101/63

Simplified Fraction

101/63

Mixed Number

1 38/63

Decimal Value

1.603175

Percentage

160.3175%

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

Step 1

Find the Least Common Denominator (LCD)

The denominators 7 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 7 × 9 = 63.

LCD(7, 9) = 63

Step 2

Convert to Equivalent Fractions with Common Denominator 63

Multiply the numerator and denominator of 5/7 by 9, and multiply the numerator and denominator of 8/9 by 7 so both fractions share the common base 63.

5 × 9/7 × 9 = 45/63 and 8 × 7/9 × 7 = 56/63

Step 3

Add the Numerators

Now add the numerators (45 + 56 = 101) and keep the common denominator 63 unchanged.

45 + 56/63 = 101/63

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 101 and 63 is 1, confirming that 101/63 cannot be reduced further—it is already in its simplest irreducible form.

101/63

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (101) is greater than the denominator (63), divide 101 by 63: it goes in 1 whole time(s) with a remainder of 38, giving the mixed number 1 38/63.

101/63 = 138/63

Step 6

Decimal & Percentage Representation

Dividing the numerator 101 by denominator 63 produces a repeating decimal (approximately 1.603175, or 160.3175%).

101 ÷ 63 = 1.603175 (160.3175%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`101/63`
Mixed Number Form	`1 38/63`
Decimal Form	`1.603175`
Percentage	`160.3175%`

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Frequently Asked Questions

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

5/7 + 8/9 in simplest fraction form is 101/63 (or 1 38/63 as a mixed number).

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

5/7 + 8/9 converted to a decimal is 1.603175.

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

5/7 + 8/9 expressed as a percentage is 160.3175%.

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

Because the numerator is greater than the denominator, the improper fraction 101/63 can be written as the mixed number 1 38/63.

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

It results in a repeating decimal (approximately 1.603175...) because the denominator contains prime factors other than 2 and 5.