What is 8/10 plus 8/9? (Answer: 76/45)

Exact Answer

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Problem: What is 8/10 plus 8/9?
Formula / Expression: 8/10 + 8/9
Final Answer: 1 31/45 (76/45)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 10 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 10 × 9 = 90.
Working: LCD(10, 9) = 90

Step 2: Convert to Equivalent Fractions with Common Denominator 90
Multiply the numerator and denominator of 8/10 by 9, and multiply the numerator and denominator of 8/9 by 10 so both fractions share the common base 90.
Working: 8 × 9/10 × 9 = 72/90 and 8 × 10/9 × 10 = 80/90

Step 3: Add the Numerators
Now add the numerators (72 + 80 = 152) and keep the common denominator 90 unchanged.
Working: 72 + 80/90 = 152/90

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 152 and 90, which is 2. Divide both the numerator and denominator by 2.
Working: 152 ÷ 2/90 ÷ 2 = 76/45

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (76) is greater than the denominator (45), divide 76 by 45: it goes in 1 whole time(s) with a remainder of 31, giving the mixed number 1 31/45.
Working: 76/45 = 1 31/45

Step 6: Decimal & Percentage Representation
Dividing the numerator 76 by denominator 45 produces a repeating decimal (approximately 1.688889, or 168.8889%).
Working: 76 ÷ 45 = 1.688889 (168.8889%)

Key Values:
- Simplified Fraction: 76/45
- Mixed Number Form: 1 31/45
- Decimal Value: 1.688889
- Percentage: 168.8889%

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Solved with FractionsCalc:
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8/10 + 8/9 = 76/45

Simplified Fraction

76/45

Mixed Number

1 31/45

Decimal Value

1.688889

Percentage

168.8889%

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Step-by-Step Solution: 8/10 + 8/9

Step 1

Find the Least Common Denominator (LCD)

The denominators 10 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 10 × 9 = 90.

LCD(10, 9) = 90

Step 2

Convert to Equivalent Fractions with Common Denominator 90

Multiply the numerator and denominator of 8/10 by 9, and multiply the numerator and denominator of 8/9 by 10 so both fractions share the common base 90.

8 × 9/10 × 9 = 72/90 and 8 × 10/9 × 10 = 80/90

Step 3

Add the Numerators

Now add the numerators (72 + 80 = 152) and keep the common denominator 90 unchanged.

72 + 80/90 = 152/90

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 152 and 90, which is 2. Divide both the numerator and denominator by 2.

152 ÷ 2/90 ÷ 2 = 76/45

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (76) is greater than the denominator (45), divide 76 by 45: it goes in 1 whole time(s) with a remainder of 31, giving the mixed number 1 31/45.

76/45 = 131/45

Step 6

Decimal & Percentage Representation

Dividing the numerator 76 by denominator 45 produces a repeating decimal (approximately 1.688889, or 168.8889%).

76 ÷ 45 = 1.688889 (168.8889%)

Visual Representation

The diagram below illustrates 8/10 plus 8/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`76/45`
Mixed Number Form	`1 31/45`
Decimal Form	`1.688889`
Percentage	`168.8889%`

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Frequently Asked Questions

What is 8/10 plus 8/9 as a fraction?

8/10 + 8/9 in simplest fraction form is 76/45 (or 1 31/45 as a mixed number).

What is 8/10 plus 8/9 as a decimal?

8/10 + 8/9 converted to a decimal is 1.688889.

What is 8/10 plus 8/9 as a percentage?

8/10 + 8/9 expressed as a percentage is 168.8889%.

How do you write 8/10 plus 8/9 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 76/45 can be written as the mixed number 1 31/45.

Does 8/10 plus 8/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.688889...) because the denominator contains prime factors other than 2 and 5.