What is 5/9 plus 8/10? (Answer: 61/45)

Exact Answer

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Problem: What is 5/9 plus 8/10?
Formula / Expression: 5/9 + 8/10
Final Answer: 1 16/45 (61/45)
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 90
Multiply the numerator and denominator of 5/9 by 10, and multiply the numerator and denominator of 8/10 by 9 so both fractions share the common base 90.
Working: 5 × 10/9 × 10 = 50/90 and 8 × 9/10 × 9 = 72/90

Step 3: Add the Numerators
Now add the numerators (50 + 72 = 122) and keep the common denominator 90 unchanged.
Working: 50 + 72/90 = 122/90

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 122 and 90, which is 2. Divide both the numerator and denominator by 2.
Working: 122 ÷ 2/90 ÷ 2 = 61/45

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (61) is greater than the denominator (45), divide 61 by 45: it goes in 1 whole time(s) with a remainder of 16, giving the mixed number 1 16/45.
Working: 61/45 = 1 16/45

Step 6: Decimal & Percentage Representation
Dividing the numerator 61 by denominator 45 produces a repeating decimal (approximately 1.355556, or 135.5556%).
Working: 61 ÷ 45 = 1.355556 (135.5556%)

Key Values:
- Simplified Fraction: 61/45
- Mixed Number Form: 1 16/45
- Decimal Value: 1.355556
- Percentage: 135.5556%

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Solved with FractionsCalc:
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5/9 + 8/10 = 61/45

Simplified Fraction

61/45

Mixed Number

1 16/45

Decimal Value

1.355556

Percentage

135.5556%

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Step-by-Step Solution: 5/9 + 8/10

Step 1

Find the Least Common Denominator (LCD)

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

LCD(9, 10) = 90

Step 2

Convert to Equivalent Fractions with Common Denominator 90

Multiply the numerator and denominator of 5/9 by 10, and multiply the numerator and denominator of 8/10 by 9 so both fractions share the common base 90.

5 × 10/9 × 10 = 50/90 and 8 × 9/10 × 9 = 72/90

Step 3

Add the Numerators

Now add the numerators (50 + 72 = 122) and keep the common denominator 90 unchanged.

50 + 72/90 = 122/90

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 122 and 90, which is 2. Divide both the numerator and denominator by 2.

122 ÷ 2/90 ÷ 2 = 61/45

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (61) is greater than the denominator (45), divide 61 by 45: it goes in 1 whole time(s) with a remainder of 16, giving the mixed number 1 16/45.

61/45 = 116/45

Step 6

Decimal & Percentage Representation

Dividing the numerator 61 by denominator 45 produces a repeating decimal (approximately 1.355556, or 135.5556%).

61 ÷ 45 = 1.355556 (135.5556%)

Visual Representation

The diagram below illustrates 5/9 plus 8/10 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`61/45`
Mixed Number Form	`1 16/45`
Decimal Form	`1.355556`
Percentage	`135.5556%`

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Frequently Asked Questions

What is 5/9 plus 8/10 as a fraction?

5/9 + 8/10 in simplest fraction form is 61/45 (or 1 16/45 as a mixed number).

What is 5/9 plus 8/10 as a decimal?

5/9 + 8/10 converted to a decimal is 1.355556.

What is 5/9 plus 8/10 as a percentage?

5/9 + 8/10 expressed as a percentage is 135.5556%.

How do you write 5/9 plus 8/10 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 61/45 can be written as the mixed number 1 16/45.

Does 5/9 plus 8/10 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.355556...) because the denominator contains prime factors other than 2 and 5.