What is 5/10 plus 5/9? (Answer: 19/18)

Exact Answer

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Problem: What is 5/10 plus 5/9?
Formula / Expression: 5/10 + 5/9
Final Answer: 1 1/18 (19/18)
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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 5/10 by 9, and multiply the numerator and denominator of 5/9 by 10 so both fractions share the common base 90.
Working: 5 × 9/10 × 9 = 45/90 and 5 × 10/9 × 10 = 50/90

Step 3: Add the Numerators
Now add the numerators (45 + 50 = 95) and keep the common denominator 90 unchanged.
Working: 45 + 50/90 = 95/90

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 95 and 90, which is 5. Divide both the numerator and denominator by 5.
Working: 95 ÷ 5/90 ÷ 5 = 19/18

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (19) is greater than the denominator (18), divide 19 by 18: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/18.
Working: 19/18 = 1 1/18

Step 6: Decimal & Percentage Representation
Dividing the numerator 19 by denominator 18 produces a repeating decimal (approximately 1.055556, or 105.5556%).
Working: 19 ÷ 18 = 1.055556 (105.5556%)

Key Values:
- Simplified Fraction: 19/18
- Mixed Number Form: 1 1/18
- Decimal Value: 1.055556
- Percentage: 105.5556%

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Solved with FractionsCalc:
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5/10 + 5/9 = 19/18

Simplified Fraction

19/18

Mixed Number

1 1/18

Decimal Value

1.055556

Percentage

105.5556%

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

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

5 × 9/10 × 9 = 45/90 and 5 × 10/9 × 10 = 50/90

Step 3

Add the Numerators

Now add the numerators (45 + 50 = 95) and keep the common denominator 90 unchanged.

45 + 50/90 = 95/90

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 95 and 90, which is 5. Divide both the numerator and denominator by 5.

95 ÷ 5/90 ÷ 5 = 19/18

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (19) is greater than the denominator (18), divide 19 by 18: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/18.

19/18 = 11/18

Step 6

Decimal & Percentage Representation

Dividing the numerator 19 by denominator 18 produces a repeating decimal (approximately 1.055556, or 105.5556%).

19 ÷ 18 = 1.055556 (105.5556%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`19/18`
Mixed Number Form	`1 1/18`
Decimal Form	`1.055556`
Percentage	`105.5556%`

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Frequently Asked Questions

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

5/10 + 5/9 in simplest fraction form is 19/18 (or 1 1/18 as a mixed number).

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

5/10 + 5/9 converted to a decimal is 1.055556.

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

5/10 + 5/9 expressed as a percentage is 105.5556%.

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

Because the numerator is greater than the denominator, the improper fraction 19/18 can be written as the mixed number 1 1/18.

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

It results in a repeating decimal (approximately 1.055556...) because the denominator contains prime factors other than 2 and 5.