What is 5/9 plus 9/10? (Answer: 131/90)

Exact Answer

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Problem: What is 5/9 plus 9/10?
Formula / Expression: 5/9 + 9/10
Final Answer: 1 41/90 (131/90)
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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 9/10 by 9 so both fractions share the common base 90.
Working: 5 × 10/9 × 10 = 50/90 and 9 × 9/10 × 9 = 81/90

Step 3: Add the Numerators
Now add the numerators (50 + 81 = 131) and keep the common denominator 90 unchanged.
Working: 50 + 81/90 = 131/90

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 131 and 90 is 1, confirming that 131/90 cannot be reduced further—it is already in its simplest irreducible form.
Working: 131/90

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (131) is greater than the denominator (90), divide 131 by 90: it goes in 1 whole time(s) with a remainder of 41, giving the mixed number 1 41/90.
Working: 131/90 = 1 41/90

Step 6: Decimal & Percentage Representation
Dividing the numerator 131 by denominator 90 produces a repeating decimal (approximately 1.455556, or 145.5556%).
Working: 131 ÷ 90 = 1.455556 (145.5556%)

Key Values:
- Simplified Fraction: 131/90
- Mixed Number Form: 1 41/90
- Decimal Value: 1.455556
- Percentage: 145.5556%

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Solved with FractionsCalc:
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5/9 + 9/10 = 131/90

Simplified Fraction

131/90

Mixed Number

1 41/90

Decimal Value

1.455556

Percentage

145.5556%

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

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 9/10 by 9 so both fractions share the common base 90.

5 × 10/9 × 10 = 50/90 and 9 × 9/10 × 9 = 81/90

Step 3

Add the Numerators

Now add the numerators (50 + 81 = 131) and keep the common denominator 90 unchanged.

50 + 81/90 = 131/90

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 131 and 90 is 1, confirming that 131/90 cannot be reduced further—it is already in its simplest irreducible form.

131/90

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (131) is greater than the denominator (90), divide 131 by 90: it goes in 1 whole time(s) with a remainder of 41, giving the mixed number 1 41/90.

131/90 = 141/90

Step 6

Decimal & Percentage Representation

Dividing the numerator 131 by denominator 90 produces a repeating decimal (approximately 1.455556, or 145.5556%).

131 ÷ 90 = 1.455556 (145.5556%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`131/90`
Mixed Number Form	`1 41/90`
Decimal Form	`1.455556`
Percentage	`145.5556%`

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Frequently Asked Questions

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

5/9 + 9/10 in simplest fraction form is 131/90 (or 1 41/90 as a mixed number).

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

5/9 + 9/10 converted to a decimal is 1.455556.

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

5/9 + 9/10 expressed as a percentage is 145.5556%.

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

Because the numerator is greater than the denominator, the improper fraction 131/90 can be written as the mixed number 1 41/90.

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

It results in a repeating decimal (approximately 1.455556...) because the denominator contains prime factors other than 2 and 5.