What is 3/10 plus 5/9? (Answer: 77/90)

Exact Answer

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Problem: What is 3/10 plus 5/9?
Formula / Expression: 3/10 + 5/9
Final Answer: 77/90
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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 3/10 by 9, and multiply the numerator and denominator of 5/9 by 10 so both fractions share the common base 90.
Working: 3 × 9/10 × 9 = 27/90 and 5 × 10/9 × 10 = 50/90

Step 3: Add the Numerators
Now add the numerators (27 + 50 = 77) and keep the common denominator 90 unchanged.
Working: 27 + 50/90 = 77/90

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 77 and 90 is 1, confirming that 77/90 cannot be reduced further—it is already in its simplest irreducible form.
Working: 77/90

Step 5: Decimal & Percentage Representation
Dividing the numerator 77 by denominator 90 produces a repeating decimal (approximately 0.855556, or 85.5556%).
Working: 77 ÷ 90 = 0.855556 (85.5556%)

Key Values:
- Simplified Fraction: 77/90
- Mixed Number Form: 77/90
- Decimal Value: 0.855556
- Percentage: 85.5556%

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Solved with FractionsCalc:
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3/10 + 5/9 = 77/90

Simplified Fraction

77/90

Mixed Number

Proper (77/90)

Decimal Value

0.855556

Percentage

85.5556%

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Step-by-Step Solution: 3/10 + 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 3/10 by 9, and multiply the numerator and denominator of 5/9 by 10 so both fractions share the common base 90.

3 × 9/10 × 9 = 27/90 and 5 × 10/9 × 10 = 50/90

Step 3

Add the Numerators

Now add the numerators (27 + 50 = 77) and keep the common denominator 90 unchanged.

27 + 50/90 = 77/90

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 77 and 90 is 1, confirming that 77/90 cannot be reduced further—it is already in its simplest irreducible form.

77/90

Step 5

Decimal & Percentage Representation

Dividing the numerator 77 by denominator 90 produces a repeating decimal (approximately 0.855556, or 85.5556%).

77 ÷ 90 = 0.855556 (85.5556%)

Visual Representation

The diagram below illustrates 3/10 plus 5/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`77/90`
Mixed Number Form	`77/90`
Decimal Form	`0.855556`
Percentage	`85.5556%`

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Frequently Asked Questions

What is 3/10 plus 5/9 as a fraction?

3/10 + 5/9 in simplest fraction form is 77/90.

What is 3/10 plus 5/9 as a decimal?

3/10 + 5/9 converted to a decimal is 0.855556.

What is 3/10 plus 5/9 as a percentage?

3/10 + 5/9 expressed as a percentage is 85.5556%.

Does 3/10 plus 5/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.855556...) because the denominator contains prime factors other than 2 and 5.