What is 3/9 plus 8/10? (Answer: 17/15)

Exact Answer

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Problem: What is 3/9 plus 8/10?
Formula / Expression: 3/9 + 8/10
Final Answer: 1 2/15 (17/15)
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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 3/9 by 10, and multiply the numerator and denominator of 8/10 by 9 so both fractions share the common base 90.
Working: 3 × 10/9 × 10 = 30/90 and 8 × 9/10 × 9 = 72/90

Step 3: Add the Numerators
Now add the numerators (30 + 72 = 102) and keep the common denominator 90 unchanged.
Working: 30 + 72/90 = 102/90

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 102 and 90, which is 6. Divide both the numerator and denominator by 6.
Working: 102 ÷ 6/90 ÷ 6 = 17/15

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (17) is greater than the denominator (15), divide 17 by 15: it goes in 1 whole time(s) with a remainder of 2, giving the mixed number 1 2/15.
Working: 17/15 = 1 2/15

Step 6: Decimal & Percentage Representation
Dividing the numerator 17 by denominator 15 produces a repeating decimal (approximately 1.133333, or 113.3333%).
Working: 17 ÷ 15 = 1.133333 (113.3333%)

Key Values:
- Simplified Fraction: 17/15
- Mixed Number Form: 1 2/15
- Decimal Value: 1.133333
- Percentage: 113.3333%

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Solved with FractionsCalc:
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3/9 + 8/10 = 17/15

Simplified Fraction

17/15

Mixed Number

1 2/15

Decimal Value

1.133333

Percentage

113.3333%

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Step-by-Step Solution: 3/9 + 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 3/9 by 10, and multiply the numerator and denominator of 8/10 by 9 so both fractions share the common base 90.

3 × 10/9 × 10 = 30/90 and 8 × 9/10 × 9 = 72/90

Step 3

Add the Numerators

Now add the numerators (30 + 72 = 102) and keep the common denominator 90 unchanged.

30 + 72/90 = 102/90

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 102 and 90, which is 6. Divide both the numerator and denominator by 6.

102 ÷ 6/90 ÷ 6 = 17/15

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (17) is greater than the denominator (15), divide 17 by 15: it goes in 1 whole time(s) with a remainder of 2, giving the mixed number 1 2/15.

17/15 = 12/15

Step 6

Decimal & Percentage Representation

Dividing the numerator 17 by denominator 15 produces a repeating decimal (approximately 1.133333, or 113.3333%).

17 ÷ 15 = 1.133333 (113.3333%)

Visual Representation

The diagram below illustrates 3/9 plus 8/10 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`17/15`
Mixed Number Form	`1 2/15`
Decimal Form	`1.133333`
Percentage	`113.3333%`

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Frequently Asked Questions

What is 3/9 plus 8/10 as a fraction?

3/9 + 8/10 in simplest fraction form is 17/15 (or 1 2/15 as a mixed number).

What is 3/9 plus 8/10 as a decimal?

3/9 + 8/10 converted to a decimal is 1.133333.

What is 3/9 plus 8/10 as a percentage?

3/9 + 8/10 expressed as a percentage is 113.3333%.

How do you write 3/9 plus 8/10 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 17/15 can be written as the mixed number 1 2/15.

Does 3/9 plus 8/10 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.133333...) because the denominator contains prime factors other than 2 and 5.