What is 6/9 plus 9/10? (Answer: 47/30)

Exact Answer

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Problem: What is 6/9 plus 9/10?
Formula / Expression: 6/9 + 9/10
Final Answer: 1 17/30 (47/30)
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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 6/9 by 10, and multiply the numerator and denominator of 9/10 by 9 so both fractions share the common base 90.
Working: 6 × 10/9 × 10 = 60/90 and 9 × 9/10 × 9 = 81/90

Step 3: Add the Numerators
Now add the numerators (60 + 81 = 141) and keep the common denominator 90 unchanged.
Working: 60 + 81/90 = 141/90

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 141 and 90, which is 3. Divide both the numerator and denominator by 3.
Working: 141 ÷ 3/90 ÷ 3 = 47/30

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (47) is greater than the denominator (30), divide 47 by 30: it goes in 1 whole time(s) with a remainder of 17, giving the mixed number 1 17/30.
Working: 47/30 = 1 17/30

Step 6: Decimal & Percentage Representation
Dividing the numerator 47 by denominator 30 produces a repeating decimal (approximately 1.566667, or 156.6667%).
Working: 47 ÷ 30 = 1.566667 (156.6667%)

Key Values:
- Simplified Fraction: 47/30
- Mixed Number Form: 1 17/30
- Decimal Value: 1.566667
- Percentage: 156.6667%

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Solved with FractionsCalc:
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6/9 + 9/10 = 47/30

Simplified Fraction

47/30

Mixed Number

1 17/30

Decimal Value

1.566667

Percentage

156.6667%

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Step-by-Step Solution: 6/9 + 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 6/9 by 10, and multiply the numerator and denominator of 9/10 by 9 so both fractions share the common base 90.

6 × 10/9 × 10 = 60/90 and 9 × 9/10 × 9 = 81/90

Step 3

Add the Numerators

Now add the numerators (60 + 81 = 141) and keep the common denominator 90 unchanged.

60 + 81/90 = 141/90

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 141 and 90, which is 3. Divide both the numerator and denominator by 3.

141 ÷ 3/90 ÷ 3 = 47/30

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (47) is greater than the denominator (30), divide 47 by 30: it goes in 1 whole time(s) with a remainder of 17, giving the mixed number 1 17/30.

47/30 = 117/30

Step 6

Decimal & Percentage Representation

Dividing the numerator 47 by denominator 30 produces a repeating decimal (approximately 1.566667, or 156.6667%).

47 ÷ 30 = 1.566667 (156.6667%)

Visual Representation

The diagram below illustrates 6/9 plus 9/10 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`47/30`
Mixed Number Form	`1 17/30`
Decimal Form	`1.566667`
Percentage	`156.6667%`

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Frequently Asked Questions

What is 6/9 plus 9/10 as a fraction?

6/9 + 9/10 in simplest fraction form is 47/30 (or 1 17/30 as a mixed number).

What is 6/9 plus 9/10 as a decimal?

6/9 + 9/10 converted to a decimal is 1.566667.

What is 6/9 plus 9/10 as a percentage?

6/9 + 9/10 expressed as a percentage is 156.6667%.

How do you write 6/9 plus 9/10 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 47/30 can be written as the mixed number 1 17/30.

Does 6/9 plus 9/10 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.566667...) because the denominator contains prime factors other than 2 and 5.