What is 3/9 plus 9/10? (Answer: 37/30)

Exact Answer

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Problem: What is 3/9 plus 9/10?
Formula / Expression: 3/9 + 9/10
Final Answer: 1 7/30 (37/30)
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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 3/9 by 10, and multiply the numerator and denominator of 9/10 by 9 so both fractions share the common base 90.
Working: 3 × 10/9 × 10 = 30/90 and 9 × 9/10 × 9 = 81/90

Step 3: Add the Numerators
Now add the numerators (30 + 81 = 111) and keep the common denominator 90 unchanged.
Working: 30 + 81/90 = 111/90

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 111 and 90, which is 3. Divide both the numerator and denominator by 3.
Working: 111 ÷ 3/90 ÷ 3 = 37/30

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (37) is greater than the denominator (30), divide 37 by 30: it goes in 1 whole time(s) with a remainder of 7, giving the mixed number 1 7/30.
Working: 37/30 = 1 7/30

Step 6: Decimal & Percentage Representation
Dividing the numerator 37 by denominator 30 produces a repeating decimal (approximately 1.233333, or 123.3333%).
Working: 37 ÷ 30 = 1.233333 (123.3333%)

Key Values:
- Simplified Fraction: 37/30
- Mixed Number Form: 1 7/30
- Decimal Value: 1.233333
- Percentage: 123.3333%

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Solved with FractionsCalc:
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3/9 + 9/10 = 37/30

Simplified Fraction

37/30

Mixed Number

1 7/30

Decimal Value

1.233333

Percentage

123.3333%

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

3 × 10/9 × 10 = 30/90 and 9 × 9/10 × 9 = 81/90

Step 3

Add the Numerators

Now add the numerators (30 + 81 = 111) and keep the common denominator 90 unchanged.

30 + 81/90 = 111/90

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 111 and 90, which is 3. Divide both the numerator and denominator by 3.

111 ÷ 3/90 ÷ 3 = 37/30

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (37) is greater than the denominator (30), divide 37 by 30: it goes in 1 whole time(s) with a remainder of 7, giving the mixed number 1 7/30.

37/30 = 17/30

Step 6

Decimal & Percentage Representation

Dividing the numerator 37 by denominator 30 produces a repeating decimal (approximately 1.233333, or 123.3333%).

37 ÷ 30 = 1.233333 (123.3333%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`37/30`
Mixed Number Form	`1 7/30`
Decimal Form	`1.233333`
Percentage	`123.3333%`

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Frequently Asked Questions

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

3/9 + 9/10 in simplest fraction form is 37/30 (or 1 7/30 as a mixed number).

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

3/9 + 9/10 converted to a decimal is 1.233333.

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

3/9 + 9/10 expressed as a percentage is 123.3333%.

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

Because the numerator is greater than the denominator, the improper fraction 37/30 can be written as the mixed number 1 7/30.

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

It results in a repeating decimal (approximately 1.233333...) because the denominator contains prime factors other than 2 and 5.