What is 3/9 plus 4/10? (Answer: 11/15)

Exact Answer

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Problem: What is 3/9 plus 4/10?
Formula / Expression: 3/9 + 4/10
Final Answer: 11/15
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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 4/10 by 9 so both fractions share the common base 90.
Working: 3 × 10/9 × 10 = 30/90 and 4 × 9/10 × 9 = 36/90

Step 3: Add the Numerators
Now add the numerators (30 + 36 = 66) and keep the common denominator 90 unchanged.
Working: 30 + 36/90 = 66/90

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 66 and 90, which is 6. Divide both the numerator and denominator by 6.
Working: 66 ÷ 6/90 ÷ 6 = 11/15

Step 5: Decimal & Percentage Representation
Dividing the numerator 11 by denominator 15 produces a repeating decimal (approximately 0.733333, or 73.3333%).
Working: 11 ÷ 15 = 0.733333 (73.3333%)

Key Values:
- Simplified Fraction: 11/15
- Mixed Number Form: 11/15
- Decimal Value: 0.733333
- Percentage: 73.3333%

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Solved with FractionsCalc:
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3/9 + 4/10 = 11/15

Simplified Fraction

11/15

Mixed Number

Proper (11/15)

Decimal Value

0.733333

Percentage

73.3333%

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Step-by-Step Solution: 3/9 + 4/10

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 4/10 by 9 so both fractions share the common base 90.

3 × 10/9 × 10 = 30/90 and 4 × 9/10 × 9 = 36/90

Step 3

Add the Numerators

Now add the numerators (30 + 36 = 66) and keep the common denominator 90 unchanged.

30 + 36/90 = 66/90

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 66 and 90, which is 6. Divide both the numerator and denominator by 6.

66 ÷ 6/90 ÷ 6 = 11/15

Step 5

Decimal & Percentage Representation

Dividing the numerator 11 by denominator 15 produces a repeating decimal (approximately 0.733333, or 73.3333%).

11 ÷ 15 = 0.733333 (73.3333%)

Visual Representation

The diagram below illustrates 3/9 plus 4/10 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`11/15`
Mixed Number Form	`11/15`
Decimal Form	`0.733333`
Percentage	`73.3333%`

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Frequently Asked Questions

What is 3/9 plus 4/10 as a fraction?

3/9 + 4/10 in simplest fraction form is 11/15.

What is 3/9 plus 4/10 as a decimal?

3/9 + 4/10 converted to a decimal is 0.733333.

What is 3/9 plus 4/10 as a percentage?

3/9 + 4/10 expressed as a percentage is 73.3333%.

Does 3/9 plus 4/10 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.733333...) because the denominator contains prime factors other than 2 and 5.