What is 4/10 plus 4/9? (Answer: 38/45)

Exact Answer

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Problem: What is 4/10 plus 4/9?
Formula / Expression: 4/10 + 4/9
Final Answer: 38/45
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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 4/10 by 9, and multiply the numerator and denominator of 4/9 by 10 so both fractions share the common base 90.
Working: 4 × 9/10 × 9 = 36/90 and 4 × 10/9 × 10 = 40/90

Step 3: Add the Numerators
Now add the numerators (36 + 40 = 76) and keep the common denominator 90 unchanged.
Working: 36 + 40/90 = 76/90

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 76 and 90, which is 2. Divide both the numerator and denominator by 2.
Working: 76 ÷ 2/90 ÷ 2 = 38/45

Step 5: Decimal & Percentage Representation
Dividing the numerator 38 by denominator 45 produces a repeating decimal (approximately 0.844444, or 84.4444%).
Working: 38 ÷ 45 = 0.844444 (84.4444%)

Key Values:
- Simplified Fraction: 38/45
- Mixed Number Form: 38/45
- Decimal Value: 0.844444
- Percentage: 84.4444%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-4-10-plus-4-9/
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4/10 + 4/9 = 38/45

Simplified Fraction

38/45

Mixed Number

Proper (38/45)

Decimal Value

0.844444

Percentage

84.4444%

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

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 4/10 by 9, and multiply the numerator and denominator of 4/9 by 10 so both fractions share the common base 90.

4 × 9/10 × 9 = 36/90 and 4 × 10/9 × 10 = 40/90

Step 3

Add the Numerators

Now add the numerators (36 + 40 = 76) and keep the common denominator 90 unchanged.

36 + 40/90 = 76/90

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 76 and 90, which is 2. Divide both the numerator and denominator by 2.

76 ÷ 2/90 ÷ 2 = 38/45

Step 5

Decimal & Percentage Representation

Dividing the numerator 38 by denominator 45 produces a repeating decimal (approximately 0.844444, or 84.4444%).

38 ÷ 45 = 0.844444 (84.4444%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`38/45`
Mixed Number Form	`38/45`
Decimal Form	`0.844444`
Percentage	`84.4444%`

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Frequently Asked Questions

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

4/10 + 4/9 in simplest fraction form is 38/45.

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

4/10 + 4/9 converted to a decimal is 0.844444.

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

4/10 + 4/9 expressed as a percentage is 84.4444%.

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

It results in a repeating decimal (approximately 0.844444...) because the denominator contains prime factors other than 2 and 5.