What is 3/8 plus 4/9? (Answer: 59/72)

Exact Answer

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Problem: What is 3/8 plus 4/9?
Formula / Expression: 3/8 + 4/9
Final Answer: 59/72
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 8 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 8 × 9 = 72.
Working: LCD(8, 9) = 72

Step 2: Convert to Equivalent Fractions with Common Denominator 72
Multiply the numerator and denominator of 3/8 by 9, and multiply the numerator and denominator of 4/9 by 8 so both fractions share the common base 72.
Working: 3 × 9/8 × 9 = 27/72 and 4 × 8/9 × 8 = 32/72

Step 3: Add the Numerators
Now add the numerators (27 + 32 = 59) and keep the common denominator 72 unchanged.
Working: 27 + 32/72 = 59/72

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 59 and 72 is 1, confirming that 59/72 cannot be reduced further—it is already in its simplest irreducible form.
Working: 59/72

Step 5: Decimal & Percentage Representation
Dividing the numerator 59 by denominator 72 produces a repeating decimal (approximately 0.819444, or 81.9444%).
Working: 59 ÷ 72 = 0.819444 (81.9444%)

Key Values:
- Simplified Fraction: 59/72
- Mixed Number Form: 59/72
- Decimal Value: 0.819444
- Percentage: 81.9444%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-8-plus-4-9/
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3/8 + 4/9 = 59/72

Simplified Fraction

59/72

Mixed Number

Proper (59/72)

Decimal Value

0.819444

Percentage

81.9444%

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Step-by-Step Solution: 3/8 + 4/9

Step 1

Find the Least Common Denominator (LCD)

The denominators 8 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 8 × 9 = 72.

LCD(8, 9) = 72

Step 2

Convert to Equivalent Fractions with Common Denominator 72

Multiply the numerator and denominator of 3/8 by 9, and multiply the numerator and denominator of 4/9 by 8 so both fractions share the common base 72.

3 × 9/8 × 9 = 27/72 and 4 × 8/9 × 8 = 32/72

Step 3

Add the Numerators

Now add the numerators (27 + 32 = 59) and keep the common denominator 72 unchanged.

27 + 32/72 = 59/72

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 59 and 72 is 1, confirming that 59/72 cannot be reduced further—it is already in its simplest irreducible form.

59/72

Step 5

Decimal & Percentage Representation

Dividing the numerator 59 by denominator 72 produces a repeating decimal (approximately 0.819444, or 81.9444%).

59 ÷ 72 = 0.819444 (81.9444%)

Visual Representation

The diagram below illustrates 3/8 plus 4/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`59/72`
Mixed Number Form	`59/72`
Decimal Form	`0.819444`
Percentage	`81.9444%`

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Frequently Asked Questions

What is 3/8 plus 4/9 as a fraction?

3/8 + 4/9 in simplest fraction form is 59/72.

What is 3/8 plus 4/9 as a decimal?

3/8 + 4/9 converted to a decimal is 0.819444.

What is 3/8 plus 4/9 as a percentage?

3/8 + 4/9 expressed as a percentage is 81.9444%.

Does 3/8 plus 4/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.819444...) because the denominator contains prime factors other than 2 and 5.