What is 4/9 plus 5/8? (Answer: 77/72)

Exact Answer

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Problem: What is 4/9 plus 5/8?
Formula / Expression: 4/9 + 5/8
Final Answer: 1 5/72 (77/72)
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 72
Multiply the numerator and denominator of 4/9 by 8, and multiply the numerator and denominator of 5/8 by 9 so both fractions share the common base 72.
Working: 4 × 8/9 × 8 = 32/72 and 5 × 9/8 × 9 = 45/72

Step 3: Add the Numerators
Now add the numerators (32 + 45 = 77) and keep the common denominator 72 unchanged.
Working: 32 + 45/72 = 77/72

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 77 and 72 is 1, confirming that 77/72 cannot be reduced further—it is already in its simplest irreducible form.
Working: 77/72

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (77) is greater than the denominator (72), divide 77 by 72: it goes in 1 whole time(s) with a remainder of 5, giving the mixed number 1 5/72.
Working: 77/72 = 1 5/72

Step 6: Decimal & Percentage Representation
Dividing the numerator 77 by denominator 72 produces a repeating decimal (approximately 1.069444, or 106.9444%).
Working: 77 ÷ 72 = 1.069444 (106.9444%)

Key Values:
- Simplified Fraction: 77/72
- Mixed Number Form: 1 5/72
- Decimal Value: 1.069444
- Percentage: 106.9444%

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Solved with FractionsCalc:
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4/9 + 5/8 = 77/72

Simplified Fraction

77/72

Mixed Number

1 5/72

Decimal Value

1.069444

Percentage

106.9444%

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Step-by-Step Solution: 4/9 + 5/8

Step 1

Find the Least Common Denominator (LCD)

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

LCD(9, 8) = 72

Step 2

Convert to Equivalent Fractions with Common Denominator 72

Multiply the numerator and denominator of 4/9 by 8, and multiply the numerator and denominator of 5/8 by 9 so both fractions share the common base 72.

4 × 8/9 × 8 = 32/72 and 5 × 9/8 × 9 = 45/72

Step 3

Add the Numerators

Now add the numerators (32 + 45 = 77) and keep the common denominator 72 unchanged.

32 + 45/72 = 77/72

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 77 and 72 is 1, confirming that 77/72 cannot be reduced further—it is already in its simplest irreducible form.

77/72

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (77) is greater than the denominator (72), divide 77 by 72: it goes in 1 whole time(s) with a remainder of 5, giving the mixed number 1 5/72.

77/72 = 15/72

Step 6

Decimal & Percentage Representation

Dividing the numerator 77 by denominator 72 produces a repeating decimal (approximately 1.069444, or 106.9444%).

77 ÷ 72 = 1.069444 (106.9444%)

Visual Representation

The diagram below illustrates 4/9 plus 5/8 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`77/72`
Mixed Number Form	`1 5/72`
Decimal Form	`1.069444`
Percentage	`106.9444%`

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Frequently Asked Questions

What is 4/9 plus 5/8 as a fraction?

4/9 + 5/8 in simplest fraction form is 77/72 (or 1 5/72 as a mixed number).

What is 4/9 plus 5/8 as a decimal?

4/9 + 5/8 converted to a decimal is 1.069444.

What is 4/9 plus 5/8 as a percentage?

4/9 + 5/8 expressed as a percentage is 106.9444%.

How do you write 4/9 plus 5/8 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 77/72 can be written as the mixed number 1 5/72.

Does 4/9 plus 5/8 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.069444...) because the denominator contains prime factors other than 2 and 5.