What is 3/8 plus 8/9? (Answer: 91/72)

Exact Answer

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Problem: What is 3/8 plus 8/9?
Formula / Expression: 3/8 + 8/9
Final Answer: 1 19/72 (91/72)
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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 8/9 by 8 so both fractions share the common base 72.
Working: 3 × 9/8 × 9 = 27/72 and 8 × 8/9 × 8 = 64/72

Step 3: Add the Numerators
Now add the numerators (27 + 64 = 91) and keep the common denominator 72 unchanged.
Working: 27 + 64/72 = 91/72

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 91 and 72 is 1, confirming that 91/72 cannot be reduced further—it is already in its simplest irreducible form.
Working: 91/72

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (91) is greater than the denominator (72), divide 91 by 72: it goes in 1 whole time(s) with a remainder of 19, giving the mixed number 1 19/72.
Working: 91/72 = 1 19/72

Step 6: Decimal & Percentage Representation
Dividing the numerator 91 by denominator 72 produces a repeating decimal (approximately 1.263889, or 126.3889%).
Working: 91 ÷ 72 = 1.263889 (126.3889%)

Key Values:
- Simplified Fraction: 91/72
- Mixed Number Form: 1 19/72
- Decimal Value: 1.263889
- Percentage: 126.3889%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-8-plus-8-9/
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3/8 + 8/9 = 91/72

Simplified Fraction

91/72

Mixed Number

1 19/72

Decimal Value

1.263889

Percentage

126.3889%

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

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 8/9 by 8 so both fractions share the common base 72.

3 × 9/8 × 9 = 27/72 and 8 × 8/9 × 8 = 64/72

Step 3

Add the Numerators

Now add the numerators (27 + 64 = 91) and keep the common denominator 72 unchanged.

27 + 64/72 = 91/72

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 91 and 72 is 1, confirming that 91/72 cannot be reduced further—it is already in its simplest irreducible form.

91/72

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (91) is greater than the denominator (72), divide 91 by 72: it goes in 1 whole time(s) with a remainder of 19, giving the mixed number 1 19/72.

91/72 = 119/72

Step 6

Decimal & Percentage Representation

Dividing the numerator 91 by denominator 72 produces a repeating decimal (approximately 1.263889, or 126.3889%).

91 ÷ 72 = 1.263889 (126.3889%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`91/72`
Mixed Number Form	`1 19/72`
Decimal Form	`1.263889`
Percentage	`126.3889%`

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Frequently Asked Questions

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

3/8 + 8/9 in simplest fraction form is 91/72 (or 1 19/72 as a mixed number).

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

3/8 + 8/9 converted to a decimal is 1.263889.

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

3/8 + 8/9 expressed as a percentage is 126.3889%.

How do you write 3/8 plus 8/9 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 91/72 can be written as the mixed number 1 19/72.

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

It results in a repeating decimal (approximately 1.263889...) because the denominator contains prime factors other than 2 and 5.