What is 4/5 plus 8/9?
4/5 plus 8/9 equals 76/45 (or 1 31/45 as a mixed number) (or 1.688889 in decimal form). Learn the step-by-step solution to add 4/5 and 8/9 using Least Common Denominator and simplification.
Exact Answer
4/5 + 8/9 = 76/45
Simplified Fraction
76/45
Mixed Number
1 31/45
Decimal Value
1.688889
Percentage
168.8889%
Step-by-Step Solution: 4/5 + 8/9
Step 1
Find the Least Common Denominator (LCD)
The denominators 5 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 5 × 9 = 45.
LCD(5, 9) = 45
Step 2
Convert to Equivalent Fractions with Common Denominator 45
Multiply the numerator and denominator of 4/5 by 9, and multiply the numerator and denominator of 8/9 by 5 so both fractions share the common base 45.
4 × 9/5 × 9 = 36/45 and 8 × 5/9 × 5 = 40/45
Step 3
Add the Numerators
Now add the numerators (36 + 40 = 76) and keep the common denominator 45 unchanged.
36 + 40/45 = 76/45
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 76 and 45 is 1, confirming that 76/45 cannot be reduced further—it is already in its simplest irreducible form.
76/45
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (76) is greater than the denominator (45), divide 76 by 45: it goes in 1 whole time(s) with a remainder of 31, giving the mixed number 1 31/45.
76/45 = 131/45
Step 6
Decimal & Percentage Representation
Dividing the numerator 76 by denominator 45 produces a repeating decimal (approximately 1.688889, or 168.8889%).
76 ÷ 45 = 1.688889 (168.8889%)
Visual Representation
The diagram below illustrates 4/5 plus 8/9 visually:
+
=
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 76/45 |
| Mixed Number Form | 1 31/45 |
| Decimal Form | 1.688889 |
| Percentage | 168.8889% |
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Frequently Asked Questions
What is 4/5 plus 8/9 as a fraction?
4/5 + 8/9 in simplest fraction form is 76/45 (or 1 31/45 as a mixed number).
What is 4/5 plus 8/9 as a decimal?
4/5 + 8/9 converted to a decimal is 1.688889.
What is 4/5 plus 8/9 as a percentage?
4/5 + 8/9 expressed as a percentage is 168.8889%.
How do you write 4/5 plus 8/9 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 76/45 can be written as the mixed number 1 31/45.
Does 4/5 plus 8/9 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.688889...) because the denominator contains prime factors other than 2 and 5.