What is 4/9 plus 4/6?
4/9 plus 4/6 equals 10/9 (or 1 1/9 as a mixed number) (or 1.111111 in decimal form). Learn the step-by-step solution to add 4/9 and 4/6 using Least Common Denominator and simplification.
Exact Answer
4/9 + 4/6 = 10/9
Simplified Fraction
10/9
Mixed Number
1 1/9
Decimal Value
1.111111
Percentage
111.1111%
Step-by-Step Solution: 4/9 + 4/6
Step 1
Find the Least Common Denominator (LCD)
The denominators 9 and 6 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 18 (which is smaller than their product 9 × 6 = 54, keeping the calculation simpler).
LCD(9, 6) = 18
Step 2
Convert to Equivalent Fractions with Common Denominator 18
Multiply the numerator and denominator of 4/9 by 2, and multiply the numerator and denominator of 4/6 by 3 so both fractions share the common base 18.
4 × 2/9 × 2 = 8/18 and 4 × 3/6 × 3 = 12/18
Step 3
Add the Numerators
Now add the numerators (8 + 12 = 20) and keep the common denominator 18 unchanged.
8 + 12/18 = 20/18
Step 4
Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 20 and 18, which is 2. Divide both the numerator and denominator by 2.
20 ÷ 2/18 ÷ 2 = 10/9
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (10) is greater than the denominator (9), divide 10 by 9: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/9.
10/9 = 11/9
Step 6
Decimal & Percentage Representation
Dividing the numerator 10 by denominator 9 produces a repeating decimal (approximately 1.111111, or 111.1111%).
10 ÷ 9 = 1.111111 (111.1111%)
Visual Representation
The diagram below illustrates 4/9 plus 4/6 visually:
+
=
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 10/9 |
| Mixed Number Form | 1 1/9 |
| Decimal Form | 1.111111 |
| Percentage | 111.1111% |
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Frequently Asked Questions
What is 4/9 plus 4/6 as a fraction?
4/9 + 4/6 in simplest fraction form is 10/9 (or 1 1/9 as a mixed number).
What is 4/9 plus 4/6 as a decimal?
4/9 + 4/6 converted to a decimal is 1.111111.
What is 4/9 plus 4/6 as a percentage?
4/9 + 4/6 expressed as a percentage is 111.1111%.
How do you write 4/9 plus 4/6 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 10/9 can be written as the mixed number 1 1/9.
Does 4/9 plus 4/6 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.111111...) because the denominator contains prime factors other than 2 and 5.