What is 4/12 plus 7/9?
4/12 plus 7/9 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 4/12 and 7/9 using Least Common Denominator and simplification.
Exact Answer
4/12 + 7/9 = 10/9
Simplified Fraction
10/9
Mixed Number
1 1/9
Decimal Value
1.111111
Percentage
111.1111%
Step-by-Step Solution: 4/12 + 7/9
Step 1
Find the Least Common Denominator (LCD)
The denominators 12 and 9 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 36 (which is smaller than their product 12 × 9 = 108, keeping the calculation simpler).
LCD(12, 9) = 36
Step 2
Convert to Equivalent Fractions with Common Denominator 36
Multiply the numerator and denominator of 4/12 by 3, and multiply the numerator and denominator of 7/9 by 4 so both fractions share the common base 36.
4 × 3/12 × 3 = 12/36 and 7 × 4/9 × 4 = 28/36
Step 3
Add the Numerators
Now add the numerators (12 + 28 = 40) and keep the common denominator 36 unchanged.
12 + 28/36 = 40/36
Step 4
Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 40 and 36, which is 4. Divide both the numerator and denominator by 4.
40 ÷ 4/36 ÷ 4 = 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 4/12 plus 7/9 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 4/12 plus 7/9 as a fraction?
4/12 + 7/9 in simplest fraction form is 10/9 (or 1 1/9 as a mixed number).
What is 4/12 plus 7/9 as a decimal?
4/12 + 7/9 converted to a decimal is 1.111111.
What is 4/12 plus 7/9 as a percentage?
4/12 + 7/9 expressed as a percentage is 111.1111%.
How do you write 4/12 plus 7/9 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 4/12 plus 7/9 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.