What is 3/12 plus 7/9?
3/12 plus 7/9 equals 37/36 (or 1 1/36 as a mixed number) (or 1.027778 in decimal form). Learn the step-by-step solution to add 3/12 and 7/9 using Least Common Denominator and simplification.
Exact Answer
3/12 + 7/9 = 37/36
Simplified Fraction
37/36
Mixed Number
1 1/36
Decimal Value
1.027778
Percentage
102.7778%
Step-by-Step Solution: 3/12 + 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 3/12 by 3, and multiply the numerator and denominator of 7/9 by 4 so both fractions share the common base 36.
3 × 3/12 × 3 = 9/36 and 7 × 4/9 × 4 = 28/36
Step 3
Add the Numerators
Now add the numerators (9 + 28 = 37) and keep the common denominator 36 unchanged.
9 + 28/36 = 37/36
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 37 and 36 is 1, confirming that 37/36 cannot be reduced further—it is already in its simplest irreducible form.
37/36
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (37) is greater than the denominator (36), divide 37 by 36: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/36.
37/36 = 11/36
Step 6
Decimal & Percentage Representation
Dividing the numerator 37 by denominator 36 produces a repeating decimal (approximately 1.027778, or 102.7778%).
37 ÷ 36 = 1.027778 (102.7778%)
Visual Representation
The diagram below illustrates 3/12 plus 7/9 visually:
+
=
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 37/36 |
| Mixed Number Form | 1 1/36 |
| Decimal Form | 1.027778 |
| Percentage | 102.7778% |
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Frequently Asked Questions
What is 3/12 plus 7/9 as a fraction?
3/12 + 7/9 in simplest fraction form is 37/36 (or 1 1/36 as a mixed number).
What is 3/12 plus 7/9 as a decimal?
3/12 + 7/9 converted to a decimal is 1.027778.
What is 3/12 plus 7/9 as a percentage?
3/12 + 7/9 expressed as a percentage is 102.7778%.
How do you write 3/12 plus 7/9 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 37/36 can be written as the mixed number 1 1/36.
Does 3/12 plus 7/9 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.027778...) because the denominator contains prime factors other than 2 and 5.