What is 3/4 plus 9/12?
3/4 plus 9/12 equals 3/2 (or 1 1/2 as a mixed number) (or 1.5 in decimal form). Learn the step-by-step solution to add 3/4 and 9/12 using Least Common Denominator and simplification.
Exact Answer
3/4 + 9/12 = 3/2
Simplified Fraction
3/2
Mixed Number
1 1/2
Decimal Value
1.5
Percentage
150%
Step-by-Step Solution: 3/4 + 9/12
Step 1
Find the Least Common Denominator (LCD)
Notice that 12 is an exact multiple of 4 (4 × 3 = 12). The Least Common Denominator (LCD) is simply 12, meaning we only need to scale one fraction.
LCD(4, 12) = 12
Step 2
Convert to Equivalent Fractions with Common Denominator 12
Multiply the numerator and denominator of 3/4 by 3, and multiply the numerator and denominator of 9/12 by 1 so both fractions share the common base 12.
3 × 3/4 × 3 = 9/12 and 9 × 1/12 × 1 = 9/12
Step 3
Add the Numerators
Now add the numerators (9 + 9 = 18) and keep the common denominator 12 unchanged.
9 + 9/12 = 18/12
Step 4
Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 18 and 12, which is 6. Divide both the numerator and denominator by 6.
18 ÷ 6/12 ÷ 6 = 3/2
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (3) is greater than the denominator (2), divide 3 by 2: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/2.
3/2 = 11/2
Step 6
Decimal & Percentage Representation
Dividing the numerator 3 by denominator 2 yields an exact terminating decimal of 1.5 (or 150%).
3 ÷ 2 = 1.5 (150%)
Visual Representation
The diagram below illustrates 3/4 plus 9/12 visually:
+
=
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 3/2 |
| Mixed Number Form | 1 1/2 |
| Decimal Form | 1.5 |
| Percentage | 150% |
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Frequently Asked Questions
What is 3/4 plus 9/12 as a fraction?
3/4 + 9/12 in simplest fraction form is 3/2 (or 1 1/2 as a mixed number).
What is 3/4 plus 9/12 as a decimal?
3/4 + 9/12 converted to a decimal is 1.5.
What is 3/4 plus 9/12 as a percentage?
3/4 + 9/12 expressed as a percentage is 150%.
How do you write 3/4 plus 9/12 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 3/2 can be written as the mixed number 1 1/2.
Does 3/4 plus 9/12 result in a terminating or repeating decimal?
It results in an exact terminating decimal (1.5) because the denominator in simplest terms contains only prime factors 2 and/or 5.