What is 4/8 plus 9/12?
4/8 plus 9/12 equals 5/4 (or 1 1/4 as a mixed number) (or 1.25 in decimal form). Learn the step-by-step solution to add 4/8 and 9/12 using Least Common Denominator and simplification.
Exact Answer
4/8 + 9/12 = 5/4
Simplified Fraction
5/4
Mixed Number
1 1/4
Decimal Value
1.25
Percentage
125%
Step-by-Step Solution: 4/8 + 9/12
Step 1
Find the Least Common Denominator (LCD)
The denominators 8 and 12 share a common factor (GCD = 4). Finding their Least Common Multiple gives an LCD of 24 (which is smaller than their product 8 × 12 = 96, keeping the calculation simpler).
LCD(8, 12) = 24
Step 2
Convert to Equivalent Fractions with Common Denominator 24
Multiply the numerator and denominator of 4/8 by 3, and multiply the numerator and denominator of 9/12 by 2 so both fractions share the common base 24.
4 × 3/8 × 3 = 12/24 and 9 × 2/12 × 2 = 18/24
Step 3
Add the Numerators
Now add the numerators (12 + 18 = 30) and keep the common denominator 24 unchanged.
12 + 18/24 = 30/24
Step 4
Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 30 and 24, which is 6. Divide both the numerator and denominator by 6.
30 ÷ 6/24 ÷ 6 = 5/4
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (5) is greater than the denominator (4), divide 5 by 4: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/4.
5/4 = 11/4
Step 6
Decimal & Percentage Representation
Dividing the numerator 5 by denominator 4 yields an exact terminating decimal of 1.25 (or 125%).
5 ÷ 4 = 1.25 (125%)
Visual Representation
The diagram below illustrates 4/8 plus 9/12 visually:
+
=
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 5/4 |
| Mixed Number Form | 1 1/4 |
| Decimal Form | 1.25 |
| Percentage | 125% |
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Frequently Asked Questions
What is 4/8 plus 9/12 as a fraction?
4/8 + 9/12 in simplest fraction form is 5/4 (or 1 1/4 as a mixed number).
What is 4/8 plus 9/12 as a decimal?
4/8 + 9/12 converted to a decimal is 1.25.
What is 4/8 plus 9/12 as a percentage?
4/8 + 9/12 expressed as a percentage is 125%.
How do you write 4/8 plus 9/12 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 5/4 can be written as the mixed number 1 1/4.
Does 4/8 plus 9/12 result in a terminating or repeating decimal?
It results in an exact terminating decimal (1.25) because the denominator in simplest terms contains only prime factors 2 and/or 5.