What is 3/7 plus 9/12?
3/7 plus 9/12 equals 33/28 (or 1 5/28 as a mixed number) (or 1.178571 in decimal form). Learn the step-by-step solution to add 3/7 and 9/12 using Least Common Denominator and simplification.
Exact Answer
3/7 + 9/12 = 33/28
Simplified Fraction
33/28
Mixed Number
1 5/28
Decimal Value
1.178571
Percentage
117.8571%
Step-by-Step Solution: 3/7 + 9/12
Step 1
Find the Least Common Denominator (LCD)
The denominators 7 and 12 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 7 × 12 = 84.
LCD(7, 12) = 84
Step 2
Convert to Equivalent Fractions with Common Denominator 84
Multiply the numerator and denominator of 3/7 by 12, and multiply the numerator and denominator of 9/12 by 7 so both fractions share the common base 84.
3 × 12/7 × 12 = 36/84 and 9 × 7/12 × 7 = 63/84
Step 3
Add the Numerators
Now add the numerators (36 + 63 = 99) and keep the common denominator 84 unchanged.
36 + 63/84 = 99/84
Step 4
Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 99 and 84, which is 3. Divide both the numerator and denominator by 3.
99 ÷ 3/84 ÷ 3 = 33/28
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (33) is greater than the denominator (28), divide 33 by 28: it goes in 1 whole time(s) with a remainder of 5, giving the mixed number 1 5/28.
33/28 = 15/28
Step 6
Decimal & Percentage Representation
Dividing the numerator 33 by denominator 28 produces a repeating decimal (approximately 1.178571, or 117.8571%).
33 ÷ 28 = 1.178571 (117.8571%)
Visual Representation
The diagram below illustrates 3/7 plus 9/12 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 33/28 |
| Mixed Number Form | 1 5/28 |
| Decimal Form | 1.178571 |
| Percentage | 117.8571% |
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Frequently Asked Questions
What is 3/7 plus 9/12 as a fraction?
3/7 + 9/12 in simplest fraction form is 33/28 (or 1 5/28 as a mixed number).
What is 3/7 plus 9/12 as a decimal?
3/7 + 9/12 converted to a decimal is 1.178571.
What is 3/7 plus 9/12 as a percentage?
3/7 + 9/12 expressed as a percentage is 117.8571%.
How do you write 3/7 plus 9/12 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 33/28 can be written as the mixed number 1 5/28.
Does 3/7 plus 9/12 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.178571...) because the denominator contains prime factors other than 2 and 5.