What is 2/7 plus 9/12?
2/7 plus 9/12 equals 29/28 (or 1 1/28 as a mixed number) (or 1.035714 in decimal form). Learn the step-by-step solution to add 2/7 and 9/12 using Least Common Denominator and simplification.
Exact Answer
2/7 + 9/12 = 29/28
Simplified Fraction
29/28
Mixed Number
1 1/28
Decimal Value
1.035714
Percentage
103.5714%
Step-by-Step Solution: 2/7 + 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 2/7 by 12, and multiply the numerator and denominator of 9/12 by 7 so both fractions share the common base 84.
2 × 12/7 × 12 = 24/84 and 9 × 7/12 × 7 = 63/84
Step 3
Add the Numerators
Now add the numerators (24 + 63 = 87) and keep the common denominator 84 unchanged.
24 + 63/84 = 87/84
Step 4
Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 87 and 84, which is 3. Divide both the numerator and denominator by 3.
87 ÷ 3/84 ÷ 3 = 29/28
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (29) is greater than the denominator (28), divide 29 by 28: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/28.
29/28 = 11/28
Step 6
Decimal & Percentage Representation
Dividing the numerator 29 by denominator 28 produces a repeating decimal (approximately 1.035714, or 103.5714%).
29 ÷ 28 = 1.035714 (103.5714%)
Visual Representation
The diagram below illustrates 2/7 plus 9/12 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 29/28 |
| Mixed Number Form | 1 1/28 |
| Decimal Form | 1.035714 |
| Percentage | 103.5714% |
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Frequently Asked Questions
What is 2/7 plus 9/12 as a fraction?
2/7 + 9/12 in simplest fraction form is 29/28 (or 1 1/28 as a mixed number).
What is 2/7 plus 9/12 as a decimal?
2/7 + 9/12 converted to a decimal is 1.035714.
What is 2/7 plus 9/12 as a percentage?
2/7 + 9/12 expressed as a percentage is 103.5714%.
How do you write 2/7 plus 9/12 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 29/28 can be written as the mixed number 1 1/28.
Does 2/7 plus 9/12 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.035714...) because the denominator contains prime factors other than 2 and 5.