What is 2/5 plus 9/14?
2/5 plus 9/14 equals 73/70 (or 1 3/70 as a mixed number) (or 1.042857 in decimal form). Learn the step-by-step solution to add 2/5 and 9/14 using Least Common Denominator and simplification.
Exact Answer
2/5 + 9/14 = 73/70
Simplified Fraction
73/70
Mixed Number
1 3/70
Decimal Value
1.042857
Percentage
104.2857%
Step-by-Step Solution: 2/5 + 9/14
Step 1
Find the Least Common Denominator (LCD)
The denominators 5 and 14 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 5 × 14 = 70.
LCD(5, 14) = 70
Step 2
Convert to Equivalent Fractions with Common Denominator 70
Multiply the numerator and denominator of 2/5 by 14, and multiply the numerator and denominator of 9/14 by 5 so both fractions share the common base 70.
2 × 14/5 × 14 = 28/70 and 9 × 5/14 × 5 = 45/70
Step 3
Add the Numerators
Now add the numerators (28 + 45 = 73) and keep the common denominator 70 unchanged.
28 + 45/70 = 73/70
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 73 and 70 is 1, confirming that 73/70 cannot be reduced further—it is already in its simplest irreducible form.
73/70
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (73) is greater than the denominator (70), divide 73 by 70: it goes in 1 whole time(s) with a remainder of 3, giving the mixed number 1 3/70.
73/70 = 13/70
Step 6
Decimal & Percentage Representation
Dividing the numerator 73 by denominator 70 produces a repeating decimal (approximately 1.042857, or 104.2857%).
73 ÷ 70 = 1.042857 (104.2857%)
Visual Representation
The diagram below illustrates 2/5 plus 9/14 visually:
+
=
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 73/70 |
| Mixed Number Form | 1 3/70 |
| Decimal Form | 1.042857 |
| Percentage | 104.2857% |
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Frequently Asked Questions
What is 2/5 plus 9/14 as a fraction?
2/5 + 9/14 in simplest fraction form is 73/70 (or 1 3/70 as a mixed number).
What is 2/5 plus 9/14 as a decimal?
2/5 + 9/14 converted to a decimal is 1.042857.
What is 2/5 plus 9/14 as a percentage?
2/5 + 9/14 expressed as a percentage is 104.2857%.
How do you write 2/5 plus 9/14 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 73/70 can be written as the mixed number 1 3/70.
Does 2/5 plus 9/14 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.042857...) because the denominator contains prime factors other than 2 and 5.