What is 1/2 plus 9/14?
1/2 plus 9/14 equals 8/7 (or 1 1/7 as a mixed number) (or 1.142857 in decimal form). Learn the step-by-step solution to add 1/2 and 9/14 using Least Common Denominator and simplification.
Exact Answer
1/2 + 9/14 = 8/7
Simplified Fraction
8/7
Mixed Number
1 1/7
Decimal Value
1.142857
Percentage
114.2857%
Step-by-Step Solution: 1/2 + 9/14
Step 1
Find the Least Common Denominator (LCD)
Notice that 14 is an exact multiple of 2 (2 × 7 = 14). The Least Common Denominator (LCD) is simply 14, meaning we only need to scale one fraction.
LCD(2, 14) = 14
Step 2
Convert to Equivalent Fractions with Common Denominator 14
Multiply the numerator and denominator of 1/2 by 7, and multiply the numerator and denominator of 9/14 by 1 so both fractions share the common base 14.
1 × 7/2 × 7 = 7/14 and 9 × 1/14 × 1 = 9/14
Step 3
Add the Numerators
Now add the numerators (7 + 9 = 16) and keep the common denominator 14 unchanged.
7 + 9/14 = 16/14
Step 4
Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 16 and 14, which is 2. Divide both the numerator and denominator by 2.
16 ÷ 2/14 ÷ 2 = 8/7
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (8) is greater than the denominator (7), divide 8 by 7: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/7.
8/7 = 11/7
Step 6
Decimal & Percentage Representation
Dividing the numerator 8 by denominator 7 produces a repeating decimal (approximately 1.142857, or 114.2857%).
8 ÷ 7 = 1.142857 (114.2857%)
Visual Representation
The diagram below illustrates 1/2 plus 9/14 visually:
+
=
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 8/7 |
| Mixed Number Form | 1 1/7 |
| Decimal Form | 1.142857 |
| Percentage | 114.2857% |
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Frequently Asked Questions
What is 1/2 plus 9/14 as a fraction?
1/2 + 9/14 in simplest fraction form is 8/7 (or 1 1/7 as a mixed number).
What is 1/2 plus 9/14 as a decimal?
1/2 + 9/14 converted to a decimal is 1.142857.
What is 1/2 plus 9/14 as a percentage?
1/2 + 9/14 expressed as a percentage is 114.2857%.
How do you write 1/2 plus 9/14 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 8/7 can be written as the mixed number 1 1/7.
Does 1/2 plus 9/14 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.142857...) because the denominator contains prime factors other than 2 and 5.