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WWW-awu aleks, com/alekscgi/x/isl.exe/ 10 u-IgNsikr7jge Fractions Addilion or sutiraction of fractions wilt the same denominator andm. Add. Write your answer as a fraction in simnlest form, \[ \frac{11}{16}+\frac{9}{16} \]

Ask by Fernandez Pollard. in the United States
Jan 29,2025

Real Tutor Solution

Tutor-Verified Answer

Answer

\[ \frac{5}{4} \]

Solution

To add the fractions \(\frac{11}{16}\) and \(\frac{9}{16}\), follow these steps: ### Step 1: Ensure the Denominators Are the Same Both fractions have the same denominator (16), which makes the addition straightforward. ### Step 2: Add the Numerators Add the numerators (the top numbers) while keeping the denominator (the bottom number) the same. \[ \frac{11}{16} + \frac{9}{16} = \frac{11 + 9}{16} = \frac{20}{16} \] ### Step 3: Simplify the Fraction Simplify \(\frac{20}{16}\) by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 4. \[ \frac{20 \div 4}{16 \div 4} = \frac{5}{4} \] ### Final Answer \[ \frac{5}{4} \] This is the sum of \(\frac{11}{16}\) and \(\frac{9}{16}\) in its simplest form.

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The Deep Dive

Adding fractions with the same denominator is straightforward! Just add the numerators together while keeping the denominator the same. So, \(\frac{11}{16} + \frac{9}{16} = \frac{11 + 9}{16} = \frac{20}{16}\). Now, simplify \(\frac{20}{16}\) by dividing both the numerator and denominator by their greatest common divisor, which is 4. This gives us \(\frac{5}{4}\) or 1.25 in decimal form! Now, let's make sure we're not forgetting to simplify in future problems! A common mistake is leaving fractions in their more complex forms. Always check if you can reduce to make things easier! For instance, in this problem, after obtaining \(\frac{20}{16}\), you had to simplify it to get the final answer in simplest form, \(\frac{5}{4}\). Keep an eye on that!

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