Mixed Number Addition And Subtraction Practice Problems

Hey guys! Let's dive into some mixed number addition and subtraction problems. I know fractions can seem tricky, but we'll break it down step by step. We're going to work through some examples together, focusing on how to add and subtract mixed numbers and express our answers in the correct forms. So, grab your pencils and let's get started!

Addition of Mixed Numbers

Problem a) $3+2\frac{5}{6}$

Okay, so we're starting with a pretty straightforward one. We need to add a whole number, 3, to a mixed number, $2\frac{5}{6}$. Remember, a mixed number is just a whole number combined with a fraction. When we're adding whole numbers to mixed numbers, it's actually quite simple. The key here is understanding the components of a mixed number.

First, identify the whole numbers: We have 3 and 2. We can add these together directly: $3 + 2 = 5$. Now, we just need to deal with the fractional part, which is $\frac{5}{6}$. Since we're only adding whole numbers to the mixed number, the fraction $\frac{5}{6}$ remains unchanged.

Combine the results: We combine the sum of the whole numbers (5) with the fraction $\frac{5}{6}$. This gives us our final answer as a mixed number: $5\frac{5}{6}$.

So, $3 + 2\frac{5}{6} = 5\frac{5}{6}$. See, that wasn't so bad! This type of problem is great for getting us warmed up and comfortable with mixed numbers. The important thing is to remember that you're just adding the whole number parts together and then tacking on the fraction. This is a fundamental concept, and mastering it will help you tackle more complex problems later on. Always double-check your work to ensure accuracy, and don't hesitate to practice with more similar problems to build your confidence. The more you practice, the more natural these steps will become.

Problem b) $2\frac{2}{5}+4\frac{1}{4}$

Alright, let's level up a bit. This time, we're adding two mixed numbers together: $2\frac{2}{5}$ and $4\frac{1}{4}$. This is where we need to be a bit more careful and remember our fraction rules. The main challenge here is that the fractions have different denominators, so we can't just add them directly. We'll need to find a common denominator first.

Step 1: Add the whole numbers: Just like before, we start by adding the whole number parts: $2 + 4 = 6$. This gives us the whole number part of our final mixed number.

Step 2: Find a common denominator: Now, we need to add the fractions $\frac{2}{5}$ and $\frac{1}{4}$. To do this, we need a common denominator. The least common multiple (LCM) of 5 and 4 is 20. So, we'll convert both fractions to have a denominator of 20.

• Convert $\frac{2}{5}$: To get the denominator to 20, we multiply both the numerator and the denominator by 4: $\frac{2}{5} \times \frac{4}{4} = \frac{8}{20}$.
• Convert $\frac{1}{4}$: To get the denominator to 20, we multiply both the numerator and the denominator by 5: $\frac{1}{4} \times \frac{5}{5} = \frac{5}{20}$.

Step 3: Add the fractions: Now that we have a common denominator, we can add the fractions: $\frac{8}{20} + \frac{5}{20} = \frac{13}{20}$.

Step 4: Combine the results: Finally, we combine the sum of the whole numbers (6) with the sum of the fractions $\frac{13}{20}$. This gives us our final answer as a mixed number: $6\frac{13}{20}$.

So, $2\frac{2}{5} + 4\frac{1}{4} = 6\frac{13}{20}$. We had to do a bit more work this time, but by breaking it down into steps, it becomes much more manageable. Finding a common denominator is a crucial skill when adding or subtracting fractions, so make sure you're comfortable with this process. Practice makes perfect, so keep at it!

Problem c) $3\frac{2}{3}+2\frac{4}{5}$

Okay, guys, let's tackle another addition problem with mixed numbers: $3\frac{2}{3}+2\frac{4}{5}$. This one is similar to the last one, but it's always good to get more practice. We'll follow the same steps as before, focusing on finding that common denominator.

Step 1: Add the whole numbers: First, we add the whole number parts: $3 + 2 = 5$. This is the whole number part of our final answer.

Step 2: Find a common denominator: Now we need to add the fractions $\frac{2}{3}$ and $\frac{4}{5}$. The denominators are 3 and 5. The least common multiple (LCM) of 3 and 5 is 15. So, we'll convert both fractions to have a denominator of 15.

• Convert $\frac{2}{3}$: To get the denominator to 15, we multiply both the numerator and the denominator by 5: $\frac{2}{3} \times \frac{5}{5} = \frac{10}{15}$.
• Convert $\frac{4}{5}$: To get the denominator to 15, we multiply both the numerator and the denominator by 3: $\frac{4}{5} \times \frac{3}{3} = \frac{12}{15}$.

Step 3: Add the fractions: Now that the fractions have the same denominator, we can add them: $\frac{10}{15} + \frac{12}{15} = \frac{22}{15}$.

Step 4: Simplify the fraction (if necessary): Notice that $\frac{22}{15}$ is an improper fraction because the numerator (22) is greater than the denominator (15). We need to convert this to a mixed number. To do this, we divide 22 by 15. 22 divided by 15 is 1 with a remainder of 7. So, $\frac{22}{15} = 1\frac{7}{15}$.

Step 5: Combine the results: We now have the sum of the whole numbers (5) and the simplified fraction $1\frac{7}{15}$. We add these together: $5 + 1\frac{7}{15} = 6\frac{7}{15}$.

So, $3\frac{2}{3} + 2\frac{4}{5} = 6\frac{7}{15}$. This problem involved an extra step of simplifying an improper fraction, but we handled it like pros! Remember, if your fraction is improper, always convert it to a mixed number before combining it with the whole number part.

Subtraction of Mixed Numbers

Now, let's switch gears and dive into subtraction. Subtraction with mixed numbers has its own set of challenges, but we can tackle those challenges by approaching them systematically. We'll focus on expressing our answers as common fractions, which sometimes means we'll need to borrow from the whole number part.

Problem a) $5-1\frac{1}{3}$

Okay, our first subtraction problem is $5 - 1\frac{1}{3}$. We're subtracting a mixed number from a whole number. This means we'll need to think a little differently about how we set up the problem.

Step 1: Convert the whole number to a mixed number: To subtract a mixed number, it helps to rewrite the whole number as a mixed number with a fraction. We can rewrite 5 as $4\frac{3}{3}$. We chose $\frac{3}{3}$ because it's equal to 1, and having a denominator of 3 will help us subtract the fraction in the next step. So, $5 = 4 + 1 = 4\frac{3}{3}$.

Step 2: Subtract the whole numbers: Now we subtract the whole number parts: $4 - 1 = 3$.

Step 3: Subtract the fractions: Next, we subtract the fractions: $\frac{3}{3} - \frac{1}{3} = \frac{2}{3}$.

Step 4: Combine the results: Now we know that we need to express the answer as a common fraction, so we need to convert the mixed number into a fraction:

$\frac{2}{3}$.

Therefore $5-1\frac{1}{3}=\frac{2}{3}$.

Great job, guys! We've covered adding and subtracting mixed numbers, and we've seen how important it is to find common denominators and simplify our answers. Remember, practice is key to mastering these skills. Keep working on these types of problems, and you'll become a fraction whiz in no time!