Calculate Andy's Skating Hours: A Math Problem

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Calculate Andy's Skating Hours: A Math Problem

Hey everyone! Let's dive into a cool math problem today, all about Andy and his love for skating. We all know that keeping track of our time is super important, especially when we're passionate about something like skating. Andy, our main guy, usually clocks in about 6 hours per week on his skates. But this past week, things got a little more specific, and he wanted to figure out exactly how much time he dedicated to his favorite activity. It's a great way to see if he's hitting his weekly goal, right? So, he broke down his skating sessions throughout the week and noted down the exact time spent on each day. This kind of problem is fantastic for practicing our fraction skills and understanding how to add different time segments together. It's not just about the numbers, guys; it's about applying math to real-life situations, which makes learning so much more engaging. We'll be looking at his times for Monday, Wednesday, and Thursday, and then we'll see how he tried to put it all together to find his total skating time. Stick around, and we'll break down this mathematical adventure step-by-step!

Monday's Grind: 1 1/5 Hours on the Board

So, let's start with Andy's Monday skating session. On this particular Monday, Andy hit the pavement (or the rink, who knows!) for a solid 1 1/5 hours. Now, if you're new to fractions, this might look a bit intimidating, but don't sweat it! This mixed number simply means he skated for 1 full hour and then an additional 1/5 of an hour. To make things easier when we start adding up his skating times, it's often super helpful to convert these mixed numbers into improper fractions. Remember how we do that? We multiply the whole number (that's the '1') by the denominator of the fraction (that's the '5') and then add the numerator (that's the '1'). So, for 1 1/5, it becomes (1 * 5) + 1, which equals 6. We keep the same denominator, so 1 1/5 is the same as 6/5 hours. Converting to improper fractions helps us when we need a common denominator later on, which is crucial for adding fractions. This first session is a great start to his week, and understanding this conversion is key to solving the rest of the problem. It’s all about making the numbers work for us, and this simple conversion is a game-changer. So, keep that 6/5 hours in mind for Monday!

Wednesday's Effort: A Whopping 2 3/5 Hours

Next up, we've got Andy's Wednesday skating session, and he really put in the work this day! He spent a whopping 2 3/5 hours on his skates. Wowza! Again, we're dealing with a mixed number, and just like we did with Monday's time, it's super useful to convert this into an improper fraction. Let's do the math together: multiply the whole number (2) by the denominator (5), and then add the numerator (3). So, (2 * 5) + 3 equals 10 + 3, which is 13. Keeping the denominator the same, 2 3/5 hours is equivalent to 13/5 hours. This is a pretty significant chunk of time, showing Andy was really dedicated on Wednesday. These longer sessions are fantastic for building stamina and improving skills, and it's awesome to see him logging such substantial time. Thinking about this in terms of improper fractions makes it way easier to combine with other fractional amounts later. So, remember that 13/5 hours for Wednesday – that's a big one!

Thursday's Skate: 1 5/6 Hours

Finally, let's look at Andy's Thursday skating session. On this day, he spent 1 5/6 hours skating. Another mixed number for us to tackle! Remember the drill: multiply the whole number (1) by the denominator (6), and then add the numerator (5). That gives us (1 * 6) + 5, which equals 6 + 5, resulting in 11. The denominator stays the same, so 1 5/6 hours is the same as 11/6 hours. This session might not be as long as Wednesday's, but it's still a solid amount of time dedicated to skating. Every hour counts when you're aiming for a weekly total, and Andy is definitely doing that. By converting this to an improper fraction 11/6 hours, we’re setting ourselves up perfectly to add this time to his other skating sessions. It's all about preparation and making the math manageable. So, keep 11/6 hours handy for Thursday!

The Expression: Putting It All Together

Now, here's where it gets really interesting, guys. Andy wants to find his total number of hours spent skating for these three days. He’s thinking mathematically, which is awesome! He wrote down an expression to calculate this total. The expression should represent adding up the hours from Monday, Wednesday, and Thursday. Based on what we've converted, Andy's skating times are 6/5 hours (Monday), 13/5 hours (Wednesday), and 11/6 hours (Thursday). So, the expression to find the total hours would be:

6/5 + 13/5 + 11/6

This expression shows exactly what Andy did: he added the time spent on each of those days. The cool thing about these expressions is that they are like a mathematical sentence that tells a story. This one tells the story of Andy's skating week. When you look at this expression, you can immediately see the different parts of his skating journey and how they are being combined. It's a direct representation of the problem we're trying to solve. Andy is on the right track by setting up this expression. The next step, of course, would be to actually solve this expression to find the total, but for now, understanding and creating the expression itself is a huge win. It demonstrates a clear grasp of how to translate a real-world scenario into a mathematical problem. Keep this expression in mind as we move forward to the solution!

Solving the Equation: Adding Fractions Like a Pro

Alright, mathletes, it's time to solve Andy's skating hours expression: 6/5 + 13/5 + 11/6. Remember, when adding fractions, we need a common denominator. That's the magic number that both (or all) denominators can divide into evenly. Looking at our denominators – 5, 5, and 6 – the least common multiple (LCM) is the smallest number that 5 and 6 can both go into. Let's think: multiples of 5 are 5, 10, 15, 20, 25, 30... Multiples of 6 are 6, 12, 18, 24, 30... Bingo! Our least common denominator is 30. Now, we need to convert each fraction so it has a denominator of 30.

  • For 6/5: To get 30 in the denominator, we multiply 5 by 6. So, we must also multiply the numerator (6) by 6. That gives us (6 * 6) / (5 * 6) = 36/30.
  • For 13/5: Again, we multiply the denominator (5) by 6. We do the same to the numerator (13): (13 * 6) / (5 * 6) = 78/30.
  • For 11/6: To get 30 in the denominator, we multiply 6 by 5. We do the same to the numerator (11): (11 * 5) / (6 * 5) = 55/30.

Now that all our fractions have the same denominator, we can simply add the numerators:

36/30 + 78/30 + 55/30 = (36 + 78 + 55) / 30

Let's add those numerators: 36 + 78 = 114. Then, 114 + 55 = 169.

So, the total is 169/30 hours. Great job, guys! We've successfully added the fractions.

Simplifying the Result: From Improper to Mixed Number

We found that Andy spent 169/30 hours skating. This is an improper fraction, meaning the numerator is larger than the denominator. While it's mathematically correct, it's often more helpful to understand this in terms of full hours and remaining minutes, just like we usually talk about time. So, let's convert this improper fraction back into a mixed number. To do this, we divide the numerator (169) by the denominator (30).

How many times does 30 go into 169? Let's see:

  • 30 * 1 = 30
  • 30 * 2 = 60
  • 30 * 3 = 90
  • 30 * 4 = 120
  • 30 * 5 = 150
  • 30 * 6 = 180 (Too big!)

So, 30 goes into 169 5 times, with a remainder. The remainder is 169 - 150 = 19.

The whole number part of our mixed number is the number of times 30 went into 169, which is 5. The remainder (19) becomes the numerator of our fraction, and the denominator stays the same (30).

Therefore, 169/30 hours is equal to 5 19/30 hours. This is a much more intuitive way to understand Andy's skating time. He spent 5 whole hours and then an additional 19/30 of an hour. See how converting back makes it easier to visualize? We've gone from an expression to an improper fraction, and now to a mixed number that tells us precisely how much time Andy dedicated to skating during those three days. Awesome work!

Final Check: Is Andy Meeting His Goal?

We've calculated that Andy spent a total of 5 19/30 hours skating over Monday, Wednesday, and Thursday. The initial information told us that Andy usually skates for about 6 hours per week. So, is he on track this week? Well, his total for these three days is 5 19/30 hours, which is just a little bit less than his usual 6 hours. He's really close! This means he might have skated a bit on other days, or perhaps this week was a slightly lighter week for him. It's a great example of how tracking our time can give us a clear picture of our activities. The math tells us he's almost at his usual weekly mark. This kind of problem-solving is super useful for managing time, setting goals, and just understanding how our efforts add up. Keep practicing these fraction skills, guys, because as you can see, they pop up in all sorts of interesting scenarios, even when tracking how long someone skates! You guys crushed this math problem!