One-Step Equations with Multiplication and Division 03:54 minutes

Video Transcript

Transcript One-Step Equations with Multiplication and Division

Henry David lives in New York, and he is very annoyed by how crowded and loud the city is. Therefore, he has decided to go on a backpacking trip to Alaska. He has a guidebook and knows just the place to go this is exactly what he was looking for! Just pure, unadulturated peace and quiet. To plan his trip, he uses One Step Equations with Multiplication and Division. Henry David is extremely thorough in his preparations and wants to make sure he takes sufficient provisions for his journey. He needs to calculate how many days his provisions will last. Henry knows that he'll need 6 lbs. of food each day, and he can carry 30 lbs of food in his backpack. So, how many days will his provisions last? To figure this out, we first have to set up an equation. As you know, an equation is like a scale that is balanced. Both sides of an equal sign have the same value. Since we want to calculate the number of days Henry's provisions will last, let the number of days be represented by 'd'. Mathematically, 6 times 'd', or 6d, represents the amount of food, in pounds, consumed after 'd' days. Because Henry can carry 30 lbs. of food in his backpack, the number of days, 'd', times 6 lbs consumed each day equals 30 lbs. Let’s see how many days Henry's provisions will last. As you've probably guessed, One Step Equations can be solved in only one step. You just have to use the correct operation. We want to isolate the variable 'd', which is multiplied by 6 on the left side of the equation. If you see a variable multiplied by a coefficient, you can isolate the variable by dividing; in this case, by 6. But remember, since equations are like scales that need to be balanced, you have to divide by 6 on both sides of the equation. 6d divided by 6 is just 'd', so we've isolated our variable and 30 divided by 6 is 5. Henry David's got 5 days' worth of provisions. Now let's see if he can make it to his destination on foot with those provisions. How many total miles can Henry walk during his 5 days if we know his average speed is 12 miles per day? Translating our word problem into mathematics we can setup this equation.

We can use the variable 'm' for our unknown total miles. And since we already know the total number of days and his average speed we can go ahead and substitute 5 for total days and 12 for miles per day. Again, we need to isolate our variable. The variable 'm' is divided by 5. What's the opposite of division? If you said multiplication, you're right! We should multiply BOTH sides by 5. You might also see the left side written like this: This makes it easier to see that the 5s cancel each other out. So we're left with 12 times 5, giving us 'm' equals 60. This means Henry can travel 60 miles in 5 days at a rate of 12 miles per day. With his destination just 60 miles away, Henry David advances confidently in the direction of his dreams. As long as he doesn't run into any complications, he should make it to his destination on time with enough provisions. He's finally made it to the great place described in the guidebook! That really doesn’t look like what he expected.