Solve the equation 3/9 + 2/5 =
The first thing we always want to do when we have a problem with fractions is to make sure that each fraction is in it's simplest form. This will help us use the smallest and simplest numbers possible. So let's look at the first fraction. 3 _ 9 Before we go on further it's important to know what each part of the fraction is called. The top number, in this case, 3, is called the numerator while the bottom number, which would be 9, is the denominator. What we want to do is list all of the numbers that can multiply together to equal 9. I like to do this by making a little table. We know that our first multiplication will always be the number and 1. 1 x 9 2 x ? 3 x ? 4 x ? 5 x ? 6 x ? 7 x ? 8 x ? 9 x 1 Now let's think, 9 is an odd number so that means there will not be any even numbers that multiply to equal 9 so that automatically excludes 2,4,6, and 8. Also, we want to keep in mind that we will only be using whole numbers so any number larger than 9 and smaller than 1 could not be an option either. 1 x 9 3 x ? 5 x ? 7 x ? 9 x 1 Can 3 multiply into 9? Yes, 3 x 3 = 9 1 x 9 3 x 3 5 x ? 7 x ? 9 x 1 Now since 3 is our numerator we don't have to go through the rest of our numbers because we already found the number we're looking for. We want to rewrite our fraction in its multiplication form like this 3 x 1 Notice that we are multiplying by 3 on the top and bottom. We can cancel these 3's out. ____ Leaving us with just a 1 and a 3 3 x 3 1 _ 3 Now the fraction is in simplest form. Let's look to see if the second fraction is in simplest form. 2 This one is a little easier because anytime we see a 2 all we have to do is look and see if _ the other number is odd or even. If it's even it can be simplified further but if it's odd then 5 it's already in it's simplest form. Since 5 is an odd number this fraction is already in simplest form. So let's write out or equation again with our simplified fraction. 1 2 _ + _ 3 5 When we add fractions we cannot add them together until both denominators are the same number. Since both fractions are in it's simplest form that means that we will have to multiply 3 and 5 to get our denominators to be the same. But we need to make these multiplications without changing the values of our fractions. the way we do this is technically by multiplying by 1. You see, any fraction in which the top and bottom number are the same is equal to 1. So 5/5 is equal to 1, 100/100 is equal to 1, and so on. So by multiplying both the numerator and the denominator by the same number, we are multiplying it by 1 but we are able to change the numbers of the denominator so that we can add. I'll show you what that looks like below! 1 5 2 3 _ x _ + _ x _ 3 5 5 3 So let's multiply this out. 1 x 5 = 5 3 x 5 = 15 2 x 3 = 6 5 x 3 = 15 I'm going to put our new values into our equation 5 6 _ + _ 15 15 Now that we have our equation with the same denominator we can finally add these fractions together. But remember, whenever you add or subtract fractions, once you have the same denominator you DO NOT change the denominator, you just add the numerators. So when we solve this equation we will add the 5 and 6 but just move the 15 over like this. 5 6 5 + 6 _ + _ = ____ 15 15 15 Next, you will add up 5 + 6 which equals 11 and you're done! 5 6 5 + 6 11 _ + _ = ____ = __ 15 15 15 15 So 3/9 + 2/5 = 11/15
Clara wants her son Patrick to put his dirty clothes in his hamper but he continues to throw them on his floor. She has tried asking nicely, yelling, punishing him, and offering to buy him ice cream at the end of the week but nothing has worked. After doing research online, Clara decides that every time she sees Patrick's dirty clothes on the floor she will ignore them but whenever she sees him put the clothes in his hamper she gives him praise and a high five (Patrick loves high fives). What is Clara using to try and change Patrick's behavior? A. Negative punishment B. Negative reinforcement C. Positive punishment D. Positive reinforcement
In order to answer this question, we should first make sure that we understand what each of the answer choices means. Let's talk about positive and negative punishment. Do not think of positive and negative as good and bad. Instead, any time you see positive know that you're adding something and negative means taking something away. Punishment does not mean good or bad either, something can only be a punishment if it's something that the person does not like. Let's look at some examples. If Clara tried to punish Patrick by grounding him from seeing his friends this would be a negative punishment because she is taking something, in this case, Patrick's friends, away. But if Patrick's friends were out of town while he was grounded then Patrick probably wouldn't see this as aversive at all and it would cease to a punishment. If Clara deciding to add more chores, this would be positive punishment since she is adding something. Again, if Patrick didn't mind the chores then this would not be a punishment at all. Next, let's look at reinforcement. Reinforcement is when the presence of a stimulus strengthens the behavior. Positive reinforcement occurs when a behavior is followed by the presentation of a stimulus and the behavior is strengthened. An example would be if a parent rewarded their child with money each time they received a good grade. If this encourages the child to continue to get good grades then they have been positively reinforced but positive reinforcement doesn't mean something good. If a child throws a tantrum and a parent gives the child what they want, then the child has been positively reinforced to throw more tantrums because their behavior resulted in something they wanted. Negative reinforcement is a little different. Behavior is followed by removal of a stimulus and the behavior is strengthened. So let's look at an example, you have an awful headache and you take two Advil and the headache goes away. You have been negatively reinforced. The behavior, taking the Advil, removed the stimulus, the headache, and therefore you are probably more likely to take Advil again if you have a headache. Okay so now that we have a background on each of our answers let's look at our question. Now the beginning of the question sets us up but it's unnecessary to answer the question so let's just look at the last part. Clara decides that every time she sees Patrick's dirty clothes on the floor she will ignore them but whenever she sees him put the clothes in his hamper she gives him praise and give him a high five (Patrick loves high fives). That last part, Patrick loves high fives automatically eliminates any type of punishment because Patrick does not find high fives aversive. So now let's decide if this is positive or negative punishment. When Clara sees Patrick put the clothes in the hamper she gives him praise and high fives. Clara is adding a stimulus after the desired behavior in hopes that it will reinforce Patrick. Since she is adding a stimulus, this is positive reinforcement. So the answer is D.
Solve the equation. 4.4 = x − 5.6
Combining algebra and decimals can be tricky but don't let it scare you! In order to solve the equation, we need to find what x is so what we want to do is to get x by itself. Let's look at this equation. 4.4 = x − 5.6 To get x by itself we need to cancel out 5.6. Since there is a subtraction sign in front of the 5.6 we would read it as -5.6 so how can we get -5.6 to equal zero? We have to add +5.6. When you add the positive and negative of any number you will always get zero! 4.4 = x - 5.6 + 5.6 BUT, we're not done. If we add a number to one side of the equation, we have to add it to the other side as well. So we also have to add 5.6 to 4.4. Now our equation will look like this 4.4 + 5.6 = x - 5.6 + 5.6 Now that we have our equation all set up, we need to simplify each side. 4.4 Since we're adding decimals this might seem like a difficult problem but if you +5.6 remember that when adding decimals we can just move the period down like this. _____ . Ignore that the decimal is there for a moment and just add the top and the bottom of the column to the right. first, we'll add the 6 and the 4 which is equal to 10. Keep in mind that when we add and get a number with two digits that we leave the last digit directly underneath and add the second digit to the next column like this 1 4.4 +5.6 _____ .0 Next, we will add the left column which now has 1, 4, and 5. This comes out to 10 and we will write that directly below the column. 1 4.4 +5.6 _____ 10.0 In this case, 10.0 is the same as 10 so we will just write 10 back into our original equation 10 = x - 5.6 + 5.6 Now as we previously discussed 5.6 - 5.6 = 0 but I'll write that out for you just so you can see it in action 5.6 6 - 6 is equal to zero and 5 - 5 also cancel out to equal zero. - 5.6 _____ 0.0 Since the number is zero there's no reason to write it in our equation so now when simplified our equation looks like this 10 = x We could also flip that around to be x = 10 and we have our answer!