Tutor profile: Tiffany H.
Simplify the following using Orders of Operations: -(-4)^2+ 10 /2
What are the operation symbols we have in this problem? We have a square, an addition symbol and a division symbol. According to PEMDAS, P is first, then D for division then A for addition. In PEMDAS, since P comes first, we will first square the -4. So (-4)^2 = (-4)(-4) =16 The problem then becomes: -16 + 10/2 Next in PEMDAS we have D for division so we will do 10/2, which is 5. The problem now becomes: -16 +5 Now we have A for Addition. -16 + 5 = -11 So our problem simplifies out to -11/
Subject: Basic Math
Kelly was studying for her math exam last week. She studied for 3/4 hours on Monday, 1/3 hours on Wednesday and a 1/2 hour on Friday. How many hours total did she study?
To determine the total number of hours Kelly studied, we are going to add up the fraction hours she studied. This looks like: 3/4 +1/3 +1/2 Now, we might be tempted to add the numerators up and add up the denominators, but we need to remember that for fractions, we NEED to have a common denominator. At the moment we have 3 different denominators, a 4, 3 and 2. We need to find a number that they can all "go into" well, 4, 3 and 2 can all go into the number 12! So 12 is our LCD. To make the denominators the same we need to use the "Building up Property" we will multiply the denominators of our fractions by the needed number to make the denominator a 12, then multiply that same number to the numerator. For example, 3/4. To make 4 become a 12, we need to multiply the 4 by 3. Then we multiply the numerator by 3 as well. This gives us 9/12. We do the same to the other fractions. To create a 12 in the denominator for 1/3, we multiply the top and the bottom by 4, which becomes 4/12. To create a 12 in the denominator for 1/2, we multiply the top and the bottom by 6, then 1/2 becomes 6/12. So, we now have: 9/12 + 4/12 + 6/12 When adding fractions we KEEP the denominators and ADD the numerators. So (9+4+6)/12 = 19/12 Our answer is 19/12 hours. Which we can simplify to 1 7/12 hours. So Kelly studied her math for 1 7/12 hours.
Solve the following equation for x: 3x - 4 = 11
First off, we need to find out where x is, do you see it? So it is on the left side of the equal sign. Then, we need to determine what is keeping x from being by itself. Can you point out what is keeping x from being by itself? So we need to get rid of the -4 and then the 3. First we get rid of the negative 4, to do this, we add 4 to both sides of the equation. 3x -4 = 11 +4 +4 When we do this, the 4 cancels with the -4 on the left side and we get. 3x = 11+4 We can simplify this into: 3x=15 Now, we still have that 3 being multiplied to the x. How do we undo multiplication? We divide. So lets divide both sides of the equation by 3. 3x/3 = 15/3 This simplifies into: x=15/3 x=3 So our answer is x =3
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