2- Add both numerators then add both denominators.
3- Simplify if you can.
e.g.:
1/2 + 1/4=
2/4 + 1/4= 3/4
Adding Mixed Numbers: 1- Convert mixed numbers into improper fractions. 2- Find the common denominator. 3- Add both numerators and then add both denominators. 4- Convert improper fraction to mixed number. 5- Simplify if you can.
e.g.:
1 1/2 + 1 1/3=
3/2 + 4/3=
9/6 + 8/6= 17/6 = 2 5/6
Subtracting Fractions: 1- Find common denominators. 2- Subtract numerators and leave the denominator as it is. 3- Simplify if you can.
e.g.:
1/2 - 3/4=
2/4 - 3/4= 1/4
Multiplying Fractions: 1- Find common denominator. 2- Multiply both numerators and multiply both denominators. 3- Simplify if you can.
e.g.:
2/3 x 3/4=
8/12 x 9/12= 72/12 = 6
Multiplying Mixed Numbers: 1- Convert mixed numbers to improper fractions. 2- Find common denominator. 3- Multiply both numerators and then multiply both denominators. 4- Simplify if you can
e.g.:
1 1/2 x 1 2/4=
3/2 x 6/4= 18/4 = 4 2/4
Dividing Fractions: 1- Find the reciprocal of one of the fractions. 2- Multiply both of the numerators and then multiply both of the denominators. 3- Simplify if you can
e.g.:
4/8 * 2/4=
4/8 x 4/2= 16/16 = 1<-----the answer
2/4 x 4/2= 1
Dividing Mixed Numbers: 1- Convert mixed numbers to improper fractions. 2- Find the reciprocal of one of the fractions. 3- Multiply both numerators and then multiply both denominators. 4- Simplify if you can
One week, Kristi worked 3 days at a department store for 3 1/2h each day. She was paid $9/h.
A How many hours did Kristi work that week?
3 1/2 x 3/1= 21/2 =10 1/2
Kristi worked 10 and 1/2 hours in the department store.
B How much did Kristi earn that week?
9/1 x 21/2 =189/2 =94 1/2 =$94.50
#2
Jupiter completes about 2 2/5 rotations every 24 hours. How many rotations does Jupiter complete in 1 Earth week?
2 2/5 x 7/1 = 12/5 x 7/1 =84/5 =16 4/5
Jupiter completes 16 4/5 rotations around earth every week
#3 A sailboat is sailing at 8 1/2 km/h. If the weather conditions and the current do not change, how far will the sailboat travel in 1 1/3 h?
8 1/2 x 11/3= 68/6 =11 1/3
The sailboat will travel 11 1/3 km
#4
The distance to Grandma's house is 4/5 of the distance to Uncle Glen's house. If Uncle Glen's house is 3 1/2 hours away, how long will it take to get to Grandma's house if you travel at the same speed?
3 1/2 x 4/5 = 28/10 =2 8/10 =2 4/5
it would take 2 4/5 of an hour to get to grandma's house.
#5
It takes 3/5 of a tank of gas to get to work and back each day. How much gas is used over 5 work days?
3/5 x 5/1 =15/5 =3/1 =3
It would take 3 tanks of gas for every 5 work days.
#6
Owen is 2 1/4 times as old as Robin. When Robin celebrates his 8th birthday, how old will Owen be?
2 1/4 x 8/1= 2/1 x 8/1= 18/1 =18
When Robin is 8 Owen will be 18 years old.
#7
The karate club is arranging a grading for its members. It takes 3 1/4 hours to test a group of 4 candidates. How long will the club need in order to process 3 groups of 4 candidates each?
3 1/4 x 3/1 = 39/4 =9 3/4
The club will spend 9 and 3/4 of an hour grading its members.
Today we looked at Subtractive and Multiplicative Two-Step equations. So remember, isolate, cancel using the opposite, balance, cancel using the opposite, and verify. Also, Pizza(the constant), hides in the closet, and gets caught first, then chicken wing (the variable), hides in the bed, and gets caught second. Also, the proper way to use the shortcut is:
Oh, yeah, and I forgot to show it here, but you need to verify also. For the next scribble I choose Ben, unless he already did one.
Partative Division How Many Equal Parts are in the number we divide?
Quotative division
Quotative Division How many of the number fit in the number you're dividing.
Subtracting Integers The idea that you use subtraction, is completely and utterly fiction. Instead you take your minus signs, and change them to addition.
Adding Integers One plus one is two. Ten plus ten equals twenty. This is addition
Chapter 2, Script
Billy Bob: Hey Mr. Smarts! Mr. Smarts: Hello Billy Bob. Billy Bob: Hey, I got this here mathematic question for my homework, can you help me? Mr. Smarts: Alright, I'll help, what are the questions? Billy Bob: Well, ones n+3-5n+12... Mr. Smarts: Well, thats simple! Billy Bob: Really? Mr. Smarts: First you take away n+3 and -5n and put it into another group. Then you take the rest of the numbers and make 3+12. Billy Bob: Wow, you sure are smart. Mr. Smart: Well, thats no all of it. Then you take n+3 and subtract 5n, What do you think the answer is? Billy Bob: Ummm, 7n? Mr. Smart: Close, but no. The answer is 8n! Billy Bob: Wow, thanks! Mr. Smart: Now, you take the other numbers and add them together: 3+12= what? Billy Bob: Oh, I know that, it's 15! Mr. Smart: Good Job! Billy Bob: Thanks! Mr. Smart: Now just add the two groups together. The answer would be 8n + 15. Billy Bob: Thanks. Mr. Smart: Now, whats the other question? Billy Bob: Oh yeah, it's 2 + 4(3n+8). Mr. Smart: Alright, now do the same thing as the first one. What's the answer? Billy Bob: Uhh, lets see... Take 3n away... then the brackets mean that you do that first, so 8+2+4= 14... So the answer would have to be... 3n + 14? Mr. Smart: Right! Good Job! Billy Bob: Thanks for the help, Mr. Smart! Mr. Smart: You're welcome! Billy Bob: See ya! Mr. Smart: Goodbye!
One day, a guy named Bob was walking through a pumpkin patch, when a giant pumpkin monster jumped up and roared at him. He had big teeth, long claws, and was glowing orange, the same color as his skin. Bob tried to run, but the monster picked him up in one giant hand. The monster brought him up to his face, and gnashed his teeth, and Bob screamed like a 5-year old girl. The monster told him, "Answer these three questions, and I will let you go, if you fail, I will devour you.". Here is the first, what is (-5) + (+6)? Bob knew how to use integer chips, so he took out some colored buttons and a marker from his pocket, and started to do the math on the monsters hand.
Bob quickly came to this conclusion, by using zero pairs. He proudly told the monster his answer, and the monster started yelling and cussing. He soon stopped, and began to laugh.
"I'll get you on the next one!", he said. Here it is: what is (+5) + (+8)? Hmm, thought bob, I'd better use integer chips for this one.
He came to this conclusion by using the buttons as integer chips. He told the monster his answer, and this time the monster began to tear up the pumpkin patch in his rage and frustration, and almost trampled Bob. He did this for awhile, and then came back and sat down. "RRRRRR, alright, try this one, Mr. Smug.", said the monster, barely containing his anger. "What is (+100) + (+200) equal?!?" "MUAHAHAHAHAHAHAHAHAHAHAHAAAAA!", he laughed at the blank, hopeless look on his face. Okay Bob, he thought, just think. That's it!, he thought , I'll use a number line!
"Hooray!", he yelled, "I've got it!". He thought it was simple, he just had to use a number line. "Oh, alright, I'll let you go." Bob started walking along home, rejoicing. It was way to easy, I'm gonna brag to all my frei- and then the monster ate him.
