Numbers & Operations Flashcards
Percent Change (Increase or Decrease)
(Amount of Change / Original Value) x 100%
Ratios
A certain farm has only cows & chickens as livestock. The ratio of cows to chickens is 2:7. If there are 63 animals on the farm, how many cows are there?
Make sure units cancel out.
(2 cows / 9 animals)( x cows / 63 animals) = 14 animals
Ratios
The ratio of students to teachers at a certain school is 28:3. The ratio of teachers to cafeteria workers is 9:2. What’s the ratio of cafeteria workers to students?
(28 students / 3 teachers)(9 teachers / 2 cafeteria workers) = 252 students / 6 cafeteria workers = 42:1 … flip it. 1:42.
Proportionality
When x and y are directly proportional…
x1 / y1 = x2 / y2
Proportionality
When x and are inversely proportional…
x1y1 = x2y2
Counting & Listing
How many positive integers less than 500 are NOT divisible by 6?
498 is the greatest multiple of 6 that is less than 500. 498 / 6 = 83, meaning there are 83 multiples of 6 that are less than 500.
499 integers less than 500 - 83 multiples of 6 = 416
Counting & Listing
Mike’s arranging 7 of his awards on a shelf in his office. If he insists that his Class of 1999 Math Award be placed n the center, in how many different orders could he arrange the seven items?
Position 1: Invisible Man Award: 6 choices Position 2: Acne League: 5 choices Position 3: Push Ups: 4 choices Position 4: Math Award: 1 choice Position 5: Spin Bottle: 3 choices Position 6: Science Fair: 2 choices Position 7: Shortest Fight: 1 choice
6 x 5 x 4 x 1 x 3 x 2 x 1 = 720
Patterns
A farmer is planting a row of plants. First, he plants 2 broccoli plants, then 3 cabbage plants, then 1 apple tree, then 2 orange trees, then 1 dill weed plant. He repeats this pattern until he has filled up all the land on his farm. What kind of plant is the 782nd one he plants?
1st –> B B C C C A O O D B B C C C A O O D B B C C C A O O D
