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PEMDAS

PEMDAS. 2011-2012 Qualifying Test 4 th Grade. Directions:

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PEMDAS

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  1. PEMDAS 2011-2012 Qualifying Test 4th Grade

  2. Directions: Solve each of these problems and write your answer in the box given. All answers should be completely simplified. If you finish early, go back and rework the problems. You will have 30 minutes for this section, and you will be notified when 3 minutes remain. There is no penalty for guessing, so if you are not sure of an answer you should guess. Any answer in dollars should be rounded to the nearest penny. You may not use a calculator on this section.

  3. 1. If you wanted to get $35 all in dimes, how many dimes would you get? • $35.00 / $.10 = OR There are 10 • 3500/10 = dimes in one • 350/1 = dollar. 10 X 35 = 350

  4. 2. One rectangle measures 15 ft x 20 ft. Another rectangle has twice the area of the first rectangle. If it is also 15 ft wide, how long is it? 40 ftor twice as long

  5. 3. What is the sum (that’s adding) of half of 36 and a third of 48? • ½ of 36 = 18 • 1/3 of 48 = 16 • 18 + 16 = 34

  6. 4. The Pastry chef made 48 cakes for the 288 kids that came to the party. What fraction of a cake will each kid get if everyone gets the same amount of cake? 1/6 • What do you have to do here? • Division. • 48 cakes divided by 288 = • 48 = 12 = 1 288 72 6 *Make sure your fractions are simplified!

  7. 5. If we make a code where each letter is represented by the number of its place in the alphabet (that would make a=1, b=2, c=3,...., z=26), what is the total when you add all those numbers together for the word math? • 42 • M = 13 • A = 1 • T = 20 • H = 8 13 + 1 + 20 + 8 = 42

  8. 6. What number is 5 less than 2 more than 52? 49 52 + 2 = 54 54 – 5 = 49

  9. 7. Leonard Euler was born in 1707, so this year we are celebrating his 304th birthday. It might have been nice if someone had thought to celebrate his 125th birthday. What year would that have been? • 1707 • + 125 • 1832

  10. 8. What is 5 2/3 more than 7 1/3? 7 1/3 +5 2/3 13

  11. 9. Three friends and I put dimes in a piggy bank. After the 4 of us put in equal numbers of dimes, 1 had 3 dimes left over. I put those in the piggy bank, too. The total number of dimes we put in the bank could have been A. 23 B. 24 C. 25 D. 26 • Before I put in my last three dimes the number of dimes in the bank was a multiple of 4.(8, 12, 16 20, 24…) To which I added 3. Which of these numbers is a (multiple of 4) + 3? A. 23 (20 +3)

  12. 10. The perimeter of my square hammock is 64. How long is each side of my hammock? • You know that a square has 4 equal sides. • Divide 64 by 4. 64/4 = 16 • Check by multiplying 16 by 4 = 64.

  13. 11. The product of 2 different whole numbers is 7. Their sum is _______? • A product is the answer to a multiplication problem. Only two numbers, when multiplied, will give you the answer 7. • 7 and 1. • 7 X 1 = 7 • A sum is the answer to an addition problem. • 7 + 1 = 8

  14. 12. The sum of 2 positive whole numbers is greater than their product if one of the numbers is ____? • The sum is the answer to an addition problem. • The product is the answer to a multiplication problem. • WHEN would it be possible for the sum to be larger than the product? Try Guess & Check…zero isn’t a whole number so try 1. 1+ any number is GREATER than 1 X any number. • So the answer is 1

  15. 13. If paper clips cost 48¢ a dozen, then _______ paper clips cost $1.00. • A dozen is 12. So divide 48 by 12. 48/12 = 4¢ each • How many times does 4¢ go into 100¢ ($1.00)? • 100/4 or 25 times • 25

  16. 14. 27 ÷ 3 = 3 X _____? • You know that one side of this equation equals the other side of the equation. • So 27 ÷ 3 (or 27/3) equals 9. • Now the problem reads 9 = 3 X _____? • The answer is 3

  17. 15. Pete paid for 4 identical frozen pizzas with a $20.00 bill. If Pete got $3.60 in change, how much did one frozen pizza cost? • This problem has 2 parts. a. How much did Pete pay for 4 pizzas? $20.00 – $3.60 = $16.40 b. If 4 pizzas cost $16.40, divide $16.40 by 4 or 1640/4 to get the cost of one pizza. • One pizza cost $4.10

  18. 16. (perimeter of my square) ÷ (sum of 2 side-lengths of my square) = ?? • You know that a square has 4 equal length sides. The perimeter is the sum of the lengths of all 4 sides. • If you sum (add) two side-lengths, that is only half of the perimeter, • so the answer to how many (÷) 2 side-lengths there are in the square is 2

  19. 17. What is the next number in the pattern 11, 13, 15, 17, 15, 13, …. • The pattern adds 2 until 17 then it subtracts 2 so the next number would be 11

  20. 18. How many eight ounce glasses of water are in a 2-gallon container? • (1 gallon = 4 quarts, 1 quart =32 ounces) This is a three part problem. a. 1 gallon contains 4 (quarts) X 32 ounces = 128 ounces. b. 2 gallons = 128 +128 = 256 ounces c. 256 (ounces) divided by 8 (ounces) = 32 glasses

  21. 19. One side of an equilateral triangle is 6 cm long. The triangle’s perimeter is _______cm. You know that a triangle has 3 sides. You know that an equilateral triangle has 3 sides that are the same length. To find the perimeter you add the lengths of the sides. So 6cm + 6cm + 6cm = 18cm

  22. 20. Add the whole numbers from 1 to 100. • If you looked at a number line you might notice that 1+99 =100, 2+98=100, 3+97=100, etc. all the way to • 1, 2, 3, ……. (50) 97, 98, 99 100 How many times does that work? 49 (50 is left out!) How many 100’s is that 49 X 100 = 4900 But don’t forget 50 & 100 that were left out of the pattern. So 4900 +100 + 50 = 5, 050

  23. Phew! It’s over! So many of these problems ask you to think about what you KNOW about numbers, not just spit out answers. • Now, go back over the problems and think about how they are worded and then how they are worked. • REMEMBER that word problems require reading. Always! • Make sure you read the question carefully and understand what is required for the answer. What are they asking for? • Think about what you will need to do to arrive at that answer. What operations will I need to perform? • Once you’ve done that, pick up your pencil! Do the computations! • Youknow how to solve the problems!

  24. PEMDASactually means Parentheses ( ) Exponents 22 Multiplication X or * Division ÷ or / Addition + Subtraction - • These are the order of operations in an equation. • You ALWAYS do the problem in the parentheses first. • Then solve any exponential numbers. Then do any multiplication, division, addition & subtraction, in that order.

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