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Operations with INTEGERS

Operations with INTEGERS. ADDING INTEGERS. SUBTRACTING INTEGERS. MULTIPLY INTEGERS. DIVIDE INTEGERS. ADDING INTEGERS. Same Signs = ADD and Keep the Sign Different Signs = SUBTRACT and take the sign of the larger number.

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Operations with INTEGERS

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  1. Operations with INTEGERS ADDING INTEGERS SUBTRACTING INTEGERS MULTIPLY INTEGERS DIVIDE INTEGERS

  2. ADDING INTEGERS • Same Signs = ADD and Keep the Sign • Different Signs = SUBTRACT and take the sign of the larger number On a certain day in NYC, the temperature was -4 degrees. On that same day, the temp in Austin was 47 degrees. What was the difference in the two temperatures? -6 + 3 = 9 + 12 = 15 + -8 = -24 + -10 =

  3. On the left side of your notebook, let’s try a few using a number line to help us….

  4. “Left Side” Reflection Copy the sentence and fill in the blanks with your own words: To add integers with the same signs, I have to _______________________________. To add integers with different signs, I have to ______________________________.

  5. SUBTRACTING INTEGERS • KEEP, CHANGE, SWITCH!!! (Leave, Change, Opposite) • Same Signs = ADD • Different Signs = SUBTRACT The temperature at noon was -3 degrees. By 10 pm on the same day the temperature decreased by 5.4 degrees. What was the temp. at 10 pm? -6 - 9 = 15 – (-7) = -22 – (-11)= 8 – 10 =

  6. Now, try these on your own: -30 – 14 = 9 + -15 = 4 – (-6) = 3 – 18 = -14 + -2 – 10 =

  7. “Left Side” Reflection Copy the sentence and fill in the blanks with your own words: To add integers with the same signs, I have to _______________________________. To add integers with different signs, I have to ______________________________. If I am subtracting integers, I must ____________________________________________________________________________

  8. Practice with Integers • Complete the Integers Practice Sheet (front and back). Show all of your work and check your answers by using a number line! • Complete 5 problems at a time. Then, take your paper to a solution station to check your answers. Make corrections to the ones you miss and ask questions if you do not understand!

  9. MULTIPLY INTEGERS • Multiply the numbers • Same Signs = POSITIVE • Different Signs = NEGATIVE A submarine dives into the ocean at -200 ft. per min. How far down can the submarine go in 15 min.? 12 x 4 = -6 x 5 = 9 x -3 = -11 x -8 =

  10. DIVIDE INTEGERS • Divide the numbers • Same Signs = POSITIVE • Different Signs = NEGATIVE What is the average of -15, 7, -4 and 10? Calvin earned $1, 425 by working five days in a week. He then received a $200 cut for being late. What is the average amount that he earned per day? 18 ÷ (-2) = -25 ÷ (-5)= 48 ÷ 12 = -56 ÷ (7)=

  11. “Left Side” Reflection Copy the sentence and fill in the blanks with your own words: The rules for multiplying and dividing integers are __________________________________________________________________________________________________________________

  12. Operations with Decimals ADDING DECIMALS SUBTRACTING DECIMALS MULTIPLY DECIMALS DIVIDE DECIMALS

  13. ADDING DECIMALS • Line up the decimals! • Fill spaces with zeros! • Add the numbers • Bring down the decimal Sheila spent $5 on binders, $2.95 on pencils, and $14.50 on locker decorations. How much did she spend on her school supplies? 4.75 + 23.6 = 3.5 + (-7.63) =

  14. SUBTRACTING DECIMALS • Line up the decimals! • Fill spaces with zeros! • Subtract the numbers • Bring down the decimal Tyler had $80.45 in his bank account on Monday. He deposited $20.50 on Tuesday and withdrew $37.75 on Weds. How much did Tyler have in his account on Thursday? 305.6 – 22.99 = -25 – (-13.3) =

  15. Now, on the left side of your notebook, let’s do a few more practice problems: 34.5 + (-15) = -20 – (-10.75) = -8.9 + - 4.22 = -120 – 85.02 =

  16. “Left Side” Reflection Copy the sentence and fill in the blanks with your own words: When I am adding or subtracting numbers with decimals, I have to __________________________________________________________________________________________________________________

  17. MULTIPLY DECIMALS – Copy the notes and examples on to your BLUE foldable in your INB. When you are finished copying, check your homework at the solution stations. • Multiply the numbers like whole numbers! • Do NOT line up the decimals! • After you multiply the numbers, count your decimal places and move your decimal. Derek spends $3.25 on breakfast and $5.50 on lunch every school day. How much does he spend in one school week? What is the product of -2 and 4.3? 15.4 x 6.22 =

  18. DIVIDING DECIMALS • Set it up in the house • You can NOT divide by a decimal – make your divisor a whole number by moving the decimal!! • Monkey see, monkey do! If you move the decimal outside, you gotta move it inside. • Line up the decimal to your answer. A jug of orange juice contains 18.75 fluid ounces. If it is shared equally among 2 ½ cups, how many ounces of orange juice does each cup receive? What is the quotient of 6.3 ÷ (-0.7)? 14.02 ÷ .002 =

  19. “Left Side” Reflection Copy the sentence and fill in the blanks with your own words: To multiply decimals, I have to __________________________________________________________________________. To divide decimals, I have to ___________________________________________________________________________.

  20. Fly Swatter Activity Sound is used to measure ocean depth. Sound travels 1.5km per second through water. If it takes 3.7 seconds for a sound to reach the bottom of the ocean, how deep is the water? -15.8 x 0.3 -4.74 5.55 -47.8 x -0.04 A scale model of a race car is 18.2 cm long and 6.9 cm wide. Each centimeter on the model represents 0.3 m on the actual car. How long is the actual car? 1.912 5.46 2.08 ÷ -1.6 A package of M&M’s candies contains 5 colors of M&M’s and weighs 1.68 oz. If each candy weighs 0.03 oz., how many are in the package? -1.3 56 A machine uses 2.5 liters of fuel each hour it runs. Its fuel tank was filled with 10 L, but 1.5 L have already been used. How many more hours will the machine run? 93.25 3.4

  21. Operations with FRACTIONS ADDING FRACTIONS SUBTRACTING FRACTIONS MULTIPLY FRACTIONS DIVIDE FRACTIONS

  22. ADDING FRACTIONS • Least Common Denominator! • If you change the bottom, change the top! Monkey see, monkey do! • Add the numerators • The denominator stays the same Amy ate ¼ of a box of cereal. Blake ate 2/9 of the same box. What fraction of the box of cereal did they eat together? 1/6 + 3/4 = 2 ½ + 1 1/3 =

  23. SUBTRACTING FRACTIONS • Least Common Denominator! • If you change the bottom, change the top! Monkey see, monkey do! • Subtract the numerators • The denominator stays the same Amy ate ¼ of a box of cereal. Blake ate 2/9 of the same box. How much more did Amy eat than Blake? 4/5 – 2/3 = 5 1/8 – 2 ¼ =

  24. “Left Side” Reflection Copy the sentence and fill in the blanks with your own words: When I am adding or subtracting fractions, I have to _________________________________________________________________________________________________________________.

  25. Now, on the left side of your notebook, you try these on your own:

  26. MULTIPLY FRACTIONS Multiply: 3/5 x 2/3 = - 4/7 x 1/8 = - 1 ¾ x - 3 ½ = • Multiply straight across! • Mixed numbers must be turned into improper fractions! Alfred paid $350 for a rug. Bill paid 2/5 of the price that Alfred paid for the same rug. How much did Bill pay? An artist is cutting pieces of ribbon. Each piece he cuts measures 7/8 inch. The artist cuts off 5 pieces. How many total inches of ribbon has he cut off?

  27. “Left Side” Reflection Copy the sentence and fill in the blanks with your own words: The rules for multiplying fractions are _____________________________________. If it is a mixed number, I have to ____________________________________.

  28. Now, let’s try some with fractions and integers!

  29. DIVIDE FRACTIONS 3/4 ÷ 1/6 = 1/2 ÷ - 4/9 = 2/3 ÷ 2 6/7 = - 5 ÷ - 1 ½ = • Flip the 2nd Fraction (reciprocal) • Multiply straight across Jean equally shared a box of chocolates with two friends. The box weighed 9/5 pounds. What is the weight of chocolate that each of the friends received? If you pack 22 boxes in 1 5/6 hours, what is the average number of boxes packed per hour?

  30. Now, let’s try some with fractions and integers!

  31. “Left Side” Reflection Copy the sentence and fill in the blanks with your own words: If I want to divide fractions, I have to ____________________________________. If it is a mixed number or whole number, I have to ______________________________.

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