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Mathematics 3. March 13, 2011 Class work . #1. The long multiplication of the numbers, which end with zeros, is written in this form: 310 x 3 930 26 x 20 520 28 x 30 490 x 2_ 36 x 20 #2. Compute: 30 x 50 = 70 x 90 = 8 x 300 = 600 x 5 = 800 x 80 = 3 x 7000 = 60 x 400 = 200 x 900 = #3. a There are liters of juice in 5 identical cans. How many liters of juice are there in 12 cans? a There are liters of juice in 5 cans. How many cans of this type do we need to distribute 12 liters of juice? c One bag holds kg of barley, and another bag holds three times as many kilograms as the first bag. How many more kilograms are here are in the second bag than in the first? m kg of potatoes, 20 kg per box, and n kg of carrots, 30 kg A truck delivered per box. How many boxes of vegetables did the truck deliver in all? 160 x 6_ 25 x 40 #4 a) Annie was going to New York City. On her way she met 3 men. Each man had a bag. There were 3 cats in each bag. How many living beings were traveling to New York City _____________________________________________________________ _____________________________________________________________ b) The length of a wooden log is 5 feet. Every minute we cut 1 foot of wood off. How many minutes will it take to cut the whole log? _____________________________________________________________ _____________________________________________________________ c) A man met a family of grandfather, father and son. The man asked how old they were. The grandfather answered: “We are 100 years old in all.” Then the man asked the father the same question. The father said: “Altogether my son and I are 45 years old. My son is 25 years younger than me.” The curious man was no able to find out the age of these grandfather, father, and son. Can you help him? _____________________________________________________________ _____________________________________________________________ _____________________________________________________________ Division by 10, 100, 1000… #5 Find the result using example on the picture below: Division is an operation, which is opposite to multiplication. When we divide by 10, 100, 1000 and so on, the only thing we need to do is to get rid of a zero, 2 zeroes, 3 zeroes and so on at the right end of the number. #5 Compute: 5600 10 290000 100 8400 100 60000 10 42000 1000 170000 1000 75000 100 9800000 10000 250 10 550 10 3000 100 4400 100 35000 1000 33000 1000 400000 10000 220000 10000 #7 Compute. There is something special about these examples. What do you notice? Which example can we write next? 9 x90 800 x 8 70 x 700 6 x 60000 #9 Use long multiplication to compute: 6900 x 8 790 x 600 6300 x 40 92 x 52 5400 x 70 39000 x 60 #11 . #12 ∠ABC is the complement or supplement of ∠CBD #13 Triangles: How do we call a figure shown on the picture above? The figure is called a triangle, because it has 3 angles. The segments, which construct a triangle, are called the sides of a triangle. The sum of the sides of a triangle is called a perimeter (the sum of the segments AB + BC + CA). Usually one of the sides of a triangle is drawn horizontally. Examine the triangles on the picture below. What is the difference between the triangles on the picture? One of the angles in △A1B1C1 is a right angle. A triangle with a right angle is called a right triangle. How do we call a △A2B2C2? Obtuse. Why? Can a triangle have two obtuse angles? Why or why not? Can a triangle have two right angles? Why or why not? What happens to the sides of two right angles if we extend them? Compare the sides and the angles of a △ABC. Which side is the longest? Which angle is the largest? Which side is the shortest? Which angle is the smallest? Conclusion: In a triangle, the largest angle lies opposite the longest side. In a triangle the smallest angle lies opposite a shortest side. Also the opposite is true: the shortest side is across the smallest angle. What can you say about the sides of a △ABC and its sides? A triangle, which has three congruent sides, is called an equilateral triangle, or a regular triangle. What can you tell about the sides AC and AB in a △ABC? Angles ABC and ACB? A triangle, which has 2 congruent sides is called isosceles triangle. Does any isosceles triangle have two congruent angles? Do you agree? Think! If the angles were not congruent then one of the angles would be greater than the other. For example angle ABC would be greater than angle ACB. In a case like this would the sides AB and AC be congruent? #14. How do we call the triangles on the pictures below? #15 Using a blue pencil, mark the figure, which is formed by intersection of: a) △ABC and △ACD b) △ABC and △ABD #16 Ordered pairs.