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The temperature in the morning when you leave to come to school Is -3 degrees. When the sun comes out, the temperature warms up by 2 degrees. What Is the temperature after the sun comes out? 1 0-1 -2 So by moving up 2 degrees, we see that we end up at -1 degrees. -3 To solve this problem, start by finding 3 degrees on our thermometer/ number line. We know from before, that when we are adding numbers, we move up the number line. -3+2=-1 -4 Morning temp Rise In temp b. A frog is sitting on the stairs, on the 3rd step down from the main floor. It Jumps up 2 steps.
Which step is it on now? Main Floor -1 step -2 step -3 step -4 step -5 step So by having our frog Jump up 2 steps, we see that we end up on 1 step below the main floor, or -1 . To solve this problem, start by putting our frog on the 3rd step down from the mall floor (-3). We know from before, that when we are adding numbers, we move up the number line, or In this case the stairs. 2. A. Black tokens are positive numbers, red tokens are negative numbers. There are 5 black tokens in the cup. I want to take out 3 red tokens. How many tokens are left in the cup? I have no red (negative) tokens in my cup, so I need to add some.
By adding some, that changes how many I have altogether, so I need to balance the numbers and make It so that I am adding “O”. By adding 3 black (positive) tokens to my 3 red (negative) tokens, I am adding Then, by taking away my 3 red (negative) tokens, I am left with 8 black (positive) tokens. B. On Christmas morning It Is 5 degrees Celsius In Vancouver. In Squamish the temperature Is -3 degrees Celsius. What Is the deference In temperature? Let’s start for Squamish. To find the difference, or distance between the two numbers, we’ll count how many between them. 3. A. Jane owed 4 people $2 each. How much money did she owe all together?
Tom $2 Phil $2 Kate $2 Melissa $2 $2 owed x 4 people = $8 owed -EX.=-8 b. Mike plays a game where he Jumps backwards. Each time he Jumps, he moves 2 feet backwards. If Mike Jumps 4 times, how far back is he from where he started? Mike’s starting place is O. So if he Jumps 4 times, we see that he has moved 8 feet backwards. Would probably be drawing this on a whiteboard and draw the numbers in the other direction, rather than what I have illustrated above, to maintain consistency of how we typically view a number line. But for this assignment, rather Han flip my image and having all my numbers backwards, I’ll Just leave it be for now. 4. A. Mom bought 6 cupcakes that I was to share equally with my sister. How many cupcakes did we each get? Let’s make our 6 cupcakes, and divide them into 2 groups. This puts 3 cupcakes in each group. 6+2=3 b. Mark ordered 6 truckloads of topsoil for his yard. If he puts equal amounts into the front and the back, how many truckloads will be in each yard? Here are our 6 trucks. We can direct them as they arrive to go to the front or the back yard. How many went to the back? And how many went to the front? 6 + 2 = 3 5. /3 a. Kim has 1/2 meter of ribbon. Fern has 2/5 meter of ribbon. How much ribbon do they have together?
To add these amounts, we need to have denominators that are the same. The lowest common multiple of 3 and 5 is 15. How do we make our two fractions have the same denominator of 15? Let’s do 1/2 first. 1/2 x 55 = 515 Remember, 55 is the same as 1, so we’re not actually changing how much ribbon we have, Just how we are measuring it. Now let’s do 26. 2″ 5 Now we have two fractions with the same denominator that we can add together. 5″ 15 They have 1 1/1 5 meter of ribbon together. B. Find the answer to: 26 = To be able to add the two fractions together, we need to start with the same “counter”.
By “counter”, I mean the same unit of measuring. Thirds are a different size than fifths, so we need to find a way to measure both of them with the same size piece. If we divide each third into fifths, and each fifth into thirds; we end up with fifteenths. 1/2 is equal to 515, and 26 is equal to 615. Now that we have the same size counter, or denominator, we can add them together and see that we have 1 1/15. 6. A. 1/4 x 26 meaner the total number in h off group if there is 26 of the original whole. We are wanting to know what one quarter of two-fifths is.
We could draw a picture: Each of the blue lines is 1/5 of the whole, and the little purple lines are dividing 2/5 into 4 parts (or quarters). With this picture, we can see that h of 2/5 is half of 1/5, or if we continue the little purple lines: 1/10 of the whole. B. Seeing our results from our example above, we can see how h x 26 gives us our denominators. 1 4 x 2 5=2 20=1 10 By reducing our answer of COO to the smallest equivalent fraction, we make it easier to understand the total. 7. 31/2+1/2- a. How many halves are in 3 h? If we have 4 circles, color 3 h of them. We want to know how many h pieces we have colored.
We’ll divide each of our full circles into 2 pieces (for halves), then we can count how many h pieces we have. We can see by the diagram that there are 7 halves in 3 h. B. We can also find the answer to this question without pictures. If we take our equation of 3 1/2 * 1/2 = we start by inverting our divisor (h), which makes it 2/1, or more commonly called “2”. When we invert the divisor, we must also change the operation to multiplication, because we are working with the ‘opposite’ of the divisor. Our equation then looks like this: 3 1/2* 1/2=3 = = our diagram and investigation from above proves that this method of calculation is correct.
We make 3 h an improper fraction, so that we can multiply the numerators and the denominators with each other. When we divide 2 into 14, we get the whole number of 7. 8. -0. 3 – 0. 03 a. Subtracting from a negative number may be easier to understand if we look at subtraction as going down, and subtraction from a negative number is going down some more. We start at -0. 3 and move down our number line 0. 03 spaces. We’ll find that we end up at -0. 33 b. Another way to look at subtracting from an negative number is to remember that subtracting takes us to a number farther to the left of O if we think of a horizontal number line. 0. 3 – 0. 03 = -0. 35-0. 34-0. 33 -0. 32-0. 31 -0. 3-0. 29-0. 28 0 So we’ll start at -0. 3 and move 0. 03 spaces to the left, bringing us to -0. 33. 0. 3 x -0. 03 a. From our understanding of multiplying, we know that this equation meaner to have 0. 3 groups of -0. 03. When we are multiplying with negative numbers, we start with the rule that “a positive number multiplied by a negative number creates a negative number. ” (5. Multiplying Negative Numbers) Knowing this, our answer will be negative, we can continue with the remainder of the multiplication equation.
First, we will multiply the numbers as though there were no decimals: ex.=9. Now that we have that, we need to include the appropriate decimal places. (5. 2 Multiplying Decimals) We find the number of digits to the right of the decimal place in each of our original numbers: 0. 3 has one digit to the right of the decimal, and -0. 03 has two to the right of the decimal, giving us a total of three. Therefore, our answer, when we incorporate the ideas from above, is negative, has 3 sits to the right of the decimal, and 9: giving us an answer of -0. 09 b. 0. 3 x -0. 03 = This equation can also be done easily with fractions. 0. 3 = 310-0. 03 -3100 By multiplying the fractions: 3′ 10 Remembering the rule that “a positive multiplied by a negative is negative. ” Our answer of -91000 , returned to a decimal form is -0. 009 10. -0. 3 + 0. 03 a. Similarly to multiplication, “a negative divided by a positive is negative. ” So we know our answer will once again be negative. The standard method of dividing decimals is to move the decimal to the right until we are dividing with a whole number.
In this case, we would be moving the decimal two places to the right or multiplying by 100, making our 0. 03 the whole number of 3. If we do this to the divisor, we must also do this to the dividend, making our -0. 3 the whole number of -30. By multiplying both the divisor and dividend by the same number, it is similar to having multiplied by one. Now our equation has become -30 + 3 which is easily answered as -10. B. If we do this equation with fractions, -0. 3 = -310 0. 03 = 3100 Our equation becomes: -310 + 3100 = -310 x 1003 = -30030 = -10 Remembering the rule that “a negative divided by a positive is negative. “