Decimal Operations
Negative Numbers!
Solve This Equation
Match the Image
Word Problem
100
True or False: 39.56 = 39.560000
Explain why
TRUE, because adding zeros after the decimal point does not affect the value of a number.
100
What happens when you add two negative numbers? "The result will be ... "
The result will be even more negative!
100
If you subtract 4 from the left side of the following equation, what do you have to do to the right side and why?
2(x+3) + 4 = 18
You must subtract it from the right side as well to keep the equation in balance!
100
What is the distance between the position of the octopus and the position of the seagull?
The distance between 10 and -10 is 20!
100
Clare has $150 in her bank account. She buys a bike for $200. What is Clare's account balance now?
Her balance is -$50
200
True or False: 39.56 = 39.056
Explain why
FALSE, because adding zero after a decimal point but before other digits changes the PLACE VALUE of the number.
200
Do these two numbers have the same ABSOLUTE VALUE?
-23 and 23
Absolute Value is the distance of any number FROM ZERO, so yes, they do.
200
How do you CHECK if you solved the equation correctly?
Demonstrate with the equation x + 4 = 12
You plug the value for "x" back into the equation. For example:
x + 4 = 12
x = 12 - 4
x = 8
Plug "8" into "x" in the original equation:
8 + 4 = 12
12 = 12
Alright!
200
What negative number addition equation does this number line represent? 
-20 + 15 = -5
200
Tyler is overdrawn at the bank by $180. His brother has $70 more than him. How much money does Tyler’s brother have?
Tyler has -$180. His brother has -$180 + $70.
-180 + 70 is like -(180 - 70) = -110
Tyler's brother has -$110.
300
What is the place value of "5" in the following number:
6.345
"5" is in the THOUSANDTHS place value.
300
Why is subtracting a negative like adding a positive?
Subtracting a negative is like adding a positive, because when you take away a negative number, you make your overall result MORE POSITIVE!
300
Make a tape diagram for the following equation and solve it:
6 (x+1) = 24
6 (x+1) = 24
x + 1 = 24/6
x + 1 = 4
x = 4 - 1
x = 3
300
Write the equation for the following tape diagram:
5(x + 2) = 19
300
A tortoise travels 0.945 miles in 3.5 hours.
If it moves at a constant speed, how many miles per hour is it traveling?
0.27 miles per hour
400
What happen to the decimal point in the following operations:
ADDITION/SUBTRACTION
MULTIPLICATION
In addition/subtraction operations, line up the numbers BY THE DECIMAL POINT, then move the decimal point down to the result.
In multiplication, line up the numbers BY THE RIGHT EDGE, then add the number of places FROM THE RIGHT EDGE before the decimal points in both of the factors. In your product, count that number from the right and insert your decimal point.
400
In your own words, try to explain why multiplying two negatives gives you a positive. You can use a model or a number line to explain!
One explanation:
When you multiply and negative by a positive, you're adding negative groups, so the result is negative. When you multiply a negative by a negative, you're SUBTRACTING negative groups. Subtracting a negative is like adding a positive, therefore, when you are subtracting negative groups, your result becomes more positive.
400
Solve the equation that's on the hanger:
2 (x + 3) = 14
x + 3 = 7
x = 7 - 3
x = 4
400
Which equation does this diagram NOT match? Explain why.
3 (x + 6) = 30
400
What did she do wrong and how would you fix it? Solve the equation.
She should have shown two separate "x"s!
To solve this equation, get rid of 16, then divide by two to find x.
2x + 16 - 50
2x = 50 - 16
2x = 34
x = 34/2
x = 17
500
What is the result of the following long division problem? Show your work on the board for complete points.
12.265 / 5.5 = ???
2.23 but you've got to show your work!
500
A submarine is descending to examine the seafloor 2,100 feet below the surface. It takes the submarine 2 hours to make this descent. What is its rate of descent in feet/hour?
2,100 / 2 = 1,550 feet/hour
500
Choose 2 equations to solve on the white board in the next 2 minutes:
We'll talk about the solutions together.
500
What is the equation for the following model?
5 x + 1 = 3 x + 5
500
Priya, Han, and Elena, are members of the running club at school.
Priya was busy studying this week and ran 7 fewer miles than last week. She ran 9 times as far as Elena ran this week. Elena only had time to run 4 miles this week.
How many miles did Priya run last week?
First let's find how far Priya ran THIS WEEK:
She ran 9 times as far is Elena, or (Elena's distance) x 9
Elena ran 4 miles, so THIS WEEK Priya ran 4 x 9 = 36 miles.
Let's figure out how far she ran LAST WEEK:
She ran 7 FEWER miles this week than she ran last week.
LAST WEEK - 7 = THIS WEEK
LAST WEEK - 7 = 36
LAST WEEK = 36 + 7
LAST WEEK = 43
Priya ran 43 miles last week. That's a lot of miles!