Natural Numbers an Integers
Consider the two statements, "all natural numbers are integers" and "all integers are natural numbers". Which statement is not correct? Provide an example to support your answer.
"All integers are natural numbers" is not correct. For example, -5 is an integer but it is not a natural number.
In the past two and a half years, a tree grows an average of 4 inches each month. Today, the tree is 225 feet tall. How tall was the tree two and a half years ago.
215 feet tall. The tree grew by 30 *4=120 inches. That is equivalent to 10 feet. So, the tree was 225-10=215 feet tall two and a half years ago.
Which of the expressions below is NOT equivalent to the fraction 2/3 ? You must explain to get points.
(2(5))/(3(5) (2/5)/(3/5) 1/(3/2) (2+5)/(3+5)
(2+5)/(3+5) is not equivalent to 2/3 .
If a 24-foot tall building casts a shadow of 14 feet, how tall is a tree that casts a shadow of 56 feet?
96 feet tall.
If 8/m=-2/7 , then what is the value of m/8 ?
m/8=-7/2
Rewrite the product below using our base-10 system.
11*11
11*11=121=100+20+1=1*10^2+2*10^1+1*10^0
Consider the statement -2(a+b)=a-2b
When a=0, is this statement always true, sometimes true, or never true?
It is always true.
You eat one half of a cake. The next day you eat one third of what is left. The next day you eat one fourth of what is left. After this, what fraction of the cake remains?
One fourth of the cake is left.
The racetrack at Charlotte Motor Speedway is 3/2 miles long. If the "Coca Cola 600" is a 600-mile race, how many times will the winner go around the track?
400 times
If 3/2y-5/6y=5/9+1/9 ,what is the value of y?
y=1
What is the largest natural number?
There is no largest natural number. The set of natural numbers is infinitely large - for any large number, a larger one can be obtained by just adding 1.
Consider the equation -3(a+7)=12b-21
What must be true of the ratio a/b in order for this equation to be an identity?
(Assume that a≠0 and b≠0).
a/b=-4
Using eight different numbers one time each, write four fractions in order from least to greatest.
Different answers are possible. One example is
1/8, 2/7, 3/6, 4/5
Nate walks 39.7 meters in 45.3 seconds. If he walks at the same rate, approximately how many meters will he walk in 6 minutes? (60 seconds = 1 minute)
Approximately 320 meters.
Are rational numbers closed under division? Create an argument to show that they are or provide an example to show that they are not.
Yes, rational numbers are closed under division. The argument is that if you take any two rational numbers and divide them, the result is another rational number:
a/b÷c/d=(ad)/(bc)