Number Systems
What is an integer?
An integer is a whole number that can be positive or negative, and also 0. Whole numbers and natural numbers are also integers.
What is a mixed number? What is an improper fraction?
A mixed number are numbers with whole and fraction parts, and improper fractions are fractions in which the numerator is greater than the denominator.
When adding or subtracting fractions, what number must be the same in order to solve?
The denominator of both fractions must be the same number in order to add or subtract. If the denominators are unlike, you can find the LCM of both fractions to find like denominators.
What is a variable? Why do we use them?
A variable is a placeholder for an unknown value. We use variables when we are missing a piece of information and need to find it. Once the unknown value is found, we can get rid of the variable and replace it with the found value.
GCF is the highest number that divides exactly into two or more numbers. LCM is the smallest number that multiplies into two or more numbers
What is a rational number?
A rational number is any number that can be presented by a fraction. Natural, whole, and integers are all rational numbers.
Convert 15/4 into a mixed number
3 3/4
Find the common denominator between the fractions 17/10 and 1/5.
The common denominator would be 50.
If we wanted to add them, we would then need to adjust the numerators to match the new denominators. 17/10 would become 85/50 and 1/5 would become 10/50.
What is the value of 6x + y – 2 if x = 4 and y = 0?
22
What is the GCF of 24 and 18?
What is the LCM of 24 and 18?
GCF is 6
LCM is 72
What makes a number irrational?
A number is irrational if it cannot be represented as a fraction. Numbers that go on forever/are non-terminal (like pi, 3.14159265359....) and imperfect square roots are examples of irrational numbers
Convert 2 7/9 into an improper fraction.
25/9
What is 3/5 + 5/8?
49/40
Simplify -3cd by evaluating c = 5.
A. -15d
B. 15c
C. -75
D. -15cd
A. -15d
Create three numbers who all have the GCF of 6.
12, 18, 30, etc.
Is it possible to have a number that is an integer and irrational number? Show or explain your reasoning.
No, because an integer is a rational number, meaning that they can be represented by a fraction. Irrational numbers are in their own category.
How can you represent 2 3/4 using a visual model? (HINT: You could use cubes, circles, etc. to show the value)
Check with your teacher!
What is 1/3 + 1/6 - 1/12?
5/12
Evaluate 6n – 3(n + 2) for n = -5.
-21
12 is the GCF of which two numbers?
A. 8 and 12
B. 12 and 28
C. 24 and 36
D. 24 and 48
Write a number that is a rational number and an integer, but not a whole number.
All negative numbers or negative fractions with the denominator 1 are rational and integer numbers but not whole. Whole numbers are all natural numbers (positive w/o decimal) and the number 0.
Ex. -1, -4, -16/1
Add the improper fractions below and them convert the sum into a mixed number
13/8 + 21/5 = ?
5 33/40
What is 5 1/3 - 2 5/6?
2 1/2
Find the value of r
−3(r−7)=−24
r = 15
Kiara has 36 orange candies and 54 yellow candies. She wants to divide them into identical bags. What is the greatest number of bags she can divide them between?
Kiara can make 18 bags of candies