Fractions and mixed numbers
How to subtract integers
Change the sign of the second integer and then follow rules of addition (-3)-(-4)=(-3)+(+4)=+1
Which is greater 3/4 or 2/3
Change to equivalent fractions the common denominator would be 12 - 3*3=9, 4*3=12 so first fraction is 9/12 do the same for the second fraction is now 8/12. Which is greater 9/12 or 8/12 9/12>8/12
How to divide two integers
Divide absolute values of the integers. The answer is positive if both integers have the same sign or negative if they have different signs
Change fraction 5/8 to a decimal
Divide the numerator by the denominator 5 divided by 8 = 0.625
Multiply fractions
Do cancellation first. 4/5 * 3/8 4 will go into 8 so it will change the 4 to a 1 and the 8 to 2. Your new fractions are 1/5 * 3/2 then multiply two numerators And that is your new top number, then multiply two denominators and that is your new denominator = your new answer is 3/10
Distance formula
Distance = rate x time
Do you make denominators match in multiplication and division
No
Do you turn mixed numbers into improper fractions when multiplying?
No
Solve (5)(-2)=
-10
Integers
0, all counting numbers 1,2,3,4 etc and the negatives of the counting numbers -1,-2,-3,etc
5*3/8=
1 7/8
List the order of operations
1. Simplify within each grouping symbol by beginning with the most inner most parentheses 2. When an expression contains two or more operations with no grouping symbol indicating the order of operations A. Multiply and divide from left to right then B. Add and subtract in order from left to right
Write 3.2 as a fraction
3 2/10 which can be reduced to 3 1/5
How many feet are in a yard
3 feet in a yard
Make a mixed number into a fraction
4 2/3 = 4*3+2 over 3 - answer 14/3
Volume of a Sphere
4/3 x pie x radius cubed
2 x 6 2/5
12 4/5
5*3/16=
15/16
Make improper fraction to a proper fraction
17/5 = 17 divided by 5 = 3 with a remainder of 2 = 3 2/5
140 / 7/9
180
What is the sum of the interior angles of a triangle
180 degrees
1 5/7 x 1 5/9 =
2 2/3
3/8 / 4/9
28/32
Surface area of a box
2LW + 2LH + 2WH
6 x 7 3/8
44 1/4
360 / 4/5
450
7 x 6 2/3
46 2/3
3/8 + 4/9
59/72
Solve (9) + (-3)
6
3 x 2 1/4
6 3/4
Surface Area of a 3D cube
6S squared
Add or subtract fractions - part 2
8/12 + 9/12 = 17/12 then simplify to 1 5/12
Solve (-3) - (-4)
= (-3) + (4) =1
Solve (-5) - (8)
= (-5) + (-8) = -13
Solve -12/6
=-2
Solve 7-8 divided by 2 x 3=
=-5
Solve (-4)(-3)
=12
Solve -8/-4
=2
What is the Commutative Property of 2*3
=3*2
What is the Commutative Property of 2+3
=3+2
Round 3.567 to the nearest hundredth
=3.57
A is b% of what number
A=b•xb
-8 over -4 =
Answer +2
(+5)(-2)=
Answer -10
-12 over +6 =
Answer -2
Two legs of a right triangle have side lengths of 5 and 12. What is the hypotenuse
Answer 13
Multiply 4 * 2/9 =
Answer 8/9
Where do you stop and why when dividing 2.6/0.345
Answer is 7.5 - stop when the remainder is less than half of the divisor
Terminating decimal
Any decimal number which ends (has a last number)
Repeating decimal
Any. Umber behind the point that over and over in some set pattern
How do you indicate an absolute value
Enclose the number in vertical bars |1| or |-4|
How do you estimate the product in multiplication 9.71 and 87.43
Estimate each of the numbers 9.71 =10 87.43=87 10*87=870
Absolute Value
Except for zero absolute value is always a positive number.
Add or subtract fractions - step 1
Find a common denominator. 2/3 + 3/4 the common denominator is 12, 4*3=12, 3*3=9 so this makes 3/4 into 9/12. Do same for other fraction.
What percent of 19.95 is 4.5
Find a percent (hundredths) 4.5/19.95 approximates to 5/20 = 25/100 =25%
What are the rules for operations with integers with different signs (-7) + (4) =
Find the difference in the integers and put the sign of the largest absolute value before the answer (-7) + (4) = -3
What position is the 8 in 3.187
Hundredth
Divide Fraction
Invert the divisor (second fraction) and then multiply. 3/4 divided by 5/6 = 3/4 * 6/5 do a cancelation would make it 3/2 * 3/5 then 3*3 = 9 and 2*5=10 so answer is 9/10
In the statement: what is A% of B What does is and of mean?
Is= answer Of = multiply X=a • b
Volume of a box
LWH
Divide 0.7935/0.23
Move decimal on the divisor to the right until it is a whole number. Then move the decimal in the divided number the same. Umber of places to the right. 0.23 = 24 and 0.7935 = 079.35. In your final answer your decimal should line up with the divided numbers decimal.
How to multiply integers
Multiply absolute values of the integers. The answer is positive if both integers have the same sign or negative if they have different signs (-4)(-3)=+12
Surface area of a right cylindar
SA = 2 x pie x radius squared
Surface area of a sphere
SA = 4 x pie x radius squared
What are the rules for operations with integers with like signs (+5) + (+3) =
Since both integers have a + in front of them your answer is +8 Remember that you do not have to write the +
What are the rules for operations with integers with like signs (-5) + (-3) =
Since both integers have a - in front of them your answer is -8
On a number line are the smallest numbers in the left or right
Smallest numbers (negative numbers) are on the left
What is associative property
States you can add or multiply regardless of how the numbers are grouped (meaning it does not matter where you put the parenthesis) Example 3+4+1=3+4+1 equals (3+4) +1=3+(4+1) equals (7)+1=3+(5) equals 8=8
What types of numbers are not identities
Subtraction and division
What position is the 1 in 3.187
Tenth
Divisor
The number that you are dividing by.
Subtrahend
The second integer in a problem
How do you recognize when two expressions are equivalent
They have the same evaluation for any number replacements of the variables.
What position is the 7 in 3.187
Thousandth
Reciprocal
To invert a fraction also known as when you flip a fraction. The reciprocal of 3/4 is 4/3
Commutative properties
To move around numbers or letters Example: a+b=b+a or 2+3=3+2
What is the numerator
Top number of a fraction
Volume of a 3D cube
V = S cubed
Volume of a right cylindar
V = pie x Radius squared x height
Quotent
Whole number part of a mixed number 4 2/3, Quotient = 4
What is the formula for the area of a square
Width x height or A = a squared
Reduce Fraction
You can reduce fractions if the numerator and denominator can both be decided by the same number 12/18 both can be divided by 6 so new number is 2/3
What is the absolute of -8
|-8|=8
What is the absolute of 7
|7|=7
Write a. Number with a repeating decimal
3.7777777
Round 4893 to the tens place
=4890
3*3/10
=9/10
Write a number with a terminating decimal
3.67
How do you estimate the division 483.45/62.1
=8
Solve (4-7*2)+6*5-12
=8
Round 83.649 to one decimal place
=83.6
What is the Commutative Property of a+b
=b+a
What is the Commutative Property of ab
=ba
Area of a triangle
A = 1/2 x B x H
Area of a semicircle
A = 1/2 x pie x radius squared
Dividend
A number to be divided by another number
Distributive property
A property used to multiply a single term and two or more terms inside a set of parentheses example 2(3+6)
Pythagorean Theorem
A squared + b squared = c squared. Three sides of a right triangle. A and b are the lengths of the legs and c is the length of the hypotenuse.
What is a square root of a number
A squared is the number that represents A times itself
What is the denominator
Bottom number of a fraction