BY : ERNESTO TOVAR

Math Journal Chapters 1 and 3

Describe how to round a number to a given place value or significant figure.

When Rounding a number you always have to

check the number on the right. If it’s lower

than 5 then you can’t round it and all the other

numbers on the right become 0. If it’s greater

than 5 then you can round it to the next

significant figure.

Rounding Examples

Round 89,475 to the hundredth place. The hundredth place is 4 and the tenth’s place, 7, which is

greater than 5, therefore you can round 4 to the next value which is 5.The result is 89,500

If you want to round to one significant figure then you go backwards 89,475, so the 8 will be the significant figure and when you round it it becomes 9 so it will be 90,000

If you want to round to two significant figures it will be the 9 round it and it will be 89,000

Translating English to Math

When translating English into Math, firstly you must know the math to English dictionary. For example Max scored 2 times more goals than bob, It will be M=2B,also we don’t 2xB because in algebra when you write 2B you know it’s 2xb.

Example 2. John has 4 more apples than Carlos= J=4tC

Example 3. Alex has 3 apples less than Ralph= R= A-3

Example 4. Jackie and Bruce scored 3 times less goals than Justin and Jason= J+B= U+N/3

Index Notations

Index notations are a different way to express numbers as a result of multiplication.

Example 1. 3x3x3=27

Example 2.6x6x4=36x4=144

Example 3.7x7x7x2=343x2=686

Square Number

A square number is a number by the power of 2. We don’t say by the power of two we usually say 2 squared. We call it a square number because square numbers are like finding the area of a square.

Example 1: 2=22 = 4

Example 2: 3=32 = 9

Example 3: 4=42 = 16

Cube Numbers

A cube number is the same thing as a square, but instead of power of 2 is power of 3 and we write it like this 43. We call it a cube number because cube numbers are like finding the volume of a cube.

Example 1: 4=43 = 64

Example 2: 5=53 = 125

Example 3: 6=63 =216

Order of Operations

The order of operations is how math problems can be organized so you get the right answer. It is really important if they give you a problem like this: 50(10+15)-30 you’ll be able to figure it out. If we didn’t have the order of operations everyone would get a different answer

Step 1. ParenthesisStep 2. ExponentsStep 3. DivisionStep 4. MultiplicationStep 5. Addition and SubstractionRemember always start from left to right

Order of Operations Examples

Example 1. 65+(10-5)-9=61, Always do parenthesis first .

Example 2. 49(8/64)+23=424, In algebra when the number is next to the math problem you don’t add you multiply.

Example 3. 37+(4/8x10)100= 570, Always remember the order of operations and always go from left to right or you will get it wrong.

Factors

The numbers that are being multiplied in a multiplication are called the factors of the final number.

Example 1. The factors of 12 are 1,2,3,4,6,12

Example 2. Factors of 6: 1,2,3,6

Example 3: Factors of 14: 1,2,7,14

Intergers

Intergers are all the numbers below and above zero, or all the negative and positive numbers. Intergers are important because they are used in today’s world for calculations, equations etc.

Example 1. -5

Example 2. 28

Example 3. -1200

Adding and Subtracting Intergers

Adding and subtracting intergers is pretty easy if you know the key rules. When it’s -3+7 it will be 4,but when it’s double negative like this: -5+-14, you add, so it will be -19. If it’s a double negative with brackets -3-(-4) you also add

Example 1.-14-(-13)=-1Example 2. -25+-16=-41Example 3. -14+15=1

Key Rules Addition: If signs are the same add up the numbers and keep the sign.

Key Rules Subtraction: Add the opposite.

Multiplying and Dividing Intergers

Multiplying and dividing intergers is the same thing as adding subtracting except that you have multiply and divide and you have to know the key rules.

Key Rules: If there are two different signs the answer has to be a negative number. If the signs are the same it has to be a positive number.

Example 1. -8x7=-56Example 2. -10x-10= 100Example3. -4/20=-5

Square Roots

Square roots is the opposite of square numbers. Before doing square roots you must first know the perfect squares and key rules. For example square root of 16 is 4 square root of 64 is 8.

Key Rules: “what number times itself = x”?

Example 1. Square root of 9 is 3 Example 2. Square root of 49 is 7Example 3. Square root of 6 is approximate to

2.5

Cube Roots

Cube roots are the same thing as square roots except it’s the opposite of cube numbers. Before doing cube roots you also need to remember your perfect cubes and squares and key rules.

Key Rules: “What number times itself 3 times = x”?

Example 1. Cube root of 27 is 3 Example 2. Cube root of 8 is 2 Example 3. Cube root of 6 is approximate to

1.8

How do we Find Higher Power Roots of Numbers?

Finding power roots of higher numbers is the same thing as cube roots and square roots except it’s a higher number than 3. For example fourth roots, are: “ a number times itself 4 times = x”. Same with fifth roots, sixth roots and so on.

Example 1. Fifth root of 3125 is 5, 5 times itself 5 times equals 3125

Example 2. Fourth root of 16 is 2, because 2 times itself 4 times equals 16

Example 3. Sixth root of 24 is 1.69838133, when a number like this shows up on your calculator just round it off to one or two decimal places and you will get an approximate value of the sixth root of 24. It will be 1.7, 1.7 times itself 6 times = 24