**Under the Title**

Grade 7 Math Journal

Chapters 1 and 3

Rounding/Significant Figures

How to round: After determining the place value, look at the number to the right. If it is 5 or higher, you round up by adding one to our place value digit. If it is less than 5 (4 or lower) you keep the number the same. Then change all remaining digits to the right to zero.

How to translate sentences into mathematical equations

Index or exponent notation

Grade 7 Journal

Chapters 1 and 3

Examples

73 rounded to the nearest ten=70

The End

47 rounded to the nearest ten=50

598 rounded to the nearest hundred=600

Significant Figures: The number of digits that have been determined to be significant based on the accuracy of a measurement. Count the digits from the left <sig. figs>

Examples

0.910 => 0.91

1.2000 => 1.2

0.45000 => 0.45

Translate all words that means more than into +, all words that means less than into minus, words like of, by, times into X, and words like group, break, times less than into division. When translating a word into minus or division you have to switch around the words that are placed in the left and right of the word that means minus or divide.

Never use O as variables and be careful with S, Z, I

Examples

add, sum, more => +

subtract, minus, smaller => -

times, product, of, by => X

half, split, into => division (fraction)

all verbs => =

nouns, direct objects => variables

combine, together, mix => ( )

John is 20cm taller

than Jason => J=20+S

Index or exponent notation tells us how many times a number is being multiplied by itself in a easy way. For example you could make 4 X 4 X 4 into 4 by using a index notation.

3

Examples

3 X 3=3

2=2

10 X 10 X 10=10

2

3

1

Square Number

Perfect square Number: A whole number multiplied by itself creates a perfect square.

Examples

1 X 1=1 =1

3 X 3=3 =9

10 X 10=10 =100

2

2

2

Cube Number

Perfect Cubes: Any whole number times itself 3 times.

Examples

2 X 2 X 2=2 =8

3 X 3 X 3=3 =27

10 X 10 X 10=10 =1000

3

3

3

Order of Operation

Order of Operation: the rule that we have to follow when doing equation that has 2 or more math symbols. The order is BEDMAS or PEMDAS(brackets, exponents,divide, multiply, add, subtract)

Order of operation is important, so that we all get the same answer.

Examples

8+4*3 => order of operation: * then +

(1+1)*2 => order of operation: do the adding in the bracket and then *

1+2 => order of operation: do the exponent first, then add

2

Factor

Factors: any number that is being multiplied to another number to make a product

Examples

8's factor: 1,2,4,8

10's factor: 1,2,5,10

15's factor: 1,3,5,15

Integer

Integer: The set of all positive and negative counting numbers.

Examples

Integers are important, because they are used for many things like equation, calculating, calculation money, and more.

1) 2

2) 3

3) -6

How to add/subtract Integers

Adding Integers: If the signs are the same, add them normal way and keep the same sign. If the signs are different, subtract the two numbers and keep the sign of the bigger number.

Subtracting Integers: Change the sign from - to +, change the sign of the second number. Then follow rules for adding.

Examples

Examples

1+2=3

4+9=13

-3+7=4

4-3=1

7-9=-2

-3-2=-5

How to multiply/divide Integers

Multiplying/Dividing Integers: If the signs are the same, the product is positive. If the signs are different, then the product is negative.

Examples

2X2=4

-1X3=-3

-4X-2=8

2/2=1

-4/2=-2

-8/-4=2

/ : Divide

Roots (Square root, Cube root)

Square root: Square roots are undoing the squaring of the number.

Cube root: Cube roots are undoing the cubing of the number.

Higher power roots(Roots of number): what number times itself gives the given number

Examples

4= 16

√

√

√

2= 4

3= 9

1= 1

√

3

2= 8

√

√

3

3

3= 27

2 2=second root of four

3 3=third root of 27

4 2=second root of sixteen

^

^

^

^=roots