Grade 7 Number Properties and Algebraic Terms

Question 1

Addend

Answer 1

A number which is involved in addition. Numbers being added are considered to be the addends.

Question 2

Sum

Answer 2

The result after numbers and/or variables are added

Question 3

Difference

Answer 3

The amount by which one value is greater or smaller than another.

The result when numbers are subtracted.

Question 4

Factor

Answer 4

any of the numbers (or symbols) that form a product when multiplied together

Question 5

Product

Answer 5

a quantity obtained by multiplication; the answer to a multiplication problem

Question 6

Quotient

Answer 6

The result after numbers and/or variables are divided

Question 7

Order of Operations

Answer 7

working left to right repeatedly: Parentheses, Exponents; then Multiplication, Division; then Addition, Subtraction

Question 8

Expression

Answer 8

a phrase made up of one or more numbers, variables, and operations

Question 9

Equation

Answer 9

equivalent expressions

Question 10

Variable

Answer 10

a letter that can be replaced with any number from a set

a quantity that varies or changes according to certain circumstances

a placeholder for any value

Question 11

1-Step Equations

Answer 11

identify inverse operation to isolate variable

Question 12

2-Step Equations

Answer 12

first add/subtract, then multiply/divide to isolate variable

Question 13

Function

Answer 13

relationship between two variables, can have only one x-value correspond to only one y-value

Question 14

Rate of change

positive and negative

Answer 14

slope of a line: change in y value related to change in x value
ratio that represents amount of something per time unit

Question 15

Expanded form of a number

Answer 15

a number that is expressed as the sum of multiples of ten

example 643 = (6x100)+(4x10)+(3x1)

Question 16

fraction

Answer 16

relationship of a part to a whole

numerator: represents the part
denominator: represents the whole

Question 17

special fraction information

Answer 17

fractions with a denominator of 1 are equivalent to the numerator

fractions with a numerator of 1 cannot be simplified
fractions with a numerator of 0 equal 0

fractions with a denominator of 0 are undefined because there is no such thing as “part of nothing”

Question 18

adding or subtracting fractions

Answer 18

requires the denominators be the same

Question 19

multiply or divide mixed numbers

Answer 19

before you multiply or divide mixed numbers, rewrite them as improper fractions

Question 20

multiplying fractions

Answer 20

multiply the numerators for your new numerator, multiply the denominators for your new denominator, then simplify the product

Question 21

dividing fractions

Answer 21

rewrite the first fraction, write a multiplication sign, write the reciprocal of the second fraction, multiply the fractions

Question 22

ratio

Answer 22

a relationship between two amounts

Question 23

proportion

Answer 23

relationship between two equivalent ratios

Question 24

Identity property of 0

Answer 24

adding zero

The sum of a number and zero is always that number.

Question 25

Identity property of 1

Answer 25

multiplying 1

The property which states that multiplying a number by 1 does not change the number’s value

Question 26

Commutative property of addition

Answer 26

changing the order of addends

The property which states that two or more addends can be added or that two in any order without changing the sum.

Question 27

Commutative property of multiplication

Answer 27

changing the order of factors

The property which states that two or more factors can be multiplied in any order without changing the product.

Question 28

Associative property of addition

Answer 28

changing the grouping of addends

changing the grouping of terms will not change the sum

(a + b) + c = a + (b + c);

(5+3) + 1 = 5 + (3 + 1)

Question 29

Associative property of multiplication

Answer 29

changing the grouping of factors

States that changing grouping of factors does not change the product.

(a*b)c = a(b*c)

(2 * 6) * 7 = 2 * (6 * 7)

Question 30

Distributive Property

Answer 30

multiplying grouped terms by a factor

a property indicating a special way in which multiplication is applied to addition of two or more numbers in which each term inside a set of parentheses can be multiplied by a factor outside the parentheses,

such as a(b + c) = ab + ac;

ex: 4(3 + 8) = 4(3) + 4(8)

Question 31

Integers

Answer 31

all positive and negative whole numbers

negative integers are to the left of zero, smaller negative integers are further from zero

positive integers are to the right of zero, larger positive integers are further from zero

Question 32

Absolute value

Answer 32

the distance of an integer from 0

Question 33

Addition with integers

Answer 33

if sign is the SAME – add absolute values and keep the sign

if the sign is DIFFERENT – subtract absolute values and keep the sign of the larger absolute value

Question 34

Subtraction with integers

Answer 34

change the subtraction sign to addition AND the sign of the second number

follow the guidelines for addition

Question 35

Multiplication and Division with integers

Answer 35

count the number of negative integers

if there are an even number of negative integers, the product or quotient will be positive

if there are an odd number of negative integers, the product of quotient will be negative

Question 36

Rational number

Answer 36

a number that can be expressed as a fraction, including integers

Question 37

Base and Exponent

Answer 37

The exponent is the number that indicates how many times the base is used as a factor: 4 X 4 X 4 = 4 cubed, 4 is the base; 3 is the exponent.

Question 38

Square Root

Answer 38

a number that must be multiplied by itself to equal a given number

Question 39

Calculations with exponents

Answer 39

a^n = aaaa…a (n times)
a^0 = 1
a^-n = 1/a^n
a^½ = √a
a^x * a^y = a^x+y
a^x/a^y = a^x-y
(a^x)^y = a^xy
(ab)^x = a^x * b^x
(a/b)^x = a^x/b^x

Question 40

Coefficient

Answer 40

the number that is multiplied by variable(s)

Question 41

inequality graphing hints

Answer 41

solid dot means equal to

hollow dot is not equal to

 lines to the left mean less than

lines to the right mean greater than

READ CAREFULLY the lines between two dots

Question 42

Factorial

Answer 42

product of an integer and all smaller positive integers