About the Exercises for Grades 7-8

Learn Integers, Equations, Rational Numbers and more. This tutorial contains over 800 practice exercises and lessons in the following topics:
  • Unit I. Integers
    Representing Integers, Opposites and Absolute Value, Expressions and Variables, Order of Operations, Evaluating Expressions.
  • Unit II. Equations
    Equations, Open Equations and Solutions, Properties of Operations, Distributive Property, Simplifying Equations, Addition and Substraction Equations, Multiplication and Division Equations.
  • Unit III. Rational Numbers
    Definitions, Decimals as Fractions, Adding and Subtracting Decimals, Adding and Subtracting Like Fractions, Adding and Subtracting Unlike Fractions, Dividing Fractions, Dividing Decimals.
  • Unit IV. Number Theory
    Exponents and Roots, Scientific Notation, Factors and Multiples, Greatest Common Factors, Least Common Multiple.
  • Unit V. Percent
    Ratios, Proportion and Percent, Solving Proportions.
  • Unit VI. Equations and Inequalities
    Solving Multi-step Inequalities.


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Absolute value of a numberThe number of units the number is from zero on the number line.
Algebraic expressionA combination of variables, numbers and at least one operation
Algebraic fractionFractions with variables in the numerator and /or denominator
Closure property of additionFor all rational numbers x and y, x + y is a rational number
Closure Property of multiplicationFor all rational numbers X and Y, X x Y is a rational number
Common ratioThe ratio between any two successive terms in a geometric sequence
Compound statementOne statement formed by connecting two simple statements with words such as and, or , if, then, and if and only if
Consecutive even integersNumbers given when beginning with an even integer and counting by two's
Consecutive numbersNumbers in counting order
Consecutive odd integersNumbers given when beginning with an odd integer and counting by two's
ConsistentA system of equations is consistent and independent if it has one ordered pair as its solution. A system of equations is consistent and dependent if it has infinitely many ordered pairs as its solution
ConstantA monomial that does not contain a variable.
Decimal notationA way of expressing numbers using a base ten system. 483.26 is expressed in decimal notation
Degree of a monomialThe sum of the exponents of the variables of the monomial
Density propertyBetween every pair of distinct rational numbers, there is another rational number
DomainThe domain of a relation is the set of all first components from each ordered pairs
ElementOne of the members of a set
Empty setA set with no elements
Equally likely eventsEvents that has an equal chance of occurring
Excluded valueA value excluded from the domain of a variable because that value substituted for the variable would result in a denominator of zero
FactorialThe expression n! is the product of all accounting numbers beginning with n and counting backwards to 1
FunctionA function is a relation in which each element of the domain is paired with exactly one element of the range
Functional ValueThe symbol f(3) represents the functional value of f for x = 3
Geometric sequenceA sequence in which the ratio between any two successive terms is the same.
Grouping symbolsSymbols used to clarify or change the order of operations in an expression. Parentheses, brackets, and the fraction bar are grouping symbols
Independent eventsTwo or more events in which the outcome of one event does not affect the outcome of the other event(s).
IntegersThe set of numbers {. . . , -3, -2, -1, 0, 1, 2, 3, . . }
InterceptAn intercept is a point where a graph crosses the x-axis or y-axis
Interquartile rangeThe difference between the upper quartile and the lower quartile of a set of a data is called the interquartile range. It represents the middle half of the data in the set
Irrational numbersNumbers that cannot be expressed in the form a / b, where a and b are integers, b is not equal to zero
Line plotNumerical information displayed on a number line
Linear equationAn equation for which the graph is a straight line
LogicThe study of formal reasoning
Lower QuartileThe lower quartile divides the lower half of the set of data into two equal parts
MeanThe sum of the numbers in a set of data divided by the number of pieces of data
MedianIn a set of data, the median is the number in the middle when the data are organized from least to greatest
ModeThe number or item that appears most often in a set of data
Natural numbersThe set of numbers { 1, 2, 3 . . .}
Null setA set with no elements
Open sentenceA sentence containing at least one variable. The sentence is neither true nor false
OppositeThe opposite of a number is its additive inverse
Percent of decreaseThe ratio of an amount of decrease to the previous amount, expressed as a percent
Percent of IncreaseThe ratio of an amount of increase to the previous amount, expressed as a percent
PercentageA number which is compared to another number (base) in the percent proportion
ProbabilityThe ratio that tells how likely it is that an event will take place P (event) = number of favorable outcomes / number of possible outcomes
Property of proportionsIf a / b = c / d then ad = bc
Pythagorean TheoremIn a right triangle, the square of the hypotenuse is equal to the sum of the squares of the length of the legs
RangeThe difference between the least and greatest numbers in a set of numbers.
Real numbersIrrational numbers together with rational numbers form the set of real numbers
ScaleA ratio that compares the size of a model to the actual size of the object being modeled
Stem-and-leaf plotIn a stem-and-leaf plot, each piece of data is separated into two numbers that are used to form the stem and leaf. The data are organized into two columns. The column on the left is the stem and the column on the right is the leaf
Upper quartileThe upper quartile divides the upper half of the set of data into two equal parts
VariablesPlaceholders in mathematical expressions or sentences
Whole numbersThe set of numbers { 0, 1, 2, 3, . . . }

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