Everything to Remember from 7th Grade MathOrder of Operations

Description: The order in which addition, subtraction, multiplication, and division are performed determines the answer.Order:

1. Parenthesis: Any operations contained in parentheses are done first, if there are any.

2. Exponents: Exponent expressions are simplified second, if there are any.

3. Multiplication and Division: These operations are done next in the order in which they are found going left to right.

4. Addition and Subtraction: These operations are done next in the order in which they are found going left to right.

Example:

Place Value

Absolute ValueDefinition: The absolute value of a number is its positive distance from zero.Examples:

Decimal OperationsADDITION: - Write the decimal numbers in a vertical form with the decimal points lined up.Example:

SUBTRACTION: - Write the decimal numbers in a vertical form with the decimal points lined up.- Write additional zeros after the last digit behind the decimal points (if needed) so the two numbers have an equal number of digits behind the decimal point.Example:

MULTIPLICATION:- Multiply as you would regularly (ignore the decimal points).- Count the number of digits behind the decimal point in the answer. The answer must have the same number of digits after the decimal point as there are digits behind the decimal points in all the factors.Example:

DIVISION:- Always divide by a whole number.- If the divisor is a whole number, bring the decimal point straight up and divide normally.- If the divisor is a decimal number, multiply both the divisor and dividend by a power of ten (10, 100, 1000…) to make the divisor a whole number. Then divide as above.Example:

Integer OperationsADDITION: - If the signs of the numbers are the same, ADD. - The answer has the same sign as the numbersExamples:

- If the signs of the numbers are different, SUBTRACT. - The answer takes the sign of the “bigger” (abs value) numberExample:

SUBTRACTION: - To subtract a number, add its opposite- Meaning… Change the subtraction sign to addition and also change the sign of the number directly behind the subtraction sign to the opposite of whatever it is. Then follow addition rules above.- Remember… Leave, Change, OppositeExample:

MULTIPLICATION and DIVISION:- Multiply or divide as normal, then follow these rules to determine the sign of your answer.1. If the numbers have the same signs, the answer is POSITIVE.2. If the numbers have different signs, the answer is NEGATIVE.Examples:

Everything to remember from 7th Grade Math (continued)Fraction Operations

ADDITION and SUBTRACTION:1. Change to equivalent fractions with a common denominator.2. Add/Subtract the numerators3. Keep the same denominator4. Simplify if possibleExamples:

MULTIPLICATION:Common denominators are not needed.1. Multiply the numerators2. Multiply the denominators3. Simplify if possibleExample:

DIVISION:Common denominators are not needed.- To divide by a fraction, multiply by its reciprocal.1. Change the division sign to multiplication2. Flip the fraction in back of the division sign (do not change the sign!)3. Multiply as aboveExample:

Operations with Mixed NumbersAll Operations:1. Rewrite each mixed number as an improper fraction2. Follow rules for Fraction Operations3. Final answers can be expressed as improper fractions (as long as they are in simplest form)Example:

Ratios, Proportions, and PercentsDefinitionsRATIODefinition: A comparison between two quantitiesExamples:

PERCENTDefinition: “out of 100” or “per 100”Example:

PROPORTIONDefinition: A statement of equality between two ratios or fractionsExample:

SOLVING PROPORTIONSMethod 11. Change the fractions to equivalent fractions with common denominators2. Set numerators equal to each other3. Match the missing variable to it’s equivalent partnerExample:

Method 2 (Preferred) – Cross Multiply1. Cross multiply and set the two products equal to each other2. Solve the resulting one-step equationExample:

Conversions (Fractions, Decimals, and Percents)

Fraction DecimalDivide the numerator by the denominator

Decimal Fraction1. Read the decimal “correctly”2. Write what you hear as a fraction3. Simplify if possible

Decimal PercentMultiply the number by 100 and add the percent sign

Percent DecimalRemove the percent sign and divide by 100

Solving One-Step EquationsUse the addition or multiplication property of equality (whatever you do to one side of the equal sign, you must do to the other) to isolate the variable (get the variable by itself).