Mathematics Section Numbers and Operations Measurement Data Interpretation Algebra Calculators are not allowed on the test!

Numbers and Operations Order of Operations Mathematical operations must be performed in the correct order when performing calculations with numbers. An easy acronym for order is PEMDAS: Parentheses, Exponents, Multiply or Divide, Add or Substract.

Subtraction of Whole Numbers with Regrouping When subtracting whole numbers (i.e. 1, 2, etc.), arrange the numbers in rows with like place values in like columns. Subtraction is started in the ones place. You must regroup (or borrow) in order to subtract a larger number from a smaller number.

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One- and Two-Step Word Problems with Whole Numbers Read the problem carefully and determine what is being asked. Set up and solve the problem. Check your answer. Does it make sense?

Addition and Subtraction of Fractions Convert the mixed numbers into fractions. Determine the least common denominator of the fractions. Rewrite each fraction as an equivalent fraction sharing a least common denominator. Add or subtract the numerators. Simplify the fraction.

Multiplication of Fractions Convert the mixed numbers into fractions. To multiply fractions, simplify factors in the numerator with factors in the denominator. Next, multiply the numerators together and the denominators together.

Division of Fractions Convert the mixed numbers into fractions. To divide fractions, keep the first fraction as it is written, change the division sign to multiplication, and flip (invert) the second fraction. Next, simplify factors in the numerator with factors in the denominator, and multiply the factors with each other.

Decimal Placement in a Product Set up the problem as if the numbers are whole (forget about the decimal points). Multiply the numbers. Count the total number of decimal places in the factors. Count back the number of decimal places and place the decimal into the product.

Decimal Placement in a Quotient Set the divisor as a whole number by moving the decimal point. Move the decimal point in the dividend the same number of places. Place the decimal point in the quotient in the same place as the dividend. Divide.

Solving Percent Problems Change the written statement into a mathematical equation. Solve for the unknown quantity. Rewrite the statement and make sure that the answer is reasonable.

Calculation of Percent Increase or Decrease Percent increase = original value – new value x 100 original value Percent decrease = new value – original value x 100 original value

Converting from fractions to decimals Divide the numerator by the denominator.

Converting from decimals to fractions There are two different methods available. Write the digits of the decimal number in the numerator of the fraction. Or, write a number that is a power of 10 as the denominator. The number should have as many zeros as there are decimal places to the right of the decimal. Then write the decimal fraction in its simplest form.

Converting from fractions to percents Convert the fraction to a decimal. Then convert the decimal to a percent.

Converting from percents to fractions Remove the % symbol. Rewrite the number as a fraction with 100 in the denominator. Simplify the fraction.

Converting from percents to decimals Remove the % symbol and move the decimal point left two places.

Converting from decimals to percents Move the decimal point right two places and add the % symbol.

Comparison of Rational Numbers A rational number can be a decimal or a fraction. When comparing decimals, compare the digits in the greatest place value. When comparing fractions, find a common denominator for the fractions and compare.

Estimation of the Solution to a Problem In other words, how do you calculate the approximate value of something. Round the numbers so there is only one nonzero digit in each number. Next, perform the indicated calculations (add, subtract, multiply or divide).

Word Problems Read the problem; determine the question. Highlight important details in the question (words, numbers, keywords). Set up the problem and solve. Is your answer reasonable? Check it. Here are some examples…

Reconciliation of a Banking Account

Calculation of Take-Home Pay

Cost of a Given Set of Items

Fractional Word Problems

Decimal Word Problems

Word Problems Involving Percents Change the written statement into a mathematical equation. Solve for the unknown quantity. Rewrite the statement and make sure the answer is reasonable.

Word Problems Involving Ratios, Proportions and Rates of Change Ratios express a relationship between two quantities. A proportion states that two ratios are equal. Rate of change problems use proportions to determine the difference in completion times for a given task. Here are some examples…