GED

The Mathematical Reasoning test evaluates your ability to solve quantitative and algebraic problems. You have 115 minutes to answer approximately 46 questions in two parts: Part 1 (5 questions, no calculator) and Part 2 (about 41 questions, on- screen calculator available). Formats include multiple choice, drag-and-drop, fill-in-the-blank, drop-down, and hot spot.

A formula sheet is provided on screen. The test assesses basic arithmetic, geometry, statistics and probability, and algebraic reasoning.

Whole Numbers and Place Value

Whole numbers are the counting numbers (0, 1, 2, 3 …) with no fractions or decimals. Place value determines the value of each digit based on its position; moving left, each position is ten times greater: ones, tens, hundreds, thousands, ten- thousands, hundred-thousands, millions.

When comparing whole numbers, compare digits from left to right. A number with more digits (and no leading zeros) is larger.

Addition combines quantities. Align place values and carry when a column sum exceeds 9.

Subtraction finds the difference. When the top digit is smaller than the bottom digit, borrow from the next column.

Multiplication is repeated addition. Multiply each digit of the bottom number by the entire top number, shift one place left for each row, then add the partial products. Know the multiplication facts through 12 × 12.

Division splits a quantity into equal groups: dividend ÷ divisor = quotient. Long division repeats divide, multiply, subtract, and bring down.

Evaluate expressions in this sequence (PEMDAS): Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right). Nested parentheses are evaluated from the innermost outward.

➜

➜

➜

( ) first

powers and roots

left to right

left to right

Fractions

A fraction represents part of a whole. The numerator (top) shows how many parts you have; the denominator (bottom) shows how many equal parts make the whole.

Operation	Rule
Equivalent Multiply or divide numerator and denominator by the same non-zero number . fractions
Simplify	Dividenumeratoranddenominatorbytheirgreatestcommonfactor(GCF) .
Add/subtract Rewritewithacommondenominator(ideallytheleastcommondenominator) thenaddorsubtract , numerators .
Multiply	Multiplynumeratorstogetheranddenominatorstogether;simplify .
Divide Multiplybythereciprocalofthedivisor(thereciprocalofa/bisb/a) .
Mixed→improper	Wholenumber×denominator+numerator placedovertheoriginaldenominator , .

Decimal place value extends to the right of the decimal point: tenths, hundredths, thousandths, and so on.

Add or subtract: align the decimal points vertically, then compute as with whole numbers.

Multiply: multiply as whole numbers, then place the decimal so the product has as many decimal places as both factors combined.

Divide: move the decimal in the divisor to make it a whole number, move the dividend's decimal the same number of places, then divide.

Convert: fraction → decimal, divide numerator by denominator; decimal → fraction, use place value as the denominator (0.75 = 75/100 = 3/4).

Percent means "per hundred." To convert a percent to a decimal, divide by 100 (move the decimal two places left); to convert a decimal to a percent, multiply by 100. To convert a percent to a fraction, place it over 100 and simplify.

ProblemType	Method
Findapercentofanumber Multiplythenumberbythepercentwrittenasadecimal .
Findwhatpercentonenumberisofanother	Dividethepartbythewhole thenmultiplyby100 , .
Findthewholefromapartandapercent Dividethepartbythepercentwrittenasadecimal .
Percentincrease	(New−Original)÷Original×100

Percent decrease

(Original − New) ÷ Original × 100

Ratios and Proportions

A ratio compares two quantities and can be written a:b, a to b, or a/b; simplify ratios to lowest terms. A proportion states that two ratios are equal. To solve, cross-multiply: if a/b = c/d, then ad = bc.

A unit rate expresses a ratio with a denominator of 1 (for example, miles per hour or price per ounce). Divide the numerator by the denominator to find it; unit rates make comparisons straightforward.