FAST Math Grade 4 cheat sheet

Place value: each position is 10 times the value of the position to its right, so in 4,582 the 5 means 500 and the 8 means 80.

Rounding rule: find the target place, then look at the digit to its right; 5 or more rounds up, 4 or less keeps the digit.

Standard form uses digits (7,304), expanded form writes the value of each digit (7,000 + 300 + 4), and word form spells it out.

Multiplication is repeated addition and division is the inverse of multiplication, so 6 × 7 = 42 means 42 ÷ 6 = 7 and 42 ÷ 7 = 6.

Multi-digit multiplication: multiply by each place value, then add partial products; 34 × 12 = 34 × 10 + 34 × 2 = 340 + 68 = 408.

Division algorithm: divide, multiply, subtract, bring down; a remainder must be less than the divisor.

Order of operations: evaluate parentheses first, then multiplication and division left to right, then addition and subtraction left to right.

Factors divide a number evenly; multiples are products of that number and whole numbers; 1 is a factor of every whole number.

A number is prime if its only factors are 1 and itself (2, 3, 5, 7, 11...); 1 is neither prime nor composite.

Equivalent fractions come from multiplying or dividing numerator and denominator by the same nonzero number: 2/3 = 8/12.

To compare fractions, rewrite with a common denominator or compare to 1/2; 3/5 > 1/2 because 3/5 = 6/10 and 1/2 = 5/10.

Adding and subtracting fractions requires a common denominator; the denominator names the size of the pieces and does not get added.

Multiplying a fraction by a whole number: a/b × n = (a × n)/b, so 3/4 × 2 = 6/4 = 1 1/2.

A fraction a/b equals a ÷ b, so 3/4 = 0.75 and 7/2 = 3.5.

Decimal place values to the right of the point are tenths, hundredths, thousandths; 0.6 = 6/10 and 0.60 = 60/100 = 6/10.

To compare decimals, line up the decimal points and compare digits place by place, so 0.45 < 0.5 because 45 hundredths < 50 hundredths.

A mixed number combines a whole number and a fraction; convert with (whole × denominator) + numerator over the same denominator.

Multiplying a decimal by 10 shifts the digits one place left; dividing by 10 shifts them one place right.

A variable is a letter or symbol standing for an unknown number, as in n + 5 = 12.

An expression has numbers, operations, and variables but no equals sign; an equation states that two expressions are equal.

Evaluate an expression by substituting the value of the variable, then following order of operations: 3x + 4 when x = 2 gives 6 + 4 = 10.

Inverse operations undo each other: addition undoes subtraction, multiplication undoes division.

Solve an equation by applying the inverse operation to both sides to keep it balanced.

A pattern rule describes how a sequence changes; in 3, 7, 11, 15 the rule is add 4, and the tenth term is 3 + 9 × 4 = 39.

Input-output tables pair a rule with values: if the rule is multiply by 3, input 5 gives output 15.

The commutative property allows order changes in addition and multiplication (a + b = b + a); the associative property regroups (a + b) + c = a + (b + c).

Customary length: 12 inches = 1 foot, 3 feet = 1 yard, 5,280 feet = 1 mile.

Customary capacity and weight: 8 fluid ounces = 1 cup, 2 cups = 1 pint, 4 quarts = 1 gallon, 16 ounces = 1 pound.

Metric conversions move by powers of 10: 1 kilometer = 1,000 meters, 1 meter = 100 centimeters, 1 kilogram = 1,000 grams.

Elapsed time is found by counting forward from the start time or subtracting start from end, regrouping 60 minutes as 1 hour.

Area of a rectangle = length × width; perimeter = 2 × (length + width).

A line plot shows data values as X marks above a number line; the value with the tallest stack is the most common.

Mean of a data set = sum of values ÷ number of values; it is a fair-share average.

An angle is measured in degrees; a right angle is 90°, a straight angle is 180°, and a full turn is 360°.

A point has no size, a line extends forever in both directions, a line segment has two endpoints, and a ray has one endpoint.

Parallel lines never meet and stay the same distance apart; perpendicular lines meet at a 90° angle.

Triangles are classified by angles (acute, right, obtuse) and by sides (equilateral, isosceles, scalene).

The three angles of any triangle add to 180°, so two known angles determine the third.

Quadrilaterals have four sides; a square is a rectangle and a rhombus, and every square is a parallelogram.

A line of symmetry divides a figure into two matching halves that fold onto each other.

A right triangle's area is half the product of its two legs: area = (base × height) ÷ 2.

Angle types: acute is less than 90°, right is exactly 90°, obtuse is between 90° and 180°, straight is exactly 180°.

A protractor measures angles; align the vertex with the center mark and one ray with the 0° line, then read the scale that starts at 0°.