FAST Math Grade 5 flashcards

32 cards. Read the term and the definition here. The deck at the top of this page is optional.

Place value

The value of a digit depends on its position in the number. Moving one place left multiplies the digit's value by 10; moving right divides it by 10.

Standard algorithm for multiplication

Multiply by each digit of the second factor, shift each partial product one place left, then add the partial products to get the final product.

Remainder as a fraction

In whole-number division, the remainder can be written over the divisor. Dividing 17 by 5 gives 3 remainder 2, or 3 2/5.

Order of operations

Evaluate grouped parts first, then exponents, then multiplication and division from left to right, then addition and subtraction from left to right.

Rounding decimals

Find the rounding place, then check the digit to its right. A 5 or greater rounds up; 4 or less keeps the digit. Drop digits after the place.

Equivalent fractions

Fractions that name the same amount. Multiplying or dividing numerator and denominator by the same nonzero number creates an equivalent fraction, such as 2/3 = 8/12.

Common denominator

A shared denominator that lets fractions be added or subtracted. Rewrite each fraction as an equivalent fraction with that denominator, then combine numerators.

Multiplying fractions

Multiply numerators together and denominators together. The result can be simplified, and multiplying by a fraction less than 1 makes the product smaller.

Reciprocal

The fraction formed by swapping numerator and denominator. A fraction times its reciprocal equals 1, and dividing by a fraction means multiplying by its reciprocal.

Mixed number to improper fraction

Multiply the whole number by the denominator, add the numerator, and place the result over the original denominator. Example: 2 3/4 becomes 11/4.

Fraction as division

A fraction a/b means a divided by b. So 3/4 equals 3 ÷ 4, which converts to the decimal 0.75.

Expression versus equation

An expression is a combination of numbers, operations, and variables with no equals sign. An equation sets two expressions equal and can be solved.

Variable

A letter or symbol that represents an unknown or changing number. In 4n + 2, the variable n stands for a number you can substitute.

Distributive property

Multiplying a sum by a number equals multiplying each addend by that number and adding: a(b + c) = ab + ac. Useful for mental math.

Numerical pattern rule

A rule describing how terms change. In 5, 9, 13, 17 the rule is add 4 each time, and the nth term is 4n + 1.

Solving one-step equations

Undo the operation by applying its inverse to both sides. For x + 7 = 12, subtract 7 from both sides to get x = 5.

Volume of a rectangular prism

Multiply length by width by height. A prism measuring 4 by 3 by 5 units has a volume of 60 cubic units.

Area of a triangle

Half the product of base and height, where height is perpendicular to the base. A triangle with base 10 and height 6 has area 30.

Perimeter

The distance around a figure, found by adding side lengths. For a rectangle, perimeter equals 2 times the sum of length and width.

Unit cube

A cube with edges of 1 unit, having volume 1 cubic unit. Filling a prism with unit cubes counts its volume in cubic units.

Metric length conversions

1 kilometer equals 1,000 meters, 1 meter equals 100 centimeters, and 1 centimeter equals 10 millimeters. Multiply to change to smaller units.

Ordered pair

Two numbers (x, y) locating a point on the coordinate plane. The first number moves along the x-axis; the second moves along the y-axis.

Mean

The sum of all data values divided by the number of values. For 4, 6, 8, 10 the sum is 28 and the mean is 7.

Median

The middle value when data are ordered from least to greatest. With an even count, average the two middle values.

Mode and range

The mode is the value appearing most often. The range is the greatest value minus the least value, showing how spread out the data are.

Probability of an event

The number of favorable outcomes divided by the total number of equally likely outcomes. Values range from 0 (impossible) to 1 (certain).

Complement rule

The probability that an event does not happen equals 1 minus the probability that it does. If rain chance is 0.3, no rain is 0.7.

Line plot

A number line with an X or dot above each value for every time it occurs. Clusters, gaps, and the most common value are easy to see.

Estimation check

Round numbers to convenient values, compute mentally, and compare with the exact answer. A large mismatch signals a calculation error.

Tape diagram

A bar model that shows parts and wholes. Equal segments represent equal quantities, helping translate a word problem into an equation.

Checking a solution

Substitute the answer back into the original equation or situation, or reverse the operations, to confirm the result satisfies every condition.

Explaining reasoning

State a claim, support it with the computation or model used, and explain why that method fits the problem's structure.