SK SSA Math 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. Moving one place left multiplies the value by 10, so in 5,482 the 4 is worth 400 and the 8 is worth 80.

Order of operations

The agreed sequence for evaluating expressions: parentheses or brackets, then exponents, then multiplication and division left to right, then addition and subtraction left to right.

Rounding to a place

Find the target place and look at the single digit to its right. If that digit is 5 or more, increase the target digit by one; otherwise leave it unchanged.

Equivalent fractions

Fractions naming the same amount, such as 1/2, 2/4, and 5/10. Multiply or divide numerator and denominator by the same nonzero number to create them.

Dividing by a fraction

Multiply by the reciprocal of the divisor. For example, 3/4 ÷ 2/5 becomes 3/4 × 5/2, which equals 15/8 or 1 7/8.

Percent as a decimal

A percent is a ratio out of 100, so divide by 100 to get a decimal: 45% = 0.45. To find 45% of 60, multiply 0.45 by 60 to get 27.

Variable and expression

A variable is a letter representing an unknown or changing number. An expression combines numbers, variables, and operations but has no equals sign, unlike an equation.

Solving one-step equations

Apply the inverse operation to both sides to isolate the variable. In x + 9 = 14, subtract 9 from both sides to get x = 5; in 4x = 28, divide by 4.

Distributive property

Multiplying a sum by a number gives the same result as multiplying each addend separately and adding: a(b + c) = ab + ac. For example, 6(20 + 3) = 120 + 18 = 138.

Arithmetic sequence nth term

A sequence with a constant difference d has nth term a + (n − 1)d, where a is the first term. For 5, 8, 11, ..., the 10th term is 5 + 9×3 = 32.

Geometric sequence

A sequence in which each term is the previous term multiplied by a constant factor. In 2, 6, 18, 54 the factor is 3, so the next term is 162.

Combining like terms

Add or subtract terms that have exactly the same variable part, so 7x + 3x = 10x but 7x + 3 cannot be combined. Constants combine with constants.

Inequality sign reversal

When both sides of an inequality are multiplied or divided by a negative number, the direction of the sign reverses: −2x > 8 becomes x < −4.

Perimeter versus area

Perimeter is the distance around a figure, measured in linear units. Area is the surface covered, measured in square units, so the two are never interchangeable.

Area of a triangle

Area equals one-half times base times height, where the height must be perpendicular to the chosen base. A triangle with base 10 cm and height 6 cm has area 30 cm².

Trapezoid area

Area equals one-half times the sum of the two parallel bases times the height: A = ½(b₁ + b₂)h. With bases 4 and 8 and height 5, the area is 30.

Circle circumference and area

Circumference equals 2πr or πd, the distance around a circle. Area equals πr², the space inside. Both use the radius, which is half the diameter.

Volume of a prism

Volume equals length times width times height for a rectangular prism, reported in cubic units. A box 3 by 4 by 5 units has volume 60 cubic units.

Triangle angle sum

The three interior angles of any triangle add to 180°. If two angles measure 65° and 50°, the third measures 180 − 115 = 65°.

Supplementary and complementary

Supplementary angles add to 180°; complementary angles add to 90°. An angle of 35° is complementary to 55° and supplementary to 145°.

Metric unit conversion

Multiply when converting to a smaller unit and divide when converting to a larger unit. Since 1 m = 100 cm, 2.5 m = 250 cm and 340 cm = 3.4 m.

Mean of a data set

The sum of all values divided by the number of values. For 4, 7, 8, 9, 12 the sum is 40 and there are 5 values, so the mean is 8.

Median and mode

The median is the middle value of an ordered list, or the mean of the two middle values. The mode is the value that appears most often.

Range and outliers

Range is the maximum minus the minimum value. An outlier is a value far from the rest; it pulls the mean toward it but affects the median much less.

Simple probability

Probability of an event equals favorable outcomes divided by total equally likely outcomes. Drawing a red marble from 3 red and 7 blue gives 3/10.

Complement rule

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

Independent events

Events whose outcomes do not affect each other. Multiply their probabilities to find both occurring: two coin flips both heads give ½ × ½ = ¼.

Theoretical versus experimental probability

Theoretical probability comes from counting equally likely outcomes; experimental probability comes from observed results. Experimental values approach theoretical ones as trials increase.

Estimation before computing

Round numbers to compatible values to get a rough answer, then compute exactly. If 48 × 21 estimates as 50 × 20 = 1000, an answer far from 1000 signals an error.

Working backward

Reverse each operation in reverse order to undo a sequence of steps. If a number is doubled then increased by 6 to give 20, subtract 6 then halve to get 7.

Unit rate method

Find the value of one unit, then scale to the amount needed. If 4 notebooks cost $10, one costs $2.50, so 7 notebooks cost $17.50.

Proportion cross-multiplication

Two equal ratios can be solved by cross-multiplying. From 3/4 = x/12, multiply 3 × 12 = 4x, giving 36 = 4x and x = 9.