Question | Answer |
addition property of equality | adding the same number to each side of an equation produces an equivalent equation.
x-3=2
x-3+3=2+3 |
conversion factor | a ratio of two equivalent measures in different units.
the ratio 1ft/12 in. is a conversion factor. |
cross products | in the proportion a/b=c/d the products ad and bc are called cross products. you can use following property of cross products to solve proportions. |
cross products property | the cross products of a proportion are equal.
3/4=9/12, so 3(12)=4(9), or 36=36 |
division property of equality | dividing each side of an equation by the same nonzero number produces an equivalent equation.
5x=20
5x/5=20/5 |
equivalent equations | equations that have the same solution.
9/3=3 and9/3 +a are equivalent equations |
formula | an equation that states a relationship among quantities
the formula for the volume v of a cylinder is V=3.14^2h, where r is the radius of the cylinder and h is its height
the formula for the volume V of a cylinder is V-3.14^2h, where r is the |
identity | an equation that is true for every value.
5-14x=(1-14/5x) |
inverse operations | operations that undo one another
addition and subtraction are inverse operation. |
isolate | using properties of equality operations to get a variable with a coefficient of 1 alone on one side of the equation.
x+3=7
x+3-3=7-3
x=4 |
literal equation | A literal equation is an equation that involves two or more variables. |
multiplication property of equality | multiplying each side of an equation by the same nonzero number produces an equivalent equation.
x/3=2
x/3.3=2.3 |
percent error | the ratio of the absolute value of the difference of the measured value and an actual value compared to the actual value, expressed as a percent. |
percent change | the ratio of the amount of change to the original amount expressed as a percent.
the price of a sweater was $20. the price increases $2. the percent change is 2/20=10% |
percent decrease | the percent change found when the original amount decreases
the price of a sweater was $22. the price decrease $2. the percent change is 2/22~9% |
percent increase | the percent change found when the original amount increases. |
proportion | an equation that states that two ratios are equal
7.5/9=5/6 |
rate | a ratio of a to b where a and b represent quantities measured in different units.
125 miles/ 2hours 0r 62.5 mi/h |
ratio | a ratio is the comparison of two quantities by division
7:3 5/7 |
relative error | the ratio of the absolute value of the difference of a measured value and an actual value compared to the actual value.
|5-5.5|=|-0.5|+0.5=1
5.5 5.5 11 |
scale | the ratio of any length in a scale drawing to the corresponding actual length. the lengths may be in different units.
the scale on the road map is 1.5 inches=12 miles |
scale drawing | an enlarged or reduced drawing similar to an actual object or place.
a blue print is a scale drawing of a house or building. |
similar figures | similar figures are two figures that have the same shape, but not necessarily the same size.
similar figures could be a big triangle and a smaller triangle that look just alike. |
scale model | a three-dimensional model that is similar to a three-dimensional object.
a ship in a bottle is a scale model. |
Subtraction property of equality | subtracting the same number from each side of an equation produces an equivalent equation.
x+3=2
x+3-3=2-3 |
Unit analysis | including units for each quantity in calculation to determine the unit of the answer.
to change 10ft to yards, multiply by the conversion factor 1yd/3ft. 10ft(1yd/3ft)=3 1/3yd |
Unit rate | a rate with a denominator of 1.
the unit rate for 120 miles driven in 2 hours is 60 mi/h. |