7th Grade Math Formula Sheet
Every formula and rule, each with an example
Ratios, proportions and percents
Unit rates with fractions
WorksheetDivide the amount by the number of units, even when both are fractions: miles ÷ hours = miles per hour.
Example: 12 mile in 14 hour: 12 ÷ 14 = 2 miles per hour
Proportional relationships
Worksheety = kx, where k = yx is the constant of proportionality (the unit rate).
The graph is a straight line through (0, 0) and (1, k).
Example: $3 per pound: y = 3x
Tax, tip and markup
Worksheetamount = rate × price (rate as a decimal)
total = price + amount = price × (1 + rate)
Example: $40 with 6% tax: 40 × 1.06 = $42.40
Discount
Worksheetsale price = price − discount = price × (1 − rate)
Example: $80 at 25% off: 80 × 0.75 = $60
Percent change
Worksheetpercent change = new − originaloriginal × 100
If the answer is negative, it is a percent decrease.
Example: 50 to 65: 1550 × 100 = 30% increase
Percent error
percent error = |estimate − actual|actual × 100
Example: Guess 45, actual 50: 550 × 100 = 10%
Ratios, proportions and percents (continued)
Simple interest
WorksheetI = Prt: principal × yearly rate (as a decimal) × years
total = P + I
Example: $500 at 4% for 3 years: I = 500 × 0.04 × 3 = $60, total $560
Scale drawings
WorksheetUse the scale as a ratio: drawing length : actual length.
actual length = drawing length × (actual units for each 1 drawing unit)
Example: Scale 1 in : 5 ft, so 3 in : 15 ft. 3 in on the plan is 3 × 5 = 15 ft
Integers and rational numbers
Adding integers
WorksheetSame signs: add, and keep the sign.
Different signs: subtract the absolute values, and keep the sign of the one farther from 0.
Example: −4 + (−6) = −10. −8 + 3 = −5
Multiplying and dividing integers
WorksheetSame signs: positive. Different signs: negative.
Example: −6 × (−4) = 24. −20 ÷ 5 = −4
Rational numbers
WorksheetThe integer sign rules work for fractions and decimals too.
Example: −12 + 34 = 14. −1.5 × 2 = −3
Fractions to decimals
Worksheetab = a ÷ b. The decimal either ends or repeats.
Example: 38 = 0.375. 23 = 0.666… (the 6 repeats)
Expressions and equations
Like terms
WorksheetCombine terms with the same variable part, and combine the plain numbers. x means 1x.
a + 0.05a = 1.05a (the same amount, written to show a 5% increase)
Example: 3x + 5 + 2x − 1 = 5x + 4
Expressions and equations (continued)
Two-step equations
Worksheetpx + q = r: undo the + or − first, then the × or ÷.
p(x + q) = r: divide by p first, then undo the + q.
Example: 3x + 5 = 20, so 3x = 15 and x = 5. 2(x + 3) = 14, so x + 3 = 7 and x = 4
Two-step inequalities
WorksheetSolve like an equation, but flip the sign when you multiply or divide both sides by a negative number.
Example: −2x + 1 > 7, so −2x > 6 and x < −3
Geometry
Circles
Worksheetd = 2r
Circumference: C = πd = 2πr
Area: A = πr to the power 2
π ≈ 3.14 or 227
Example: r = 5: C ≈ 2 × 3.14 × 5 = 31.4 units and A ≈ 3.14 × 25 = 78.5 square units
Angle pairs
WorksheetComplementary angles add up to 90°.
Supplementary angles add up to 180°.
Vertical angles are equal.
Unknown angle: write an equation, like x + 35 = 90.
Example: 35° has a complement of 55° and a supplement of 145°
Triangles
WorksheetThe three angles add up to 180°.
The two shorter sides must add up to more than the longest side.
Example: 3, 4 and 8 can’t make a triangle: 3 + 4 = 7, which is less than 8
Geometry (continued)
Area and volume
WorksheetComposite shapes: split them into simple shapes and add the areas.
Prism: V = Bh (B is the area of the base)
Surface area: add the areas of all the faces.
Example: Triangular prism with base area 12 and length (prism height) 5: V = 12 × 5 = 60 cubic units
Cross sections
WorksheetA slice parallel to the base of a prism or cylinder is the same shape as the base.
Example: Slicing a cylinder parallel to its base makes a circle
Probability and statistics
Probability
WorksheetWhen all outcomes are equally likely: P(event) = favorable outcomestotal outcomes
From 0 (impossible) to 1 (certain). 12 is as likely as not.
P(not A) = 1 − P(A)
Example: Rolling a 4 on a number cube: P = 16
Experimental probability
WorksheetP = times it happenednumber of trials
Example: 18 heads in 40 flips: 1840 = 0.45
Compound events
WorksheetList the outcomes in a table, a list or a tree diagram.
Independent events (one doesn’t change the chance of the other): P(A and B) = P(A) × P(B)
Example: Heads, then a 6: 12 × 16 = 112
Random samples
WorksheetIn a random sample, every member of the group has the same chance to be picked, so the sample can stand for the whole group.
Example: 6 of 50 sampled students walk to school: about 650 = 12% of all students do
Comparing two groups
WorksheetCompare the centers (mean or median) and the spreads (MAD or IQR).
Example: Means of 62 in and 68 in, each with a MAD of 3 in: the means are 6 in, or 2 MADs, apart