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The short version There are 63,360 inches in a mile. That comes from two facts: 1 mile = 5,280 feet, and 1 foot = 12 inches. So 5,280 × 12 = 63,360. To change miles to inches, multiply by 63,360. To change inches to miles, divide by 63,360. Half a mile is 31,680 inches, and…
The short version A numerical expression is a math phrase made only of numbers and operation signs, like 8 + 3 × 2 or (20 – 5) ÷ 3. It has no variables (no letters) and no equals sign, and it always simplifies to one exact value. To evaluate one, follow the order of operations:…
The short version A negative exponent means “take the reciprocal.” In symbols, a-n = 1 ÷ an, so 2-3 = 1/23 = 1/8. A negative exponent does not make the answer negative. 5-2 is 1/25, a small positive number. To get rid of a negative exponent, move the factor to the other side of the…
The short version A protractor is a tool for measuring and drawing angles in degrees. The common school kind is a clear half circle marked from 0° to 180°. To measure an angle, put the center point on the vertex, line the baseline up with one ray, and read where the other ray crosses the…
The short version To solve word problems, read the whole problem, find the exact question, sketch what’s happening, choose the operation based on the action in the story, solve, and check that the answer makes sense. Keyword lists (“left” means subtract, “in all” means add) fail on a lot of problems. Understanding the story works…
The short version Congruent means exactly the same shape and the same size. If you could cut one figure out and lay it perfectly on top of the other, they’re congruent. The congruent symbol is ≅. You write △ABC ≅ △DEF, and the order of the letters tells you which parts match. Sliding, turning, or…
The short version The reflexive property says anything is equal to itself: a = a. For shapes it reads AB ≅ AB, so every segment and angle is congruent to itself. You’ll see it most in geometry proofs, as the reason for a side or angle that two triangles share. It’s one of three partner…
The short version A unit is the fixed amount you measure in. In “6 feet,” the number 6 says how many and the unit, feet, says of what. Units of measurement in the US come in two systems: customary (inches, pounds, gallons) and metric (meters, grams, liters). To convert, go from a bigger unit to…
The short version Same signs: add the numbers and keep the sign. -8 + (-5) = -13. Different signs: subtract the smaller absolute value from the larger one, then use the sign of the number that’s farther from zero. -12 + 7 = -5. A number plus its opposite is always zero: -6 + 6…
The short version To subtract an integer, add its opposite. 7 – (-4) becomes 7 + 4 = 11, and -6 – 9 becomes -6 + (-9) = -15. Only two things change: the minus sign becomes a plus, and the second number flips its sign. The first number never changes. Negative minus negative turns…