Quantitative Reasoning

Integers are the whole numbers and their negatives: ..., -2, -1, 0, 1, 2, ... On the number line they are equally spaced, increasing left to right, with 0 at the center. Larger numbers lie to the right; -3 < -1 < 0 < 2.

Same signs give a positive result; different signs give a negative result. (+)(+)=+, (-)(-)=+, (+)(-)=-, (-)(+)=-. A product of an even count of negatives is positive; an odd count is negative.

Same signs: add absolute values, keep the sign. Different signs: subtract the smaller absolute value from the larger, keep the sign of the larger. Subtracting is adding the opposite: a - b = a + (-b).

Each digit's value depends on its position, with each place worth 10 times the one to its right. For 3,407: 3 thousands + 4 hundreds + 0 tens + 7 ones = 3000 + 400 + 0 + 7.

Divisible by 2 if the last digit is even (0,2,4,6,8). Divisible by 5 if the last digit is 0 or 5. Divisible by 10 if the last digit is 0.

Divisible by 3 if the sum of the digits is divisible by 3. Divisible by 9 if the sum of the digits is divisible by 9. Example: 1,287 -> 1+2+8+7=18, divisible by both 3 and 9.