Arithmetic & Number Properties 2

Question 1

Ratios

Answer 1

Compare the proportions of two quantities. Ratios are given by x:y (can also be x:y:z), x to y, or x/y. If a question says “for every x there is/are a y,” you are most likely dealing with a ratio question. Can be simplified like fractions. 3:6 is the same as 1:2. REMEMBER the total, if there is a 2:5 ratio of boys to girls at a school, the ratio of boys to total students is 2:(5 + 2) = 2:7.

Question 2

Fast Fractions

Answer 2

1/x + 1/y = (x + y) / (xy)

Question 3

Fractions (add/subtract)

Answer 3

If same denominator, add/subtract the numerators and keep the same denominator. If different denominator, first find common denominator (common multiple of the two). Then convert both to equivalent fractions with same denominator. Proceed as before.

Question 4

Fractions (multiply)

Answer 4

Multiply the two numerators and multiply the two denominators. (x/y)(w/z) = (xw)/(yz)

Question 5

Fractions (divide)

Answer 5

First invert the second fraction (i.e. find reciprocal), then multiply first fraction by inverted fraction. (x/y) / (w/z) = (x/y)(z/w) = (xz) / (yw)

Question 6

Percentages

Answer 6

“Percent” = per 100. To find what percent use part/whole = percent/100

Question 7

Percent change

Answer 7

% change = change/original value x 100

Question 8

Absolute Values

Answer 8

The absolute value of a number is its distance from a number line. |x| = x, |-x| = x