Rational numbers

Integers are positive and negative whole numbers and zero. −3.4 is not a whole number. Zero is an integer.

Above sea level is positive, so below sea level is negative: −35. +35 and 35 are the same number (35 m above).

From −4 to 4 is 8 units in 4 steps, so each step is 2. P = −4 − 2 × 2 = −8. Q = −4 + 3 × 2 = 2. −6 and −1 come from counting each step as 1.

Ascending means smallest first. −9 is furthest left on the number line. The first list treats −2 as smaller than −9; the third list is descending.

Subtracting a negative means moving right: −4 − (−9) = −4 + 9 = 5. −13 forgets to change − (−) to +.

(−6) × 7 = −42. −42 ÷ (−3) = 14 (same signs give a positive answer).

÷ and × first, from left to right: 24 ÷ (−4) = −6, −6 × 3 = −18. Then 7 + (−18) = −11. 5 comes from doing × before ÷; 3 from adding first.

a × (b + c) = a × b + a × c is the Distributive Law: the 7 is shared to both numbers in the bracket.

Each step is 15. R is 3 steps left of 0, so R = −35. −25 comes from counting 2 steps from −1 instead of from 0.

× first: 34 × (−29) = −16. Then −23 − 16 = −46 − 16 = −56. −154 comes from adding first.

Write with 3 decimal places: −1.250, −1.520, −1.205, −1.052. −1.520 is furthest left on the number line, so it is the smallest.

−1.25 = −125100 = −54. −12510 = −12.5, and 54 has lost the negative sign.