Learn – Arithmetic – Number properties

Problem set 1

For each of the problems below, figure out what comes in place of $?$ . Hint: You do not have to actually do the addition. Just use the commutative property, namely $a+b = b+a$ .

$113,791,843,684 + 359,813,946,777 = 359,813,946,777 + ?$
$-113,791,843,684 + 359,813,946,777 = 359,813,946,777 + ?$
$(-141,723,931,923) + (-715,851,646,152) = (-715,851,646,152) + ?$
$-141,723 + a = a + ?$
$x + 151,814,723 = 151,814,723 + ?$

Problem set 2

For each of the problems below, figure out what comes in place of $?$ . Hint: Use commutative property of multiplication, namely $a\times b = b\times a$ .

$114,795,846,684 \times 360,815,946,743 = 360,815,946,743 \times ?$
$(-114,795,846,684) \times 360,815,946,743 = 360,815,946,743 \times ?$
$141,723,931,923\times (-715,851,646,152) = (-715,851,646,152)\times ?$
$a\times (-516,724) = (-516,724) \times ?$
$m \times n = ? \times m$

Problem set 3

Sam and his younger sister Maya are playing a game. Sam picks two integers. He does not show Maya what numbers he picked. He just calls them $a$ and $b$ . He tells Maya that $a - b = 1001$ . He asks Maya to guess what $b - a$ is. Maya takes a shot and guesses it to be $1001$ . Could she be right?
Sam and his younger sister Maya are continuing the game. Sam again picks two integers, calls them $a$ and $b$ and tells Maya that $a \times b = -1352$ . He asks Maya to guess what $b \times a$ is. Maya guesses it to be $-1352$ . Could she be right?
Again, Sam picks two integers, and calls them $a$ and $b$ . He tells Maya that $a \div b = -10$ . He asks Maya to guess what $b \div a$ is. Maya guesses it to be $-10$ . Could she be right?
$714,623,917 - 856,754,333 = -(856,754,333 - ?)$
$-514,761,819 + (-623,654,132) = -623,654,132 + ?$

Problem set 4

For each of the problems below, figure out what comes in place of $?$ . Hint: Use the associative properties of addition and multiplication, namely $a + (b+c) = (a+b)+c$ and $a\times (b\times c) = (a\times b)\times c$ .

$-14,543,751 + (723,452,231 + ?) = (-14,543,751 + 723,452,231) + 654,321,964$
$-14,543,751 + (-723,452,231 + 654,321,964) = (-14,543,751 + ?) + 654,321,964$
$-14,543,751 \times (-723,452,231 \times 654,321,964) = (-14,543,751 \times ?) \times 654,321,964$
$(-14,543,751 \times a) \times -654,321,964 = -14,543,751 \times (? \times -654,321,964)$
$(a \times b) \times c = a \times (b \times ?)$