Multiplying and Dividing Integers

Multiplying and Dividing Integers exercise

• Multiply the positive and negatives.

  Hints

  Each equation which has a product has two negatives and one positive, unless it is three positives. See the rows in the diagram.

  • If we have $(-) \times (-)$ then the answer is $(+)$, two negatives and one positive.
  • If we have $(+) \times (-)$ then the answer is $(-)$, two negatives and one positive.

  In other words,

  • If both signs are the same the answer is $(+)$.
  • If both signs are different, the answer is $(-)$

  There are $4$ correct answers!

  Solution

  Correct answers are:

  • $(+) \times (-) = -$
  • $(-) \times (+) = -$
  • $(-) \times (-)= +$
  • $(+) \times (+) = +$

• Multiply the integers.

  Hints

  With a product, there are two negatives and one positive.

  For example, $(-) \times (-) = +$ or $(-) \times (+) = -$.

  • Same signs $= (+)$ answer, $5 \times 5 = 25$ and $-5 \times -5 = 25$.
  • Different signs $= (-)$ answer, $-5 \times 5 = -25$ and $5 \times -5 = -25$

  Solution

  • Same signs $= (+)$ answer.
  • Different signs $= (-)$ answer.

• Find the questions.

  Hints

  Multiplication and division with negative integers are done the same way.

  • $(- \times + = -)$ or $(- \div + = -)$
  • $(- \times - = +)$ or $(- \div - = +)$
  • $(+ \times - = -)$ or $(+ \div - = -)$
  • $(+ \times + = +)$ or $(+ \div + = +)$

  To have an answer of a negative, the question must have one negative and one positive integer. For example,

  • $80 \div -10 = -8$.
  • $-80 \div 10 = -8$.
  • $8 \times -10 = -80$.
  • $-8 \times 10 = -80$.

  There are $3$ correct answers here.

  Solution

  Correct answers are:

  • $-4 \times 2 = -8$
  • $16 \div -2 = -8$
  • $1 \times -8 = -8$

• Find the missing integers to make the calculation correct.

  Hints

  Multiplication and division are the inverse of each other.

  $4 \times 5 = 20$ is equal to $20 \div 5 = 4$, and $20 \div 4 = 5$

  If $10 \times ? = -20$ , we can rewrite it as $-20 \div 10 = -2$. Therefore, the missing integer is $-2$.

  • If the signs are the same the answer is positive.
  • $(-) \times (-) = +$ and $(-) \div (-) = +$
  • If the signs are different, the answer is negative.
  • $(-) \times (+) = -$ and $(+) \div (-) = -$.

  Solution

  • $-3 \times ? = -15$ is the same as $-15 \div -3 = 5$
  • $-3 \div ? = 5$ is the same as $15 \div 5 = 3$
  • $? \times -5 = 15$ is the same as $15 \div -5 = 3$
  • $-15 \div ? = 3$ is the same as $-15 \div 3 = -5$

• Divide the integers.

  Hints

  Dividing integers works the same way as multiplying. See the diagram and apply it to a division.

  • If we have $(-) \div (-)$, then we must use a $+$ for the answer.
  • If we have $(-) \div (+)$, then we must use a $-$ for the answer.

  Solution

  The correct answer is $20 \div -4 = -5$.

  • We divide the absolute values first.
  • $20 \div 4 = 5$
  • When we use the rule, signs are different so answer is positive.
  • That is $(+) \div (-) = -$.
  • Answer is therefore, $-5$.

• Multiply or divide the integers.

  Hints

  To work out the next terms, we must first work out what the term is multiplied by to get to the next. We call this the common ratio.

  For example, $4, -20, ....$ we do $-20 \div 4 = -5$. That means each term is multiplied by $-5$ to get the next term.

  To find the common ratio (the multiplier) we do,

  $2 \times ? = -6$ or $-6 \div 2 = ?$

  Solution

  The correct answer is $-54$ and $162$.

  • To find the common ratio, we do $2 \times ? = -6$
  • Which is the same as $-6 \div 2 = -3$
  • $-3$ is the multiplier, so to get the next term we multiply by $-3$
  • $-6 \times -3 = 18$
  • $18 \times -3 = -54$
  • $-54 \times -3 = 162$