1.01 Multiplying and dividing integers
Are the following statements true or false?
The product of a positive number with a negative number is negative.
The product of an even number of negative numbers is negative.
State whether the following expressions will be positive or negative:
\left(-147\right) \times 183
\left(-151 \right) \times \left( - 185 \right)
\left( - 180 \right) \times \left( - 168 \right)
157 \times \left( - 142 \right)
Consider the equation 6 \times 4 = 24, and find the value of the following:
\left( - 6 \right) \times 4
6 \times \left( - 4 \right)
\left( - 6 \right) \times \left( - 4 \right)
Consider the equation 19 \times 17 = 323, and find the value of the following:
\left( - 19 \right) \times 17
19 \times \left( - 17 \right)
\left( - 19 \right) \times \left( - 17 \right)
Consider the equation 37 \times 31 = 1147, and find the value of the following:
\left( - 37 \right) \times 31
37 \times \left( - 31 \right)
\left( - 37 \right) \times \left( - 31 \right)
Consider the equation 3 \times 2 \times 5 = 30, and find the value of the following:
3 \times \left( - 2 \right) \times 5
\left( - 3 \right) \times 2 \times \left( - 5 \right)
\left( -3 \right) \times \left( - 2 \right) \times 5
\left( -3 \right) \times \left( - 2 \right) \times \left( - 5 \right)
Evaluate:
- 4^{2}
\left( - 4 \right)^{2}
\left( - 4 \right)^{3}
\left( - 12 \right)^{2}
- \left( - 12 \right)^{2}
- \left( - 8 \right)^{3}
\left( - 6 \right)^{3}
5 \times \left( - 9 \right)
\left( - 12 \right) \times \left( - 10 \right)
\left(- 11 \right) \times 4
\left( - 4 \right) \times \left( - 4 \right)
\left( - 4 \right) \times \left( - 4 \right) \times \left( - 4 \right)
Solve the following equations:
\left( - 11 \right) \times r = - 66
n \times \left( - 3 \right) = - 36
7 \times q = - 28
t \times 7 = - 42
Complete the following equations:
⬚ \times \left( - 5 \right) = 55
-6\times ⬚=-66
⬚ \times 8 = - 56
7 \times ⬚ = - 84
Find the value of n in the following statements:
A number n is multiplied with - 3 to give 21.
A number n is multiplied with - 10 to give - 40.
Explain why there is no solution to the equation x^2=-1.
Is the quotient of a positive integer and a negative integer positive or negative?
State whether the following expressions will be positive or negative:
\left( - 2432 \right) \div 32
\left( - 855 \right) \div \left( - 15 \right)
1587 \div \left( - 23 \right)
\left( - 7614 \right) \div \left( - 81 \right)
Consider the equation 42 \div 7 = 6, and find the value of the following:
\left( - 42 \right) \div 7
42 \div \left( - 7 \right)
\left( - 42 \right) \div \left( - 7 \right)
Consider the equation 667 \div 29 = 23, and find the value of the following:
\left( - 667 \right) \div 29
-667 \div \left( - 29 \right)
\left( - 667 \right) \div \left( - 29 \right)
Consider the equation 924 \div 28 = 33, and find the value of the following:
\left( - 924 \right) \div 28
924 \div \left( - 28 \right)
\left( - 924 \right) \div \left( - 28 \right)
Evaluate:
12 \div \left( - 4 \right)
\left( - 20 \right) \div 4
\left( - 72 \right) \div \left( - 9 \right)
Solve the following equations:
\left( - 108 \right) \div n = - 12
p \div \left( - 8 \right) = 11
\left( - 48 \right) \div t = 6
k \div 8 = - 6
Complete the following equations:
⬚ \div \left( - 6 \right) = - 9
⬚ \div 5 = -7
⬚ \div 5=-11
\left( - 72 \right) \div ⬚ = 9
Find the value of n in the following statements:
A number n, when divided by 3, gives - 9.
A number n when divided by - 5 gives - 4.
Evaluate:
Which quadrant(s) could the point \left(x, y\right) lie in if:
In golf your score for each hole is determined by comparing it to the par (or expected) number of shots for that hole. Taking one less shot than expected will give a score of -1, one more shot will give +1, and so on.
Ivan played 18 holes of golf, and the frequency of each score he obtained is shown in the adjacent table:
Find Ivan's total score for his 6 scores of + 2.
Find Ivan's total score for his 5 scores of - 1.
Find Ivan's total score for the total 18 holes.
| Score | Frequency |
|---|---|
| - 1 | 5 |
| \text{Par} | 3 |
| + 1 | 4 |
| + 2 | 6 |
Victoria earns \$1100 a month, and deposits it into her bank account. She also withdraws \$200 a month to pay for rent.
How much, in total, does Victoria deposit into her bank account in one full year?
How much, in total, does Victoria withdraw from her bank account in one full year?
Find the total change in her bank account over the year. An increase will be represented by a positive number and a decrease will be represented by a negative number.