We can solve some real-world problems using the four operations on rational numbers.
We use addition when there is an increase in the data.
We use subtraction to find a difference or when there is a decrease in the data.
We use multiplication when a quantity is a multiple larger (or higher) than another. In particular, "double" means to multiply by and "triple" means to multiply by
We use division when a quantity is a multiple smaller (or lower) than another.
Let's see some examples.
Marcus has an overdraft facility authorized by his bank. His balance at the starting of October was To reduce his debt, Marcus makes a bank deposit, so his new balance is a third of the balance he had at the starting of the month. What is Marcus's balance after making the deposit?
To determine Marcus's new bank balance, we divide the starting balance by This gives
Therefore, Marcus's new bank balance is
Mark removes a liquid from the refrigerator with a temperature of $-4.2^{\circ} \, \textrm{C}$ and places it on a table. After $10$ minutes, the liquid temperature is $\dfrac{2}{3}$ of the initial temperature measured in degrees Celsius. What is the temperature of the liquid after $10$ minutes outside the refrigerator?
|
a
|
$-1.9^{\circ} \, \textrm{C}$ |
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b
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$-2.8^{\circ} \, \textrm{C}$ |
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c
|
$-2.4^{\circ} \, \textrm{C}$ |
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d
|
$-3.1^{\circ} \, \textrm{C}$ |
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e
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$-1.6^{\circ} \, \textrm{C}$ |
The average temperature in Washington, USA, in January $2018$ was $-4.5^{\circ} \, \textrm{C}.$ If the average temperature in February was half the temperature in January measured in degrees Celsius, what was the temperature in Washington in February of that year?
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a
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$- 2.25^{\circ} \, \textrm{C}$ |
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b
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$- 2.75^{\circ} \, \textrm{C}$ |
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c
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$- 1.25^{\circ} \, \textrm{C}$ |
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d
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$- 1.50^{\circ} \, \textrm{C}$ |
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e
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$- 1.75^{\circ} \, \textrm{C}$ |
Vanessa has an overdraft facility authorized by her bank. Her balance at the start of September was $- \$150.40.$ To reduce her debt, Vanessa makes a bank deposit, so her new balance is a quarter of the balance she had at the start of the month. What is Vanessa's balance after making the deposit?
|
a
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$-\$ 40.30$ |
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b
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$-\$ 43.60$ |
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c
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$-\$ 37.60$ |
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d
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$-\$ 35.30$ |
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e
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$-\$ 39.60$ |
The temperature in a chamber that holds chlorine is It's known that chlorine boils at the chamber's temperature measured in degrees Fahrenheit. What is the boiling temperature of chlorine?
To find out the boiling temperature of chlorine, we need to calculate
First, we write as an improper fraction:
Now, we can multiply the two numbers. We multiply the numerators, and we multiply the denominators:
Finally, we write the resulting improper fraction as a mixed number:
Therefore, chlorine boils at
During test drives, a submersible reached the depth of $-\dfrac{3}{4}\,\textrm{mi}$ relative to sea level. However, the depth at which the submersible usually operates is only $\dfrac{4}{5}$ of this test result. What is the depth at which the submersible usually operates?
|
a
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$-\dfrac{3}{5} \, \textrm{mi}$ |
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b
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$-\dfrac{2}{15} \, \textrm{mi}$ |
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c
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$-\dfrac{5}{4} \, \textrm{mi}$ |
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d
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$-\dfrac{11}{15} \, \textrm{mi}$ |
|
e
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$-\dfrac{4}{5} \, \textrm{mi}$ |
The temperature in a chamber that holds mercury is $-48\dfrac{1}{2}{^\circ}\textrm{C}.$ It's known that mercury melts at $\dfrac{4}{5}$ of the chamber's temperature measured in degrees Celsius. What is the melting temperature of mercury?
|
a
|
$-36\dfrac56{^\circ}\textrm{C}$ |
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b
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$-38\dfrac25{^\circ}\textrm{C}$ |
|
c
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$-34\dfrac45{^\circ}\textrm{C}$ |
|
d
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$-37\dfrac79{^\circ}\textrm{C}$ |
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e
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$-38\dfrac45{^\circ}\textrm{C}$ |
Martin has an overdraft facility authorized by his bank. His bank balance at the beginning of the month was
To reduce his debt with the bank, Martin deposited some money into his account. After making the deposit, his new balance was of the initial balance. Then, at the end of the month, Martin made a withdrawal of
What was Martin's bank balance at the end of the month?
To determine Martin's bank balance after he made the deposit, we multiply the initial balance by This gives
Martin's bank balance was updated again when he made a withdrawal. To determine the final balance, we subtract the amount of money he withdrew from This gives
Therefore, Martin's bank balance at the end of the month was
The average temperature in Montreal, Canada, in March was $-2^\circ \, \textrm{C}.$ Then, in April, the average temperature increased by $8.4^\circ \, \textrm{C}.$ Finally, the temperature in June is triple the temperature in April (measured in degrees Celsius). What is the temperature in Montreal in June?
|
a
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$17.9^\circ \, \textrm{C}$ |
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b
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$19.2^\circ \, \textrm{C}$ |
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c
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$19.6^\circ \, \textrm{C}$ |
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d
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$18.8^\circ \, \textrm{C}$ |
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e
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$18.2^\circ \, \textrm{C}$ |
Carmen has an overdraft facility authorized by her bank. Her balance at the beginning of June was $-\$124.$ After several transactions, her balance in mid-June is a fourth of the bank balance she had at the beginning of the month.
Carmen makes a $\$ 15$ deposit at the end of June. What is Carmen's bank balance at the end of the month?
|
a
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$-\$21$ |
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b
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$-\$16$ |
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c
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$-\$19$ |
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d
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$-\$14$ |
|
e
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$-\$24$ |