1.06 Practical problems with rational numbers
Select two numbers from the following list which have a difference of 26:
10, \, 19, \, - 6 , \, 19, \, - 16 , \, - 7 , \, 8, \, 25, \, - 18 , \, - 1
Fill in the blank with either < or > to make the statement true:
- 5 \times 9 \enspace ⬚ \enspace 21 \div \left( - 3 \right)
For each of the following sentences:
Translate the sentence into a mathematical expression.
Evaluate the expression.
- 6 is added to the product of 2 and - 4.
The sum of - 8 and the quotient of - 40 and 4
The quotient of - 7 and the sum of 6 and - 4
The product of -6 and the quotient of 1 and 2
Determine whether the following statements are true or false:
The sum of two positive numbers is always a positive number.
The sum of a negative number and a positive number is always a positive number.
The temperature decreases by 5\degree \text{F} each hour over six hours. Use a negative integer to describe the total decrease in temperature.
An investment loses \$22\,200. If this loss is shared equally among six, use a negative integer to describe the loss for each person.
Express the outcome of the following as an integer:
Diving 8 \text { m} downward followed by rising 2 \text { m}
An increase of 81 \text{ kg} in weight followed by a decrease of 39 \text{ kg}
Ascending 5 floors then descending 7 floors
An decrease of 101 \degree \text{F} in temperature followed by a increase of 52 \degree \text{F}
A temperature of - 60 \degree\text{F} would be a standard temperature to experience in the Antarctic. How much colder is this than a room at 70 \degree\text{F}?
What is the difference in altitude between a mountain that has an altitude of 3325\text{ ft} and a desert valley that is 180\text{ ft} below sea level?
For each of the following situations:
Write an addition problem that describes the situation.
Find the result of the addition problem.
State whether the result is a gain or a loss.
A gain of \$1116 is followed by a loss of \$778.
A loss of \$731 is followed by a gain of \$952.
A gain of \$295 is followed by a loss of \$445.
A loss of \$1872 is followed by a gain of \$1761.
Katrina is baking a muffin and a cake. She needs \dfrac{2}{3} cup of sugar for the muffin and \dfrac{1}{5} cup of sugar for the cake. How much sugar will she need to make both the muffin and the cake?
Tobias accidentally left his freezer door open overnight. In the morning, the temperature of the freezer had risen 43 \degree \text{F} from its usual temperature of -2\degree\text{F}. What temperature did Tobias's freezer reach?
Consider the table that shows the hottest and coldest spots for selected days in winter:
| Day | Place | Record High | Place | Record Low |
|---|---|---|---|---|
| 1 | \text{Brockway} | 57\degree \text{F} | \text{Dunkilderry} | -11\degree \text{F} |
| 2 | \text{Owaka} | 59\degree \text{F} | \text{Midland} | -12\degree \text{F} |
| 3 | \text{Whitby} | 73\degree \text{F} | \text{Balfour} | -7\degree \text{F} |
| 4 | \text{Humbleton} | 75\degree \text{F} | \text{Cranford} | -17\degree \text{F} |
| 5 | \text{Ogdenville} | 55\degree \text{F} | \text{North Haverbrook} | -14\degree \text{F} |
Where was the temperature the greatest during the days listed on the chart?
What was the difference in temperature between the record high and the record low on Day 2?
A small tree farm plants new trees during spring and summer and cuts down old trees during autumn and winter. They keep records of the average number of trees they plant or cut down each season, as shown in the table:
What was the overall change in trees during summer?
What was the overall change in trees during autumn?
What was the overall change in trees during summer and autumn combined?
How many trees were cut down during winter?
| Season | Weeks worked | Weekly change in trees |
|---|---|---|
| \text{Spring} | 9 | 6 |
| \text{Summer} | 8 | 5 |
| \text{Autumn} | 10 | -11 |
| \text{Winter} | 7 | -12 |
A calculator is 8.9\text{ cm} long. How far will 130 calculators reach if laid end to end? Express your answer in meters.
Dave used a calculator to evaluate 6.573 \times 8.03 but forgot to enter the decimal points. The answer he got was 5\,278\,119. What should the answer have been?
Patricia purchased a car and is paying monthly installments of \$126.30 per month to pay it off. If it takes her 40 months to pay it off, how much will she have spent on car repayments in total?
Consider the recipe for cookies shown below:
2\dfrac{1}{8} cups flour
\dfrac{2}{3} cup granulated sugar
1 teaspoon baking soda
\dfrac{3}{4} cup brown sugar
\dfrac{3}{4} teaspoon salt
1 teaspoon vanilla
1 cup margarine
- 1\dfrac{1}{4} cups chocolate chips
If we wanted to double the recipe, how many cups of flour would we need? Express your answer as a mixed number.
If \$5884.92 was shared equally between 12 people, how much would each person receive?
A piece of cord 2.87\text{ yd} long is cut evenly into smaller pieces of 0.07\text{ yd} each. How many of these pieces can be cut?
A satellite orbits the earth 10 times in 99 hours. How many hours does it take to complete 1 orbit? Express your answer as a decimal.
How many 0.17\text{ L} containers can be filled from a tank which holds 2.38\text{ L}?
How many pieces of steel, each 4.25\text{ ft} long, can be cut from a wire 153\text{ ft} long?
Three items weighing 3.41\text{ lb}, 2.58\text{ lb}, and 5.79\text{ lb} are to be posted but are too heavy to send. By how much does the total weight exceed the 11.38\text{ lb} limit?
Maria runs 50.2 \text{ m} in 15 seconds. If she continues running at the same speed, how far can she run in 2 minutes?
Jenny takes out a loan of \$2200. She pays back \$42.60 each month and doesn't have to pay interest. If she has made 5 repayments so far, how much does Jenny still owe?
At midnight, the temperature in Buffalo is 45.7\degree \text{F}. Each hour, the temperature decreases by 2.87\degree \text{F}. What is the temperature 5 hours later?
Brad is currently \$18 overdrawn in his account. He knows that he needs to pay a \$61.61 bill from this account tomorrow. How much does he need to add to this account so he can pay his bill tomorrow?
At Lidinia High, there are 442 students. The school sends 22 of them to compete in a national mathematics competition. Write the simplified fraction that shows what portion of the school's students entered the mathematics competition.
Ekronia Corporation wants to assess the success of one of its main rubber tree plantations. At this plantation, there are 65\,000 plants, but 5500 of these become infected before harvest time and so can't be used for production. Write a simplified fraction comparing the number of infected plants to the total number of plants.
After deducting taxes, Maximilian gets to keep \dfrac{10}{11} of his weekly pay. If he spends \dfrac{6}{7} of his weekly pay, what fractional part of his weekly pay will he have left?
Valentina had to pay \$700 as a deposit on a new sofa. The deposit was \dfrac{10}{19} of the full price.
What was the full price of the sofa?
How much money does Valentina have left to pay?
There are 5 men working on a truck. Three men take \dfrac{47}{7} hours to fix a truck. Assume all men work at the same rate.
How long would it take for 1 man to fix a truck? Express your answer in simplest form.
How long would it take for 5 men to fix a truck? Round your answer to the nearest minute.
A bottle is \dfrac{2}{7} full of cordial. If 230\text{ ml} of cordial is added to it, the bottle is \dfrac{5}{6} full. How much cordial does the bottle hold when full?
Quentin works in a bakery. If he requires 1\dfrac{2}{3} cups of flour for each loaf of bread and Quentin currently has 26\dfrac{2}{3} cups of flour left, how many more loaves of bread can he bake?
Valerie is making a scale model of a tall building. If each floor is to be 1\dfrac{7}{8} \text{ in} tall, and the whole model is 26\dfrac{1}{4} \text{ in} tall, how many floors does her model building have?
Ned has a 5\dfrac{1}{3}\text{ m} long piece of wood. He needs \dfrac{1}{4} of the length to build a table. What length of wood does he need to build the table? Express your answer as a mixed number.