Complete the following statements with the correct inequality sign \gt or \lt:
\dfrac{8}{9} ⬚ \dfrac{9}{10}
- \dfrac{5}{6}⬚ - \dfrac{9}{10}
- \dfrac{8}{9}⬚\dfrac{6}{7}
\dfrac{7}{8}⬚- \dfrac{5}{6}
Consider the fractions -\dfrac{2}{5}, -\dfrac{4}{5}, \dfrac{1}{5}
Plot the fractions on a number line.
Arrange the fractions from largest to smallest.
Consider the fractions -\dfrac{3}{7}, \dfrac{2}{7}, -\dfrac{4}{7}
Plot the fractions on a number line.
Arrange the fractions from smallest to largest.
Consider the fractions \dfrac{2}{9}, \dfrac{4}{9}, -\dfrac{2}{9}
Plot the fractions on a number line.
Arrange the fractions from largest to smallest.
Consider the fractions -\dfrac{7}{11} , \dfrac{2}{11},-\dfrac{3}{11}
Plot the fractions on a number line.
Arrange the fractions from smallest to largest.
Simplify:
Simplify the following, writing your answer as a mixed numeral where necessary:
Simplify the following, writing your answer as a mixed numeral where necessary:
Explain how to add and subtract fractions with different denominators.
Simplify the following, writing your answer as a mixed numeral where necessary:
Find the product of the following fractions. Give your answers as simplified fractions.
\dfrac{2}{5} \times \dfrac{3}{7}
\dfrac{4}{7} \times \left( - \dfrac{9}{5} \right)
- \dfrac{5}{9} \times \dfrac{2}{11}
- \dfrac{2}{5} \times \left( - \dfrac{9}{7} \right)
\left(\dfrac{2}{9}\right)^{2}
\left( - \dfrac{9}{5} \right)^{2}
9 \times \left( - \dfrac{4}{5} \right)
- \dfrac{3}{7} \times \dfrac{4}{7}
- \dfrac{2}{9} \times \left( - \dfrac{2}{3} \right)
- \dfrac{2}{7} \times \dfrac{3}{8}
- \dfrac{11}{9} \times \left( - \dfrac{7}{44} \right)
\dfrac{2}{45} \times \left( - \dfrac{5}{6} \right)
\dfrac{44}{15} \times \left( - \dfrac{12}{55} \right)
\dfrac{7}{4} \times \left( - \dfrac{9}{7} \right) \times \dfrac{5}{7}
Find the quotient of the following fractions. Give your answers as simplified fractions.
\dfrac{3}{7} \div \dfrac{5}{4}
\dfrac{2}{9} \div \left( - \dfrac{7}{5} \right)
\left( - \dfrac{3}{11} \right) \div \dfrac{8}{5}
\left( - \dfrac{3}{7} \right) \div \left( - \dfrac{5}{4} \right)
7 \div \left( - \dfrac{4}{7} \right)
\left( - \dfrac{3}{4} \right) \div 12
\left( - \dfrac{3}{7} \right) \div \dfrac{7}{8}
\left( - \dfrac{6}{7} \right) \div \dfrac{3}{4}
\left( - \dfrac{2}{7} \right) \div \left( - \dfrac{5}{63} \right)
\left( - \dfrac{7}{2} \right) \div \left( - \dfrac{21}{5} \right)
\left( - \dfrac{45}{4} \right) \div \dfrac{9}{28}
\dfrac{45}{28} \div \left( - \dfrac{25}{36} \right)
\dfrac{4}{81} \div \left( - \dfrac{20}{9} \right)
\left( - \dfrac{20}{27} \right) \div \left( - \dfrac{35}{24} \right)
For the each of the following pairs of decimals, state which decimal is bigger:
0.74 or 0.8
- 0.7 or - 0.67
- 0.74 or 0.8
0.67 or - 0.7
Consider the decimals 0.2, 0.5, -0.3
Plot the fractions on a number line.
Arrange the decimals from smallest to largest.
Consider the decimals -0.9, 0.3, -0.4
Plot the fractions on a number line.
Arrange the decimals from largest to smallest.
Consider the decimals -0.1, -0.42, -0.29
Plot the fractions on a number line.
Arrange the decimals from smallest to largest.
Consider the decimals 0.75, -0.5, 0.25
Plot the fractions on a number line.
Arrange the decimals from largest to smallest.
Find the product of the following:
7.3 \times 7.9
6.4 \times \left( - 7.8 \right)
\left( - 4.3 \right) \times 9.7
\left( - 3.9 \right) \times \left( - 9.8 \right)
Find the quotient of the following:
4.16 \div 0.08
7.36 \div \left( - 0.08 \right)
\left( - 3.08 \right) \div 0.07
\left( - 8.28 \right) \div \left( - 0.09 \right)
Find the value of the following:
\left(3.7\right)^{2}
\left( - 6.4 \right)^{2}
\left(3.7\right)^{3}
\left( - 6.4 \right)^{3}
Determine whether the following calculations can be evaluated:
\dfrac{- 3.88}{2.99}
\dfrac{2.99}{0}
\dfrac{1.93}{2 - 2}
\dfrac{0}{- 1.93}
Jack felt dehydrated. He drank one third of a litre at first, then drank another one ninth of a litre. How many litres did he drink in total?
Valerie walks eight sixths of a kilometre to school while Fred walks one half of a kilometre to school. How much farther does Valerie walk than Fred?
A bridge is being built to span \dfrac{3}{4} \text{ km}. After a month, the engineer reported that \dfrac{3}{8} \text{ km} has been completed so far. What part of the bridge has not yet been completed?
Jane eats \dfrac{1}{4} of a cake and Joshua eats \dfrac{1}{3} of the cake. What fraction of the cake did they eat altogether?
During a blizzard it snowed 10\dfrac{1}{2} \text{ cm}. When the sun came out the next day, 5 \dfrac{3}{4} \text{ cm} of show melted. How much snow was left on the ground?
Mr. Pemberton, the president of Zoom Motors, owns \dfrac{1}{3} of the stock of the company. His wife owns \dfrac{1}{4} of the stock. What fractional part of the stock will his daughter need to purchase in order for the family to own \dfrac{3}{4} of the stock?
Missy mailed 4 letters that have a total weight of 3 grams. One letter weighed \dfrac{1}{2} of a gram, another weighed \dfrac{3}{4} of a gram, and a third weighed \dfrac{7}{8} of a gram. How much did the fourth letter weigh?
Jack owes \$47.59 to each of his 3 friends. If he paid off all of these debts at once, how much will his bank account balance decrease by? (Note whether the change is positive or negative by the sign of the number.)
Peggy owes \$98.96 in total to 4 friends.
Assuming she owes the same amount to each friend, how much does she owe one of them?
If Peggy pays just 3 of her friends back, how much money will come out of her bank account?
Jenny takes out a loan of \$2200. She pays back \$42.60 each month without 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. Find the temperature after 5 hours.
Hadi is studying temperatures around the world and notices that Antarctica has a temperature of -29.4\degree \text{C} while Egypt has a temperature of 29.4\degree \text{C}. He thinks that this means that they have the same temperature.
Is Hadi right? Explain your answer.
A diver is 3.5 \text{ m} below the surface of the water. He descends 1.47 \text{ m/s} for 3 seconds, then rises 0.46 \text{ m/s} for 6 seconds. Note that surface level is 0 \text{ m}, and 1 \text{ m} below is represented by - 1 \text{ m}.
Find the depth of the diver after 9 seconds.
The diver is running out of oxygen and needs to get to a depth of 0.35 \text{ m} below the surface within 4 seconds. How many metres does he need to rise each second, assuming he will rise at a constant speed?
Debbie is considering installing solar panels for her home. In direct sunlight, the solar panels generate 8.71 \text{ kWh} of electricity each hour, and on average her house gets 7 hours of sunlight a day. Any unused power is returned to the main grid and you receive \\33 cents per kWh.
Over a 24-hour period, a household's usage averages out to 1.87 \text{ kWh} each hour. How much will you expect to make each day by selling back electricity if you install the solar panels?
Kendra is looking at her bank statement and notices the following transactions:
What do the negative signs in front of the last two values indicate about the transaction?
If Kendra initially had \$65.20 in her account, how much does she have after these transactions?
| Date | Transaction amount |
|---|---|
| 03/05/21 | \$25.90 |
| 04/05/21 | \$16.80 |
| 04/05/21 | -\$32.50 |
| 06/05/21 | -\$11.00 |