Evaluate the following without using a calculator:
424 + 962 + 79
42 \div 7
8394 \div 3
45\,000 \div 90
700 \div 10
6 \div 3 \times 4
6 - 15 \div 5
2 \times 12 + 30 - 28
44 \div 4 - 7 + 17
5^{2} \times 2 + 31
\left(5 + 6\right) \times 6
\left(11 - 4\right) \times \left(12 - 4\right)
\left(10 + 3\right) \times \left(8 - 4\right)
450 \div 9 \times 900
49 - \left(37 + \left( 15 \div 3\right)\right)
\left( \left(36 - \left(10 + 10\right)\right) \div 2\right) + 14 \times 6
Evaluate the following:
214 + 443
78\,726 - 38\,397
664 + 514
7000 \div 100
7432 \times 82
3864 \div 7
1876 \div 67
227 \times 78
720 \div 7 \times 7000
47 - \left(14 + \left( 14 \div 7\right)\right)
2^{5} \times 7^{3}
21 + 4031 + 904 + 7746
9 \times 2 + 96 - 52
4 \times 100\,000 + 5 \times 10\,000 + 2 \times 100 + 1 \times 10.
2^{3} \times 3 + 81
2 \times 10^{4} + 2 \times 10^{3} + 7 \times 10^{2} + 7 \times 10^{1} + 6 \times 10^{0}
\sqrt{37^{2} - 12^{2}}
Evaluate 53 \div 8. Write down the quotient and the remainder.
Write the answer to 53 \div 8 as a decimal number.
Is the answer in part (b) larger than or smaller than 6.624\,978?
Evaluate 34 \times 0.078. Write the answer as a decimal number.
Is the answer in part (a) larger than or smaller than 2.651\,299\,94?
For each of the following:
State whether the answer will be positive or negative.
Evaluate the problem.
\sqrt{\left(1.34 - 4.95\right)^{2}}
\sqrt{\left(826 - 896\right)^{2}}
- 0.1 - \left( - 8.2 \times 0.5 \right)
100 is called a 'perfect square' because it is equal to 10^{2}.
Find the value of \sqrt{8^{2} + 5^{2}} to two decimal places.
Between which two perfect square numbers does the answer to part (a) lie?
Consider the product - 692 \times 133.
State whether the product will be positive or negative.
Use your calculator to find the value of - 692 \times 133:
State whether each of the following expressions has the same value as - 692 \times 133:
692 \times 133
692 \times \left( - 133 \right)
- 692 \times \left( - 133 \right)
Consider the difference - 657 - 811.
State whether the difference will be positive or negative.
Use your calculator to find the value of - 657 - 811.
Will - 657 - 815 be smaller than or larger than - 657 - 811?
Consider the sum - 45 + 88.
State whether the sum will be positive or negative.
Use your calculator to find the value of - 45 + 88.
State whether each of the following will be smaller than or larger than - 45 + 88:
Consider the expression \dfrac{26 - 64}{- 58 + 53}.
State whether the answer will be positive or negative.
Use your calculator to find the value of \dfrac{26 - 64}{- 58 + 53}, writing your answer as a decimal.
State whether each of the following expressions has a value that is smaller than, larger than or equal to\dfrac{26 - 64}{- 58 + 53}:
\dfrac{26 + 64}{- 58 - 53}
\dfrac{64 - 26}{58 - 53}
\dfrac{64 - 26}{53 - 58}
\dfrac{- 26 + 64}{- 53 + 58}
Use your calculator to evaluate:
A factory will produce 84\text{ kg} of fabric this week. If it already has 160\text{ kg} of fabric left over from last month's production, what will be the total stock of fabric at the factory by the end of this week?
The number of motor accidents at a particular intersection was reported by traffic police to be 45 last year. The local council then decided to put up warning signs for motorists approaching this intersection. The following year the police reported only 29 accidents there. How many fewer accidents were there after the signs were introduced?
A collection effort by a charity to help those affected by a storm finds that it has gathered 319 pairs of sandals. There are 11 shelters that house a roughly equal number of people who have been affected. The charity decides to distribute the pairs of sandals equally between these. How many pairs of sandals does each shelter receive?
Mae performs an experiment where she pours 90\text{ mL} of honey, 81\text{ mL} of vegetable oil, and 200\text{ mL} of water into a tall glass. What is the total volume of liquid she has poured into the glass?
Maria, Buzz and Neil jointly purchase a gift for their father on Father's Day. If the gift cost \$55 and Maria and Buzz contributed \$30 and \$10 respectively, how much did Neil spend on the gift?
On a certain island, a species of hawk sustains itself by eating the local rabbits. In the first survey of animals on the island, there were found to be 3 rabbits for every hawk. The latest survey shows that this is still the case, but that the rabbit population has grown to 153 individuals. How many hawks does the island now support?
At a factory that produces radio components at a rate of 5000 every month, it is found that 27 items are defective in the January batch, 28 items in the February batch and 14 items in the March batch. Find the average number of defective items per month.
James wants to share some ice blocks between his football teammates. He brings 40 ice blocks expecting all 10 of them to be at practice, but three have taken ill and do not come.
How many whole ice blocks will each of the teammates present now receive? (Everyone must receive the same amount).
How many ice blocks are left over?
Iain borrows \$265 from his friend Jimmy. They agree that if Iain pays back Jimmy within one month, there will be a \$15 borrowing fee on top of the amount borrowed, but if he pays him back after one month, the borrowing fee will be \$25 instead.
Over the month, Iain returns amounts of \$45 and \$70 to Jimmy.
If Iain is able to make a final payment to repay the total amount before the end of the month, how much more does he need to repay?
Suppose Iain can only make the final payment after five weeks have passed since he first borrowed the money. How much more does he need to pay back?
A cargo ship encounters a storm on the high seas and is delayed by two weeks. Once it reaches its destination, the crew discover that 3 out of the 84 crates of fruit it carried have spoilt. The remaining (not spoilt) crates are to be divided equally among the 14 customers and whatever remains can be sold separately.
How many whole crates of fruit will each customer receive?
If each crate contained 35\text{ kg} of fruit and each kilogram of fruit could be sold for \$2, what is the loss incurred by the crew because of the spoilage?
Sandy is playing a number game. She starts with any number, and if it is even she divides the number by 2. If it is odd, she triples the number and adds 1.
This gives her a new number, and she repeats the same steps on this new number.
She keeps going until her number is 1. An example of a list of numbers she makes is shown below:
| Starting number | List |
|---|---|
| 5 | 5, 16, 8, 4, 2, 1 |
Sandy starts a new list with the number 3. Write down the complete list she creates.
A collection effort by a charity to help those affected by a flood finds that it has gathered 448 first aid kits. The charity decides to distribute the first aid kits equally between 16 shelters. How many first aid kits does each shelter receive?