Operations with Natural Numbers
At a corner store in Santiago you buy $3$ fried-dough snacks (yaniqueques) at $\text{RD}\$40$ each and $2$ juices at $\text{RD}\$60$ each, and you pay with a $\text{RD}\$500$ bill. How much change do you get? You can solve it in a single line if you know how to translate the problem into numbers and follow the correct order of operations.
From a word problem to an operation
Write the numerical expression corresponding to each statement and work out its value: a) Three times the sum of eight and five. b) Twice twenty minus the quotient of…
Write the numerical expression corresponding to each statement and work out its value:
- a) Three times the sum of eight and five.
- b) Twice twenty minus the quotient of twelve divided by four.
- c) The difference between the product of six and three, and the number seven.
Look at the following grid representing a storage area in a logistics warehouse. Work out the total number of packages using a single multiplication and addition…
Look at the following grid representing a storage area in a logistics warehouse. Work out the total number of packages using a single multiplication and addition operation, knowing that each square represents a box.
In a comic shop, a teenager buys $3$ manga books at $480$ pesos each and $2$ posters at $300$ pesos each. If he pays with a $3\,000$ pesos note, how much change should…
In a comic shop, a teenager buys $3$ manga books at $480$ pesos each and $2$ posters at $300$ pesos each. If he pays with a $3\,000$ pesos note, how much change should he receive? Express all the calculations in a single line.
Order of operations in practice
Remember the order: parentheses and brackets, then powers and roots, then multiplication and division, and finally addition and subtraction. When there are parentheses inside brackets, start with the innermost ones.
Work out the result of the following combined operations, paying attention to the order of operations: a) $25 + 5 \times 4 - 10$ b) $36 : 6 + 2 \times 7$ c)…
Work out the result of the following combined operations, paying attention to the order of operations:
- a) $25 + 5 \times 4 - 10$
- b) $36 : 6 + 2 \times 7$
- c) $18 - 12 : 3 + 4$
Work out the result of the following combined operation step by step, respecting the order of operations: $15 \times (13 - 3^2) + 4^2 : \sqrt{64} - 2 \times 5$
Work out the result of the following combined operation step by step, respecting the order of operations:
$15 \times (13 - 3^2) + 4^2 : \sqrt{64} - 2 \times 5$
Work out the value of the following expression, applying correctly the order of operations and the laws of indices: $$ \sqrt{10^2 - 8^2} + [2^5 : (2^2 \times \sqrt{16})…
Work out the value of the following expression, applying correctly the order of operations and the laws of indices:
$$ \sqrt{10^2 - 8^2} + [2^5 : (2^2 \times \sqrt{16}) + 5^2] - (3^3 - 5^2)^2 $$Remember to solve the innermost brackets first, followed by powers and roots, then multiplications and divisions, and finally additions and subtractions.
Problems with combined operations
To solve a problem: read it, identify what is added, subtracted, multiplied, or shared, write a single expression with parentheses where needed, and calculate it following the order of operations.
In a video game competition, participants must complete 25 challenges. For each challenge completed, they score $12$ points, but for each mistake, they are penalised $5$…
In a video game competition, participants must complete 25 challenges. For each challenge completed, they score $12$ points, but for each mistake, they are penalised $5$ points. If a player decides not to attempt a challenge, they neither gain nor lose points.
Calculate the final score of a contestant who has attempted $22$ challenges, of which $18$ were successful.
A farmer has harvested $350$ kg of apples. He sorts them and removes $26$ kg that are unsuitable for sale. He packs the rest into boxes of $12$ kg each. If he sells each…
A farmer has harvested $350$ kg of apples. He sorts them and removes $26$ kg that are unsuitable for sale. He packs the rest into boxes of $12$ kg each. If he sells each box for $1\,080$ pesos, how much money will he get from selling his whole crop?
We are designing the logo for a new mobile app. The logo consists of two perfect squares joined so that one full side of the small square rests against a side of the…
We are designing the logo for a new mobile app. The logo consists of two perfect squares joined so that one full side of the small square rests against a side of the large square. The total area of the logo is $169 \text{ mm}^2$. If the side length of the larger square is $12 \text{ mm}$:
- a) What is the area of the small square?
- b) What is the total perimeter of the resulting shape (the outer outline)?
The distributive property and common factor
A cinema has a screen with $12$ rows of $18$ seats each. For a premiere, tickets for the first $4$ rows (VIP area) are sold for $900$ pesos and the remaining tickets for…
A cinema has a screen with $12$ rows of $18$ seats each. For a premiere, tickets for the first $4$ rows (VIP area) are sold for $900$ pesos and the remaining tickets for $540$ pesos. If all seats have been sold, what was the total revenue for the screen?
Apply the distributive property to factorise out the common factor and work out as quickly as possible the value of the following store billing calculation: $$ 125…
Apply the distributive property to factorise out the common factor and work out as quickly as possible the value of the following store billing calculation:
$$ 125 \times 48 + 125 \times 64 - 125 \times 12 $$If the total result is to be divided into bags containing $5^3$ items each, how many bags will be filled? Express the process using powers.
Back to the beginning: we translate the problem into a single operation: $500 - (3 \cdot 40 + 2 \cdot 60) = 500 - (120 + 120) = 500 - 240 = 260$. You get $\text{RD}\$260$ in change.