Exercises: Operations with natural numbers

Work out the result of the following combined operations, paying attention to the order of operations:

1. a) $25 + 5 \times 4 - 10$

1. b) $36 : 6 + 2 \times 7$

1. c) $18 - 12 : 3 + 4$

Write the numerical expression corresponding to each statement and work out its value:

1. a) Three times the sum of eight and five.

1. b) Twice twenty minus the quotient of twelve divided by four.

1. 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 operation, knowing that each square represents a box.

In a comic shop, a teenager buys $3$ manga books at $160$ pesos each and $2$ posters at $100$ pesos each. If he pays with a $1\,000$ pesos note, how much change should he receive? Express all the calculations in a single line.

Work out the result of the following combined operation step by step, respecting the order of operations:

$15 \times (13 - 3^2) + 4^2 : \sqrt{64} - 2 \times 5$

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 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 $300$ pesos and the remaining tickets for $180$ pesos. If all seats have been sold, what was the total revenue for the screen?

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 $360$ pesos, how much money will he get from selling his whole crop?

Work out the value of the following expression, applying correctly the order of operations and the laws of indices:

Remember to solve the innermost brackets first, followed by powers and roots, then multiplications and divisions, and finally additions and subtractions.

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 $12 \text{ mm}$:

1. a) What is the area of the small square?
2. b) What is the total perimeter of the resulting shape (the outer outline)?

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:

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.