Back to homeMathematics · 2nd ESO · Change subject
Start for free
ESO Y2 · Mathematics
Numbers · Natural numbers

Operations with natural numbers

You buy $3$ manga books at $8$ € each and $2$ posters at $5$ € each, and you pay with a $50$ € note. 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.

Before you start, make sure you know: Natural numbers (1st ESO)

From a statement to an operation

Translating verbal statements into expressions with combined operations “Three times the sum of 8 and 5” 3 · (8 + 5) “Double 20 minus the quotient of 12 divided by 4” 2·20 − 12:4
Practice★☆☆Not started
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:

  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.
Solve
Practice★☆☆Not started
In a comic shop, a teenager buys $3$ manga books at $8$ € each and $2$ posters at $5$ € each. If he pays with a $50$ € note, how much change should he receive? Express…

In a comic shop, a teenager buys $3$ manga books at $8$ € each and $2$ posters at $5$ € each. If he pays with a $50$ € note, how much change should he receive? Express all the calculations in a single line.

Solve

Order of operations in practice

Remember the order: brackets, then powers and roots, then ·/:, and finally +/−.

Diagram of the four levels of the order of operations 1. Brackets 2. Powers and roots 3. · y : 4. + y −
Practice★☆☆Not started
Work out the result of the following combined operations, paying attention to the order of operations: a) $25 + 5 \cdot 4 - 10$ b) $36 : 6 + 2 \cdot 7$ c)…

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

  1. a) $25 + 5 \cdot 4 - 10$
  1. b) $36 : 6 + 2 \cdot 7$
  1. c) $18 - 12 : 3 + 4$
Solve
Practice★★☆Not started
Work out the result of the following combined operation step by step, respecting the order of operations: $15 \cdot (13 - 3^2) + 4^2 : \sqrt{64} - 2 \cdot 5$

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

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

Solve

The distributive property and common factors

Step-by-step procedure for taking out a common factor in a combined operation 125 · 48 + 125 · 64 − 125 · 12 = 125 · (48 + 64 − 12) = 125 · 100 = 12.500
Practice★★☆Not started
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 $15$ € and the remaining tickets for $9$…

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 $15$ € and the remaining tickets for $9$ €. If all seats have been sold, what was the total revenue for the screen?

SCREEN 18 seats per row 4 rows 8 rows 12 rows in total VIP AREA 15 € / ticket STANDARD 9 € / ticket
Solve
Practice★★★Not started
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 \cdot…

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:

$$ 125 \cdot 48 + 125 \cdot 64 - 125 \cdot 12 $$

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.

Solve

Back to the beginning: We translate the problem into a single operation: $50 - (3 \cdot 8 + 2 \cdot 5) = 50 - (24 + 10) = 50 - 34 = 16$ €. You get $16$ € change.

Summary

See all the exercises in this section