Operations with decimal numbers
You mix $2{,}5$ kg of nuts and dried fruit at $14{,}20$ €/kg with $1{,}75$ kg at $12{,}60$ €/kg: what price per kilo should you sell the mixture at to make a profit? You already know how to operate with decimals one at a time; now it is time to chain them together in real problems, without losing the order of operations.
Review: the four operations with decimals
Marcos is saving up to buy a video game. On Monday he had $24,50$ € in his piggy bank. On Tuesday his aunt gave him $15,75$ € and on Wednesday he decided to buy a phone…
Marcos is saving up to buy a video game. On Monday he had $24,50$ € in his piggy bank. On Tuesday his aunt gave him $15,75$ € and on Wednesday he decided to buy a phone case costing $12,30$ €. How much money does Marcos have in his piggy bank right now? Perform the calculation lining up the decimal points correctly.
A monthly subscription to a music streaming service costs $9,95$ €. If a group of 10 friends decides to create a family account that costs exactly 10 times that amount…
A monthly subscription to a music streaming service costs $9,95$ €. If a group of 10 friends decides to create a family account that costs exactly 10 times that amount per year, what will be the total annual cost of the family subscription? Solve by moving the decimal point to the right.
Combined operations: the order of operations does not change with decimals
With decimals you work in the same order as with whole numbers: first brackets, then powers and roots, then multiplications and divisions, and finally additions and subtractions.
A can of fizzy drink has a capacity of $0,33$ litres. If a cardboard box holds 12 cans, how many litres of drink are there in total in a full box? Work out the…
A can of fizzy drink has a capacity of $0,33$ litres. If a cardboard box holds 12 cans, how many litres of drink are there in total in a full box? Work out the multiplication manually.
Calculate the result of the following expression according to the order of operations and the rule of signs: $15,8 - 2,5 \cdot (4,2 - 3,75) + (1,24 + 0,36) : 0,4$
Calculate the result of the following expression according to the order of operations and the rule of signs:
$15,8 - 2,5 \cdot (4,2 - 3,75) + (1,24 + 0,36) : 0,4$
Multi-step money problems
Real-life problems chain together several operations: purchases, fees, rounding, splitting costs. Before calculating, write down the whole expression.
An architect is designing a rectangular play area in a local park. The dimensions of the ground are $12,45$ metres long by $8,6$ metres wide. If she wants to enclose the…
An architect is designing a rectangular play area in a local park. The dimensions of the ground are $12,45$ metres long by $8,6$ metres wide. If she wants to enclose the entire perimeter with a protective fence costing $15,75$ € per linear metre, what will be the total budget for the fence?
An automatic savings app rounds each of your purchases up to the nearest euro and saves the difference in a digital piggy bank. During an afternoon of shopping, you made…
An automatic savings app rounds each of your purchases up to the nearest euro and saves the difference in a digital piggy bank. During an afternoon of shopping, you made the following payments:
-
Subscription to a gaming channel: $12,45$ €.
-
Afternoon snack with friends: $8,12$ €.
-
Phone case: $5,67$ €.
-
Sticker pack: $1,23$ €.
Calculate the value of the following expression to find how much money you have left in your bank account if you initially had $150$ € and, in addition to the purchases, the bank charged you a maintenance fee of $2,25$ €:
$$150 - (12,45 + 8,12 + 5,67 + 1,23 + 2,25) - H$$Where $H$ is the total sum of the roundings sent to the digital piggy bank.
Decimals in areas, mixtures and speeds
The same care with combined operations applies to formulae: areas involving $\pi$, prices of mixtures, or speed from distance and time.
A greengrocer buys $50$ kg of loose cherries for a total of $142,50$ €. When inspecting the goods, he discovers that $4,5$ kg are damaged and cannot be sold. If he wants…
A greengrocer buys $50$ kg of loose cherries for a total of $142,50$ €. When inspecting the goods, he discovers that $4,5$ kg are damaged and cannot be sold. If he wants to make a net profit of $60$ € on the total purchase, at what price per kilogram must he sell the cherries that are in good condition?
A racing drone has travelled a distance of $14,58$ kilometres in $12$ minutes and $45$ seconds. 1. Express the total flight time in hours using decimal numbers (round to…
A racing drone has travelled a distance of $14,58$ kilometres in $12$ minutes and $45$ seconds.
-
Express the total flight time in hours using decimal numbers (round to four decimal places).
-
Calculate the average speed of the drone in km/h using the previous value.
-
If the circuit record is a speed of $70,25$ km/h, by how many kilometres per hour did the drone fall short of matching the record?
Back to the start: The total cost of the mixture is $2{,}5 \cdot 14{,}20 + 1{,}75 \cdot 12{,}60 = 35{,}50 + 22{,}05 = 57{,}55$ € for $4{,}25$ kg; dividing, it works out at $57{,}55 : 4{,}25 \approx 13{,}54$ €/kg, so you must sell it for more than $13{,}54$ €/kg to make a profit.