Operations with decimal numbers

In a mobile phone accessory shop, Marc wants to buy a case costing $12.45$ € and a screen protector costing $8.90$ €. If Marc pays with a $50$ € note, how much change will he receive at the till?

Copy and complete the following statements by writing the missing decimal number to make each calculation correct:

1. a) $15.45 + \dots = 20$
2. b) $7.2 - \dots = 4.55$
3. c) $\dots \times 3 = 12.9$

Three friends decide to have an afternoon snack together. They buy a pack of soft drinks for $4.85$ €, a family-size bag of crisps for $2.30$ € and a box of small cakes for $5.45$ €. If they pay with a $20$ € note, how much money will they have left over to buy sweets afterwards?

Aoife has a wooden strip of $14.2\text{ m}$ and needs to cut a piece of $3.75\text{ m}$ to build a shelf. To calculate how much wood she has left over, she sets up the subtraction $14.2 - 3.75$ vertically and claims that the result is $11.55\text{ m}$, reasoning as follows: "in the hundredths column, since there is nothing at the top, I bring down the $5$ directly; in the tenths I subtract the smaller digit from the larger one, $7 - 2 = 5$; and in the units I subtract $14 - 3 = 11$".

1. a) Identify and explain the two conceptual mistakes made by Aoife related to the place value of the digits and the subtraction operation.
2. b) Explain why it is essential to add zeros to the right of the decimal part of the minuend before calculating.
3. c) Set up the column operation correctly and find the exact length of the strip that Aoife has left.

Work out these calculations mentally using powers of ten. Remember to move the decimal point to the correct side depending on whether you multiply or divide:

1. a) $34.57 \times 10$
2. b) $0.23 \times 100$
3. c) $458.2 : 10$
4. d) $12.5 : 1000$

Aoife went to the greengrocer's and bought $2.5$ kg of apples at $1.80$ € per kilogram. On arriving home, she notices that one of the apples is bad and decides to return it. If the apple weighed $0.25$ kg, how much money should Aoife be refunded?

An athlete is training on a circular track. Each lap of the track is $0.45$ km long. If today she completed a total of $12$ laps, how many kilometres did she cover in total? If her goal was to run $6.3$ km, how many more laps should she have completed?

In a "Back to School" offer, a pack of $5$ notebooks costs $8.25$ €, whereas if you buy them individually, each one costs $1.80$ €.

What is the total saving if we decide to buy $15$ notebooks using the pack offer instead of buying them separately?

To make a recipe, we need to divide a $1.5$ kg bag of flour into $6$ equal portions to make muffins. How many kilograms of flour will each portion weigh? Express your answer in grams as well.

A spool of filament for a 3D printer weighs exactly $1.25$ kg. If $0.015$ kg of plastic is used to make a small part, how many complete parts can be made from a single spool? How much filament will be left over at the end?

A marathon runner has completed a stage of $15.6$ km in an hour and a half ($1.5$ hours).

1. a) What was their average speed in km/h?
2. b) If they maintain the same speed, how many kilometres will they cover in $2.25$ hours?

Work out the following combined operations, respecting the order of operations (brackets, multiplications/divisions, and finally additions/subtractions):

1. a) $4.5 + 2.1 \times 3$
2. b) $(12.8 - 3.4) : 2$
3. c) $5 \times 0.25 + 1.75$

A group of $4$ friends goes to the cinema. The total for tickets and popcorn came to $45.80$ €. If they decide to split the cost equally, how much money must each person pay? If one of them only has a $10$ € note and a $2$ € coin, will they have enough money?

Calculate the result of the following combined operations, respecting the order of operations:

1. a) $12.5 + 3.8 \times (6.4 - 2.15)$

1. b) $(15.4 + 8.6) : 2.5 - 1.02 \times 4$

You go to your local grocery store with a single $\text{€}\ 15$ banknote and put the following items in your basket:

• $1$ pack of coffee for $\text{€}\ 3.95$,

• $2$ cartons of milk at $\text{€}\ 1.05$ each,

• $1$ loaf of artisanal bread for $\text{€}\ 0.98$, and

• $3$ packs of biscuits at $\text{€}\ 1.99$ each.

1. a) Before doing any written calculations with decimals, make a mental estimate by rounding the price of each item to the nearest whole euro. Using this estimate, reason whether you will have enough money with the $\text{€}\ 15$ banknote to pay for the purchase.
2. b) Now perform the exact operations in columns step by step to calculate the total amount shown on the cash register.
3. c) Check whether your initial estimate was correct, calculate exactly how much money you have left over or are missing, and reflect on situations in everyday life where it is useful to estimate before calculating.

On a receipt from a fruit shop, part of it has been erased due to a moisture stain. The only clearly legible data are the following:

• Apples: $3.5\text{ kg}$ at an unknown price per kilogram.

• Bananas: $1.2\text{ kg}$ at $1.85\text{ €/kg}$.

• Payment handed over at the till: a $\text{€}\ 20$ banknote.

• Exact change received: $\text{€}\ 11.48$.

1. a) Use the method of inverse operations: first calculate the total cost of the purchase and, subtracting the amount corresponding to the bananas, determine how much the apples cost in total.
2. b) From the total cost of the apples, set up and solve the decimal division needed to find the exact price of one kilogram of apples.
3. c) Reconstruct the full calculation forward to check that all operations and the change returned are correct.

Calculate the result of the following mixed operation, strictly respecting the order of operations and working with all decimal places obtained:

Once the final result is obtained, approximate it by rounding to the nearest hundredth and by truncating to the nearest tenth.

A Formula 1 car took $1 \text{ minute}$ and $24.352 \text{ seconds}$ to complete one lap of the circuit. If its main rival took $84.12 \text{ seconds}$ to cover the same distance:

1. a) Which of the two was faster?
2. b) Calculate the time difference between them expressed in seconds.
3. c) If the first car maintains its pace, how long will it take to complete $15$ full laps? Express the result in minutes and seconds.