Operations with Decimals

In a phone accessories store, Ethan wants to buy a case that costs $\$12,45$ and a screen protector that costs $\$8,90$. If Ethan pays with a $\$50$ bill, how much change will he be given at the register?

Copy and complete the following equalities by placing the missing decimal number so that the operation is correct:

1. a) $15,45 + \dots = 20$
2. b) $7,2 - \dots = 4,55$
3. c) $\dots \cdot 3 = 12,9$

Three friends decide to have a snack together. They buy a pack of soft drinks for $\$4,85$, a family-size bag of chips that costs $\$2,30$, and a box of pastries for $\$5,45$. If they pay with a $\$20$ bill, how much money will they have left over to buy candy on the way out?

Calculate these operations mentally using powers of ten. Remember to move the decimal point to the correct side depending on whether you are multiplying or dividing:

1. a) $34,57 \cdot 10$
2. b) $0,23 \cdot 100$
3. c) $458,2 : 10$
4. d) $12,5 : 1000$

Emma went to the grocery store and bought $2,5$ lb of apples at a price of $\$1,80$ per pound. When she gets home, she realizes that one of the apples is bad and decides to return it. If the apple weighed $0,25$ lb, how much money should Emma be refunded?

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 savings if we decide to buy $15$ notebooks using the pack offer instead of buying them separately?

To make a cooking recipe, we need to divide a $1,5$ kg packet of flour into $6$ exactly equal portions to make cupcakes. How many kilograms of flour will each portion weigh? Express the result in grams as well.

A group of $4$ friends goes to the movie theater. The total for the tickets and popcorn was $\$45,80$. If they have decided to all pay the same amount, how much money must each one put in? If one of them only has a $\$10$ bill and a $\$2$ coin, will he have enough money?

A spool of filament for a 3D printer weighs exactly $1,25$ lb. If $0,015$ lb of plastic is used to make a small part, how many complete parts can be made with a single spool? How much filament will be left over at the end?

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

1. a) $4,5 + 2,1 \cdot 3$
2. b) $(12,8 - 3,4) : 2$
3. c) $5 \cdot 0,25 + 1,75$

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

1. a) $12,5 + 3,8 \cdot (6,4 - 2,15)$

1. b) $(15,4 + 8,6) : 2,5 - 1,02 \cdot 4$

Calculate the result of the following combined operation, strictly respecting the order of operations and working with all the decimals obtained:

Once the final result is obtained, approximate it by rounding to the hundredths and by truncating to the tenths.

In an electronics store, a video game costs $\$59,95$. During "Black Friday" week, they offer a discount of a quarter of its value. If a teenager decides to buy it and hands over a $\$50$ bill, calculate:

1. a) The final price of the video game after applying the discount (round to the nearest cent if necessary).
2. b) Will he have enough money? If he is short, state by how much. If he has money left over, state the exact change he will receive.

Three friends want to buy a subscription to a streaming platform that costs $\$17,99$ a month. They decide to share the cost as follows: John will pay half, Emma will pay a third of the remainder, and Lucy will pay what is left.

Calculate the exact amount (with all its decimals) that each one must contribute. If the bank only allows payments with two decimal places, who do you think should take on the rounding of the extra cent so that the sum is exactly $\$17,99$?

A monthly telephone bill includes a fixed charge of $\$18,50$. In addition, each minute of a call costs $\$0,12$ and each text message (SMS) costs $\$0,15$. If this month $45$ minutes of calls have been made and a number of messages have been sent such that the cost of the messages is exactly a fifth of the fixed charge:

1. a) How many messages have been sent?
2. b) What is the total amount of the bill before taxes?
3. c) If $21\%$ sales tax must be added to the total (multiply by $0,21$ and add to the total), what will be the final price of the bill? (Round the final result to the nearest cent).

An athlete is training on a circular track. Each lap of the track has a length of $0,45$ miles. If today she has completed a total of $12$ laps, how many miles has she run in total? If her goal was to run $6,3$ miles, how many more laps should she have done?

A city council wants to fence a rectangular park that is $25,4$ feet long and $12,75$ feet wide. The price of the fence is $\$15,20$ per linear foot. If the total available budget is $\$1.200$, do they have enough money to surround the entire park? Justify your answer with the necessary calculations.

Draw a rectangle with base $b = 12,45 \text{ cm}$ and height $h = 8,2 \text{ cm}$.

Calculate its area and its perimeter. Then, imagine that we reduce both the base and the height by half. What will the new area be? Is the resulting area half of the original or has it changed in another way? Justify your answer by carrying out the necessary operations.

Emma wants to download three video game files on her console. The first takes up $4,35$ GB, the second twice as much as the first, and the third $1,2$ GB less than the second. If her connection downloads at a constant speed of $0,05$ GB per second, how many seconds will it take to complete the download of the three files?

A marathon runner has completed a stage of $15,6$ miles in an hour and a half ($1,5$ hours).

1. a) What was his average speed in mph?
2. b) If he maintains the same speed, how many miles will he travel in $2,25$ hours?

A Formula 1 car has taken $1 \text{ minute}$ and $24,352 \text{ seconds}$ to complete one lap of the track. If its main rival has taken $84,12 \text{ seconds}$ to complete 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.

A courier company charges a fixed rate of $\$4,50$ per shipment, plus $\$0,85$ for each pound of the package's weight. If we want to send a package weighing $3,4$ lb and we apply a discount coupon of $\$1,25$ to the final price, how much will the shipment cost us? Write the expression with combined operations and solve it.

A farmer has a water tank with a total capacity of $1\,250,5$ gallons. Due to a small crack, the tank loses $0,75$ gallons every hour. Simultaneously, a water pump pours $12,4$ gallons into the tank every $15$ minutes. If the tank currently contains $840,25$ gallons:

How many gallons will be in the tank exactly after $4$ and a half hours? Express the result to two decimal places.

We are cooking a recipe that requires $0,250 \text{ lb}$ of flour to make $6$ cupcakes. If we want to invite the whole class ($28$ students) and we want everyone to eat $2$ cupcakes:

1. a) How much flour will we need in total? Express the result in pounds.
2. b) If we buy $0,75 \text{ lb}$ bags of flour, how many bags will we have to buy at a minimum? Exactly how much flour will we have left over?