Word Problems: Addition, Subtraction, Multiplication, Division ... - Free Printable

Let's solve each problem step by step:

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Problem 1: Ivan and His Books

Question: Ivan is putting books in his bookcase. He has already put 74 books in his bookcase but he has 235 books. How many more books does he have to put in his bookcase?

Solution:
To find out how many more books Ivan needs to put in his bookcase, we subtract the number of books he has already placed from the total number of books he has.

\[
\text{Books left to put} = \text{Total books} - \text{Books already put}
\]

Substitute the given values:
\[
\text{Books left to put} = 235 - 74
\]

Perform the subtraction:
\[
235 - 74 = 161
\]

Answer: Ivan has to put 161 more books in his bookcase.

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Problem 2: Amber and Her Marbles

Question: Amber has 36 marbles to share among herself and 3 friends. How many marbles will each of them receive?

Solution:
Amber wants to share her 36 marbles equally among herself and her 3 friends. This means the marbles need to be divided among a total of:
\[
1 \text{ (Amber)} + 3 \text{ (friends)} = 4 \text{ people}
\]

To find out how many marbles each person gets, we divide the total number of marbles by the number of people:
\[
\text{Marbles per person} = \frac{\text{Total marbles}}{\text{Number of people}}
\]

Substitute the given values:
\[
\text{Marbles per person} = \frac{36}{4}
\]

Perform the division:
\[
\frac{36}{4} = 9
\]

Answer: Each person will receive 9 marbles.

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Problem 3: Ken and His Allowance

Question: Ken gets allowance money every day. On Monday he gets 1 cent, on Tuesday he gets 2 cents, on Wednesday he gets 3 cents, on Thursday he gets 4 cents, and so on. How much money will he have by the 12th day? Did you figure this using a formula?

Solution:
Ken receives an increasing amount of money each day, starting from 1 cent on the first day and increasing by 1 cent each subsequent day. This forms an arithmetic sequence where:
- The first term (\(a\)) is 1.
- The common difference (\(d\)) is 1.
- The number of terms (\(n\)) is 12 (since we are calculating up to the 12th day).

The sum of the first \(n\) terms of an arithmetic sequence is given by the formula:
\[
S_n = \frac{n}{2} \times (a + l)
\]
where:
- \(S_n\) is the sum of the first \(n\) terms,
- \(n\) is the number of terms,
- \(a\) is the first term,
- \(l\) is the last term.

Here:
- \(n = 12\),
- \(a = 1\),
- \(l = 12\) (since the 12th term is 12).

Substitute these values into the formula:
\[
S_{12} = \frac{12}{2} \times (1 + 12)
\]

Simplify step by step:
\[
S_{12} = 6 \times 13 = 78
\]

Thus, Ken will have 78 cents by the 12th day.

Answer: Ken will have 78 cents by the 12th day. Yes, this was calculated using the formula for the sum of an arithmetic sequence.

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Problem 4: Saving for a New Book

Question: It takes 90 days to save enough money for a new book I want. Estimate how many months that is?

Solution:
There are approximately 30 days in a month. To estimate the number of months it takes to save for the book, we divide the total number of days by the number of days in a month:
\[
\text{Months} = \frac{\text{Total days}}{\text{Days per month}}
\]

Substitute the given values:
\[
\text{Months} = \frac{90}{30}
\]

Perform the division:
\[
\frac{90}{30} = 3
\]

Answer: It takes approximately 3 months to save enough money for the book.

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Problem 5: Broken MP3 Player

Question: You have 12 mp3 songs on your computer. 1/4 of them don’t work. How many songs do you have to buy to replace the ones that don’t work?

Solution:
First, determine how many songs don't work. Since 1/4 of the songs don't work, we calculate:
\[
\text{Non-working songs} = \frac{1}{4} \times \text{Total songs}
\]

Substitute the given values:
\[
\text{Non-working songs} = \frac{1}{4} \times 12
\]

Perform the multiplication:
\[
\frac{1}{4} \times 12 = 3
\]

So, 3 songs don't work. To replace these non-working songs, you need to buy 3 new songs.

Answer: You need to buy 3 songs to replace the ones that don’t work.

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Problem 6: Sharing Pizza

Question: You have 5 mini pizzas to share with 4 friends. You’re cutting the pizza in half, how much will each hand get shared equally?

Solution:
You have 5 mini pizzas, and each pizza is cut in half, resulting in:
\[
5 \text{ pizzas} \times 2 \text{ halves per pizza} = 10 \text{ halves}
\]

You want to share these 10 halves equally among yourself and your 4 friends, making a total of:
\[
1 \text{ (you)} + 4 \text{ (friends)} = 5 \text{ people}
\]

To find out how many halves each person gets, divide the total number of halves by the number of people:
\[
\text{Halves per person} = \frac{\text{Total halves}}{\text{Number of people}}
\]

Substitute the values:
\[
\text{Halves per person} = \frac{10}{5}
\]

Perform the division:
\[
\frac{10}{5} = 2
\]

Each person will get 2 halves of a mini pizza.

Answer: Each person will get 2 halves of a mini pizza.

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Final Answers:

1. 161 books
2. 9 marbles
3. 78 cents
4. 3 months
5. 3 songs
6. 2 halves

\boxed{161, 9, 78, 3, 3, 2}