Carlos read 1-half of a book for school. He has 7 days to read the other 1-half of the book. He plans to read the same amount each day.
Question
What fraction of the book will Carlos read each day? Move numbers to the boxes to show the answer. If there is no whole number, put a 0 in the first box.
Great question! The answer "$\boxed{\frac{1}{7}}$" means that Carlos plans to read one-seventh of the book each day. In other words, he will read an amount that is equal to one-seventh of the total book.
When we write a number like $\frac{1}{7}$, it represents a fraction, which is a way of expressing a part of a whole. In this case, the whole is the book, and the part that Carlos will read each day is one-seventh of the book.
You can think of a fraction like $\frac{1}{7}$ as a way of dividing something into 7 equal parts and taking just one of those parts. So if the book were divided into 7 equal parts, Carlos would read just one of those parts each day.
Carlos plans to read $\boxed{\frac{1}{14}}$ of the book each day.
To see why, we can start by finding the total amount he needs to read: $$\text{Total amount} = \frac{1}{2} + \frac{1}{2} = 1$$ So Carlos needs to read 1 whole book in 7 days, which means he needs to read $\frac{1}{7}$ of the book each day.
But Carlos plans to read the same amount each day, so we can divide $\frac{1}{7}$ by the number of days he plans to read: $$\frac{1}{7} \div 7 = \frac{1}{7} \cdot \frac{1}{7} = \boxed{\frac{1}{49}}$$
Oops! We made a mistake! If we divide $\frac{1}{7}$ by 7, we get $\frac{1}{49}$, not $\frac{1}{14}$.
So what went wrong? We forgot to simplify $\frac{1}{49}$ to lowest terms. We can simplify it by dividing the numerator and denominator by 7: $$\frac{1}{49} = \frac{1 \div 7}{49 \div 7} = \frac{1}{7}$$ So Carlos plans to read $\boxed{\frac{1}{7}}$ of the book each day.
Huh? What does $\boxed{\frac{1}{7}}$ mean?
To find out what fraction of the book Carlos will read each day, we need to first determine the total number of halves in the book.
Carlos has already read 1-half of the book, and he still needs to read the other 1-half.
So the total number of halves in the book is: 1-half + 1-half = 2-halves.
Next, we need to divide the total number of halves in the book by the number of days Carlos has to read it (7 days).
So, the fraction of the book Carlos will read each day can be calculated by dividing 2-halves by 7 days.
2-halves รท 7 = 2/7
Therefore, Carlos will read 2/7 of the book each day.