Remainder and Mixed Number

In this article, we will learn about the remainder in a mixed number as well as how to identify it effortlessly!
Let's begin by reviewing mixed fractions.

Reminder –
A mixed number is a number that consists of two parts – a whole number and a fraction
Hence its name, it mixes both a whole number and a fraction.

For example:
$5 \frac{2}{3}$

In this mixed number there are $5$ wholes and a fraction of $2 \over 3$

Easy!
The remainder is always the non-whole part!
This means that the remainder is always the fractional part in a mixed number.

Let's look at an example:
Determine the fractional part in $4 \frac{1}{4}$?
The answer is of course $1 \over 4$

Do you want to understand why the remainder is always the fractional part? Read the following explanation!
A remainder can be defined as the part that's left over when we perform a division operation and the number that we divided doesn't divide evenly.
For example - if I have $4$ notebooks and I have $3$ children it will result in a remainder due to the fact that each child will get one notebook and one notebook will be left over. I'll need to divide the spare notebook into $3$ equal parts.
The equal part that will be shared among everyone will make up remainder given that it's the part that doesn't divide evenly.
However, if for example I had $6$ notebooks and $3$ children, I could give each child $2$ notebooks and I wouldn't have a remainder.
Therefore, a remainder is always that part that doesn't divide evenly and needs to be divided equally among everyone!

Advanced Exercise -
Anat and Batya are sisters in 3rd grade. Anat brought $7$ fruits to the end-of-year party and Batya brought $5$ fruits to the end-of-year party.
There were $3$ children at the party.
Anat and Batya's mom asked them to distribute the fruits equally among the children without remainders - meaning to bring the remainder home (fruit that needs to be cut will not be divided and will be returned home) because she wants to make a fruit salad from the remaining fruits.
How many fruits did Anat return and how many fruits did Batya return?

Solution -
In this question we were asked to understand what would be the remainder for Anat and what would be the remainder for Batya.
Let's start with Anat - she has $7$ fruits and she needs to divide them without a remainder.

$\frac {7}{3} = 2\frac{1}{3}$

We can deduce that she can distribute $2$ fruits equally to each child and will be left with $1$ fruit that she needs to divide by $3$ - meaning she distributes $6$ fruits and takes $1$ fruit back home.
Let's move to Batya - she has $5$ fruits and there are $3$ children

$\frac{5}{3} = 1\frac{2}{3}$

She can only distribute one fruit equally to each person leaving her with $2$ fruits that she will need to divide between everyone, which means she distributes $3$ fruits in total and returns $2$ home.

In total, Anat and Batya returned $3$ fruits.

Sometimes you will encounter an improper fraction, and it would be beneficial to convert it to a mixed number to immediately identify the remainder.
When in an improper fraction the numerator equals the denominator - there is no remainder, the number is whole.
In an improper fraction where the numerator is greater than the denominator - we can easily convert it to a mixed number in the following way:
We ask how many times does the denominator fit into the numerator?
This will be our whole number.
What remains will be the numerator in the fraction part of the mixed number.
For example, to convert the improper fraction $5\over2$ to a mixed number,
We ask - how many times does $2$ go into $5$?
The answer is $2$ - this will be our whole number.
What remains - $1$, will be the numerator in the mixed number. Therefore we obtain the following:

$\frac{5}{2} = 2\frac{1}{2}$

Converting an improper fraction to a mixed number and finding the remainder exercise -
Bar brought $5$ strawberries to class and wanted to divide them equally between $4$ friends.
How did Bar divide the strawberries equally and what is the remainder?

Solution:

Bar wanted to divide $5$ by $4$ which means $5 \over4$.
We learned that if we convert an improper fraction to a mixed number, we can immediately see the remainder -
So we'll convert $5 \over4$ to a mixed number and obtain $1 \frac{1}{4}$.
This means Bar first gave one whole strawberry to each of the $1$ of four friends, and then she had one strawberry left which she divided into $4$ equal parts between all of them.
The remaining part that was divided between everyone is $1\over 4$ and this can also be seen from the appearance of the mixed number.

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