Remainder and Mixed Number

🏆Practice mixed numbers and fractions greater than 1

Remainder and Mixed Number

In a mixed number, the remainder will always be the fraction and not the whole number.

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Write the fraction as a mixed number:

\( \frac{10}{7}= \)

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Remainder and Mixed Number

In this article, we will learn what the remainder is in a mixed fraction and we'll be able to identify it easily without any effort!
First, let's remember, what is a mixed fraction?

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:
5235 \frac{2}{3}

In this mixed number there are 55 wholes and a fraction of 232 \over 3

How do we know what the remainder is in a mixed number?

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:
What is the fraction part in 4144 \frac{1}{4}?
The answer is of course 141 \over 4

Want to understand why the remainder is always the fractional part? Read the following explanation!
A remainder is actually the part that's left over when we perform a division operation and the number we divided doesn't divide evenly.
For example - if I have 44 notebooks and I have 33 children, I'll probably have a problem because each one will get a notebook and then I'll have one notebook left that I'll need to divide into 33 equal parts.
The equal part that will be shared among everyone will be my remainder because it's the part that doesn't divide evenly.
But, if for example I had 66 notebooks and 33 children, I could give each child 22 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 77 fruits to the end-of-year party and Batya brought 55 fruits to the end-of-year party.
There were 33 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 77 fruits and she needs to divide them without a remainder.

73=213\frac {7}{3} = 2\frac{1}{3}

We can see that she can only divide 22 fruits to each child evenly and will be left with 11 fruit that she needs to divide by 33 - meaning she distributes 66 fruits and takes 11 fruit back home.
Let's move to Batya - she has 55 fruits and there are 33 children

53=123\frac{5}{3} = 1\frac{2}{3}

She can only divide one fruit to each person and 22 fruits she will need to divide between everyone, which means she divides 33 fruits and returns 22 home.

In total, Anat and Batya returned 33 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 go 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 525\over2 to a mixed number,
We ask - how many times does 22 go into 55?
The answer is 22 - this will be our whole number.
What remains - 11, will be the numerator in the mixed number. Therefore we get:

52=212\frac{5}{2} = 2\frac{1}{2}

Converting an improper fraction to a mixed number and finding the remainder exercise -
Bar brought 55 strawberries to class and wanted to divide them equally between 44 friends.
How did Bar divide the strawberries equally and what is the remainder?

Solution:

Bar wanted to divide 55 by 44 which means 545 \over4.
We learned that if we convert an improper fraction to a mixed number, we can immediately see the remainder -
So we'll convert 545 \over4 to a mixed number and get 1141 \frac{1}{4}.
This means Bar first gave one whole strawberry to each of the 11 of four friends, and then she had one strawberry left which she divided into 44 equal parts between all of them.
The remaining part that was divided between everyone is 141\over 4 and this can also be seen from the appearance of the mixed number.

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Examples with solutions for Mixed Numbers and Fractions Greater than 1

Exercise #1

Write the fraction as a mixed number:

107= \frac{10}{7}=

Video Solution

Answer

137 1\frac{3}{7}

Exercise #2

Write the fraction as a mixed number:

128= \frac{12}{8}=

Video Solution

Answer

148 1\frac{4}{8}

Exercise #3

Write the fraction as a mixed number:

139= \frac{13}{9}=

Video Solution

Answer

149 1\frac{4}{9}

Exercise #4

Write the fraction as a mixed number:

1610= \frac{16}{10}=

Video Solution

Answer

1610 1\frac{6}{10}

Exercise #5

Write the fraction as a mixed number:

1711= \frac{17}{11}=

Video Solution

Answer

1611 1\frac{6}{11}

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