In a mixed number of a whole number and a fraction -
the fraction is the remainder.
In a mixed number of a whole number and a fraction -
the fraction is the remainder.
In a fraction greater than where the numerator is greater than the denominator -
The remainder consists of a denominator and numerator, which is the part left after finding how many whole numbers are in the fraction.
Write the fraction as a mixed number:
\( \frac{10}{7}= \)
A remainder is a part of a non-whole number.
It usually occurs when we divide one number by another and it doesn't divide evenly.
For example, if we want to divide pizza triangles among children.
How do we divide them?
Each child will get one pizza triangle and one third of a triangle.
The third of a triangle is the remainder.
Given that after we gave each child one triangle, there was one spare triangle that we divide into parts between each child.
A fraction has several forms that we may encounter, and it's important to understand what is the remainder in each fraction.
In every fraction, the remainder is what's left from the whole number.
Let's take a look at some examples to help us better understand this concept:
In a fraction in the form of a whole number and remainder (meaning a mixed number)-
It's easiest for us to identify what the remainder is.
For example, in this mixed number:
We can immediately identify that there are whole numbers and a remainder of -
In a fraction where the numerator is larger than the denominator -
In a fraction of this form, when the numerator is larger than the denominator, we cannot immediately identify the remainder. For example, in the fraction:
We need to understand how many times goes into as a whole number and what remains is our remainder.
What's the closest number to that is divisible by without a remainder? The answer is 8.
8 divided by is , so there are whole numbers.
In other words, we can say that goes into times as a whole number, so the whole number is .
Are we done? Not at all.
If we "put in" times , we get , but the numerator is . Therefore, we're left with .
Note -
So the remainder is
because after we put in times , we have left out of , meaning one half.
Let's look at another example.
What is the remainder in the fraction:
Let's ask, how many times does go into as a whole number?
The answer is time
Then we have a remainder of
Another example with a mathematical solution:
If it was complicated to understand the remainder concept verbally, try to understand it through a calculation exercise.
What is the remainder in the fraction -
Let's ask, what is the closest number to that is divisible by without a remainder.
The answer is .
Let's divide by to get the whole number.
Now let's subtract from the result of multiplying:
the whole number we got
and write the answer in the numerator with denominator .
The fraction we get is our remainder.
is the whole number.
The result will be the numerator and the denominator will be like in the original exercise.
The remainder is
Does every fraction where the numerator is greater than the denominator have a remainder?
Absolutely not!
Sometimes there are fractions where the numerator is larger than the denominator, but the denominator divides evenly into the numerator without a remainder, so there is no remainder.
Let's look at an example -
In the fraction
The numerator is indeed larger than the denominator but goes into twice without a remainder, so there is no remainder.
What happens when the numerator is equal to the denominator?
When the numerator equals the denominator there is no remainder and the whole number is .
Like for example in the fraction:
Bonus tip –
What is the remainder in a fraction less than , for example in the fraction
The answer is the entire fraction, meaning,
the remainder is
since the whole number is .
And now let's practice!
Write what is the remainder in each of the following numbers and explain.
Solution:
The remainder is
It can be clearly seen that there are whole numbers and one-third remainder.
What is the remainder in the fraction-
Solution:
No remainder. goes into exactly twice.
What is the remainder in the fraction:
goes into one time with a remainder
Therefore this is our remainder.
Write the fraction as a mixed number:
\( \frac{12}{8}= \)
Write the fraction as a mixed number:
\( \frac{13}{9}= \)
Write the fraction as a mixed number:
\( \frac{16}{10}= \)
Write the fraction as a mixed number:
To solve the problem, we will convert the given improper fraction to a mixed number by dividing the numerator by the denominator.
Step 1: Divide the numerator (10) by the denominator (7). This gives a quotient and a remainder.
Step 2: Calculating gives a quotient of 1 because 7 goes into 10 once.
Step 3: Multiply the quotient by the divisor ().
Step 4: Subtract the product obtained in step 3 from the original numerator to find the remainder: .
Step 5: Compose the mixed number using the quotient as the whole number and the remainder over the divisor as the fraction part: .
Thus, the mixed number representation of is .
Write the fraction as a mixed number:
To solve this problem, we need to convert the improper fraction into a mixed number.
Here's how we'll do it:
Thus, the mixed number representation is correctly simplified as .
However, when selecting from the given choices, the correct choice based on the options provided is (Choice 4), which matches the unsimplified form.
Therefore, the solution to the problem is .
Write the fraction as a mixed number:
To convert the improper fraction into a mixed number, we follow these steps:
Let's carry out these steps in detail:
Divide 13 by 9:
with a remainder of .
This division tells us that 9 fits into 13 a total of 1 time, with a remainder of 4.
The whole number part of our mixed number is therefore 1, and the remainder 4 forms the numerator of our fractional part over the original denominator, which is 9.
So, the fractional part is .
Therefore, the improper fraction as a mixed number is .
Write the fraction as a mixed number:
To solve the problem of converting the fraction to a mixed number, we proceed with the following steps:
Therefore, the mixed number form of the fraction is .
Write the fraction as a mixed number:
To convert the improper fraction to a mixed number, we proceed as follows:
Step 1: Perform the division . We find: - The quotient (whole number) is 1 since 11 goes into 17 once.
- The remainder is 6 because .
Step 2: Express the remainder as a fraction over the original denominator. Hence, the fractional part is .
Step 3: Combine the quotient and the remainder fraction to form the mixed number: .
Therefore, the mixed number equivalent of the fraction is .