In this article, we will teach you the basics of everything you need to know about mixed numbers.

If you wish to delve deeper into a specific topic, you can access the corresponding extensive article.

In this article, we will teach you the basics of everything you need to know about mixed numbers.

If you wish to delve deeper into a specific topic, you can access the corresponding extensive article.

A fraction that is greater than 1 is a fraction whose numerator is larger than its denominator, this type of fractions can be converted into mixed numbers.

**It is important that we remember similar topics:**

Multiply the whole number by the denominator.

To the obtained product, add the numerator. The final result will be the new numerator.

Nothing is changed in the denominator.

The whole number is written in the numerator and the 1 in the denominator.

You can continue reading in these articles:

\( 8\times\frac{5}{9}= \)

To add and subtract mixed numbers, we will act as follows:

We will convert mixed numbers into fractions - fractions with numerator and denominator that do not have whole numbers.

We will find a common denominator (usually by multiplying the denominators).

We will add or subtract only the numerators. The denominator will be written only once in the final result.

We will solve the multiplication of an integer by a fraction and by a mixed number in the following way:

Test your knowledge

Question 1

\( 3\times\frac{8}{12}= \)

Question 2

\( 10\times\frac{7}{9}= \)

Question 3

\( 7\times\frac{6}{8}= \)

We will convert the whole numbers and mixed numbers to fractions and rewrite the exercise.

We will multiply the numerators and the denominators separately.

The product of the numerators will be written in the new numerator.

The product of the denominators will be written in the new denominator.

Do you know what the answer is?

Question 1

Solve:

\( 7\times\frac{3}{8}= \)

Question 2

\( 8\times\frac{1}{2}= \)

Question 3

\( 3\times\frac{6}{7}= \)

We will convert mixed numbers to fractions and rewrite the exercise.

We will multiply the numerators and the denominators separately.

The product of the numerators will be written in the new numerator.

The product of the denominators will be written in the new denominator.

• The commutative property works - We can change the order of the fractions within the exercise without altering the result.

We will convert mixed numbers to fractions and rewrite the exercise.

We will convert the division into multiplication and swap between the numerator and the denominator in the second fraction.

We will solve by multiplying numerator by numerator and denominator by denominator.

Check your understanding

Question 1

\( 7\times\frac{2}{5}= \)

Question 2

\( 6\times\frac{3}{4}= \)

Question 3

\( 2\times\frac{5}{7}= \)

- In case there is any mixed number - we will convert it into a fraction

• In case there is any whole number - we will convert it into a fraction

We will convert the division into multiplication and swap between the numerator and the denominator in the second fraction.

We will solve by multiplying numerator by numerator and denominator by denominator.

$\frac{1}{2}+3\frac{1}{2}+4\frac{2}{4}=$

According to the order of operations, we will solve the exercise from left to right.

Let's note that in the first addition exercise, we have an addition between two halves that will give us a whole number, so:

$\frac{1}{2}+3\frac{1}{2}=4$

Now we will get the exercise:

$4+4\frac{2}{4}=$

Let's note that we can simplify the mixed fraction:

$\frac{2}{4}=\frac{1}{2}$

Now the exercise we get is:

$4+4\frac{1}{2}=8\frac{1}{2}$

$8\frac{1}{2}$

$7\frac{5}{6}+6\frac{2}{3}+\frac{1}{3}=$

Note that the right addition exercise between the fractions gives a result of a whole number, so we'll start with it:

$6\frac{2}{3}+\frac{1}{3}=7$

Now we get:

$7\frac{5}{6}+7=14\frac{5}{6}$

$14\frac{5}{6}$

$\frac{1}{3}+\frac{2}{3}+2\frac{3}{4}=$

According to the rules of the order of operations in arithmetic, we solve the exercise from left to right.

Let's note that:

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

We should obtain the following exercise:

$1+2\frac{3}{4}=3\frac{3}{4}$

$3\frac{3}{4}$

$\frac{6}{7}x+\frac{8}{7}x+3\frac{2}{3}x=$

Let's solve the exercise from left to right.

We will combine the left expression in the following way:

$\frac{6+8}{7}x=\frac{14}{7}x=2x$

Now we get:

$2x+3\frac{2}{3}x=5\frac{2}{3}x$

$5\frac{2}{3}x$

$4:\frac{6}{8}=$

$5\frac{1}{3}$

Do you think you will be able to solve it?

Question 1

\( 4\times\frac{2}{3}= \)

Question 2

\( 3\times\frac{1}{2}= \)

Question 3

\( 2:\frac{2}{3}= \)

Related Subjects

- The Order of Basic Operations: Addition, Subtraction, and Multiplication
- Order of Operations: Exponents
- Order of Operations: Roots
- Division and Fraction Bars (Vinculum)
- The Numbers 0 and 1 in Operations
- Neutral Element (Identiy Element)
- Order of Operations with Parentheses
- Order or Hierarchy of Operations with Fractions
- Opposite numbers
- Elimination of Parentheses in Real Numbers
- Addition and Subtraction of Real Numbers
- Multiplication and Division of Real Numbers
- Multiplicative Inverse
- Integer powering
- Positive and negative numbers and zero
- Real line or Numerical line