Fractions do not influence the order of operations, therefore, you should treat them like any other number in the exercise.

The correct order of mathematical operations is as follows:

Fractions do not influence the order of operations, therefore, you should treat them like any other number in the exercise.

The correct order of mathematical operations is as follows:

Indicate whether the equality is true or not.

^{\( (5^2+3):2^2=5^2+(3:2^2) \)}

The order of mathematical operations with fractions is no different from the order of operations without fractions.

This means that if you know how to correctly solve a certain exercise based on the order of mathematical operations, you will also know how to solve an exercise with fractions in the same way.

Let's remember the order of operations:

**Parentheses**- We always start by solving what is inside the parentheses, regardless of the type of operation it is.**Multiplications and divisions**β The exercise is read from left to right. Multiplications and divisions have the same hierarchy, therefore, we will resolve them according to their order of appearance in the exercise, from left to right.**Additions and subtractions**- After having solved the operations that were in parentheses and those of multiplying and dividing, we will continue with addition and subtraction.

They also share the same hierarchy, therefore, we will resolve them according to their order of appearance in the exercise, from left to right.

**Note** - We have not given any importance to fractions, nor have we mentioned them.

We will treat fractions like any other number, whether it is a common fraction or a decimal number, it's all the same.

$3+6 \times \frac{1}{3}=$

**Solution:**

Multiplication comes before addition, therefore, we will first solve all the multiplications.**We will obtain:**

$3+\frac{6}{3}$

Now we will add and get:

$3+2=5$

Test your knowledge

Question 1

Solve:

\( 3-4+2+1 \)

Question 2

Solve:

\( -5+4+1-3 \)

Question 3

Solve:

\( 9-3+4-2 \)

$\frac{2}{5} \times (1+3)+4=$

**Solution:**

Parentheses come first, so we will start by solving what's inside them.

**We will obtain:**

$\frac{2}{5} \times 4+4=$

Multiplication comes before addition, so we will continue with the multiplication.

**We will obtain:**

$\frac{8}{5}+4$**Now we will add and get:**

$4\frac{8}{5}=5\frac{3}{5}$

$0.3+(0.4+0.1) \times 4=$

**Solution:**

We will start with the expression inside the parentheses.

**We will solve and obtain:**

$0.3+0.5 \times 4=$

Multiplication is resolved before addition, so we will continue with it.

**We will obtain:**

$0.3+2=$

**We will add and get:**

$0.3+2=2.3$

Do you know what the answer is?

Question 1

Solve the following exercise:

\( 12+3\cdot0= \)

Question 2

Solve the following exercise:

\( 2+0:3= \)

Question 3

\( 0+0.2+0.6= \)

$8-9:18 \times 6+5=$

**Solution:**

We know that if there are no parentheses we start with multiplication and division.

But in what order?

According to the order of appearance in the exercise, from left to right.

We start reading the exercise and we come across a division, therefore, we will start with it.

**We will obtain:**

$8-\frac{9}{18} \times 6+5=$

We will continue with the multiplication. We will realize that $9 \over 18$Β is, in fact, $1 \over 2$**We will obtain:**

$8-\frac{1}{2} \times 6+5=$

$8-3+5=$

Now we will continue with the addition and subtraction operations according to the order of appearance.

When we start reading the exercise from the beginning we come across a subtraction, therefore, we will resolve it first. We will obtain:

$5+5=10$

$5 \times 3-\frac{4}{8} \times 2-3=$

**Solution:**

There are no parentheses, so we will start with the multiplication and division operations according to their order of appearance in the exercise.

We will start with the first multiplication on the left.

**We will obtain:**

$15-\frac{4}{8} \times 2-3=$

We will continue with the next multiplication and obtain:

$15-\frac{8}{8}-3=$

We will realize that $8 \over 8$Β is $1$.

We will subtract from left to right according to the order of appearance and obtain:

$15-1-3=$

$14-3=11$

Check your understanding

Question 1

\( 0:7+1= \)

Question 2

\( 100+5-100+5 \)

Question 3

\( 12+1+0= \)

Solve:

$3-4+2+1$

We will use the substitution property to arrange the exercise a bit more comfortably, we will add parentheses to the addition operation:

$(3+2+1)-4=$

We first solve the addition, from left to right:

$3+2=5$

$5+1=6$

And finally, we subtract:

$6-4=2$

2

Solve:

$-5+4+1-3$

According to the order of operations, addition and subtraction are on the same level and, therefore, must be resolved from left to right.

However, in the exercise we can use the substitution property to make solving simpler.

-5+4+1-3

4+1-5-3

5-5-3

0-3

-3

$-3$

Solve:

$9-3+4-2$

According to the rules of the order of operations, we will solve the exercise from left to right since it only has addition and subtraction operations:

$9-3=6$

$6+4=10$

$10-2=8$

8

Solve the following exercise:

$12+3\cdot0=$

According to the order of operations, we first multiply and then add:

$12+(3\cdot0)=$

$3\times0=0$

$12+0=12$

$12$

Solve the following exercise:

$2+0:3=$

According to the order of operations rules, we first divide and then add:

$2+(0:3)=$

$0:3=0$

$2+0=2$

$2$

Related Subjects

- Order of Operations: Exponents
- Order of Operations: Roots
- Order of Operations with Parentheses
- Advanced Arithmetic Operations
- The commutative property
- The Commutative Property of Addition
- The Commutative Property of Multiplication
- The Associative Property
- The Associative Property of Addition
- The Associative Property of Multiplication
- The Distributive Property
- The Distributive Property for Seventh Graders
- The Distributive Property of Division
- The Distributive Property in the Case of Multiplication
- Subtracting Whole Numbers with Addition in Parentheses
- Division of Whole Numbers Within Parentheses Involving Division
- Subtracting Whole Numbers with Subtraction in Parentheses
- Division of Whole Numbers with Multiplication in Parentheses
- The commutative properties of addition and multiplication, and the distributive property
- Exponents and Roots - Basic
- What is a square root?
- Square Root of a Negative Number
- Exponents and Exponent rules
- Basis of a power
- The exponent of a power
- Powers