A fifth grade math class on operating priorities is always beneficial.

This course on operating priorities involves the following concepts:

– definition of the 4 operations;

– vocabulary: sum, difference, product, quotient, terms, factors

– addition, subtraction, multiplication and division priorities;

– calculations containing parentheses and nested parentheses.

The student will need to know the vocabulary of the four operations as well as the rules of priority to perform calculations of numerical expressions. Operating priorities are an essential concept for performing online calculations. We will end this chapter with more complex calculations mixing operative priorities and nested parentheses as well as problem solving in the fifth grade.

## I. Vocabulary of the 4 operations

Definition:

The result of

• theaddition is called a sum and the elements that form it are called terms;
• the subtraction is called the difference and the elements that form it are called the terms;
• The multiplication is called the product and the elements that form it are called the factors;
• the division is called the quotient.

Example:

7+8=15 with 7 and 8 being terms and 15 being the sum.

12-5=7 with 12 and 5 being terms and 7 being the difference.

8×9=72 with 8 and 9 being factors and 72 being the product.

75:5=15 with 15 being the quotient.

## II. Operating priorities

Ownership:

Addition and subtraction have the same priority power.

Examples:

A=33+7+5+15

A=40+5+15

A=45+15

A=60

B=420

Ownership:

If a numerical expression contains only addition and/or subtraction, the calculations are performed in the direction of reading.

Examples:

A = 35 – 4 + 7

A = 31 + 7

A = 38

B = 15 + 3 – 12 -4

B = 18 – 12 – 4

B = 6 – 4

B = 2

### 3. multiplication and division

Ownership:

Multiplication and division have the same power of priority.

If a numerical expression contains only multiplication and/or division,

Examples:

A = 72

B = 2

### 4. The 4 operations and the operating priorities

Ownership:

If a numerical expression contains all four operations, we start with multiplication and division (the first one coming in the direction of reading) and end with addition and subtraction.

A = 5

Remark:

If, at a given moment, there are only additions and subtractions or multiplications and divisions left, we apply the rules seen previously.

### 5. Expressions containing parentheses and priorities

Ownership:

The brackets have priority over the four operations.

We start the calculations with the brackets and then apply the previous priority rules.

Examples:

A = 9 x(4+1)

A = 9 x 5

A = 45

B = 12 + [ 36 – ( 5 + 2×3)]

B = 12 +[ 36 –(5 + 6)]

B = 12 + ( 36 – 11)

B = 12 + 25

B = 37

## 6. With fractional lines

Ownership:

When a numerical expression contains fractions, the numerator and denominator can be replaced by parentheses.

Examples:

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