Subtraction of a sum
Sometimes we need to subtract a sum of elements from another element.
Rule:
a−(b+c)=a−b−c
- This is also true in algebraic expressions.
We can operate according to the rule: apply the subtraction sign to each of the elements included in the parentheses.
Likewise, we can act according to the order of mathematical operations starting with the parentheses - calculate the sum and only then subtract it.
For example, in the exercise:
21−(7+2)=
Option 1 - according to the rule:
We will subtract each element in the parentheses separately and it will give us:
21−7−2=12
Option 2 - according to the order of operations:
Subtraction of a difference
It is valid when we need to subtract a difference of elements from another element.
Rule:
a−(b−c)=a−b+c
We can operate according to the rule: apply the subtraction sign to each of the elements included in the parentheses and always remember that, minus times minus gives plus.
Likewise, we can act according to the order of mathematical operations starting with the parentheses - calculate the difference and only then subtract it.
For example, in the exercise:
33−(9−3)=
Option 1 - according to the rule:
We will separately subtract each element in the parentheses and it will give us:
33−9+3=
24+3=27
Option 2 - according to the order of operations:
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Division by product
It is also true when we need to divide a certain element by the product of others.
Rule:
a:(b⋅c)=a:b:c
- This is also valid in algebraic expressions.
We can operate according to the rule: apply the division to each of the elements included in the parentheses.
Likewise, we can act according to the order of mathematical operations starting with the parentheses - calculate the multiplication and only then divide by the product.
For example, in the exercise:
50:(2⋅5)
Option 1 - according to the rule:
We will divide separately for each element of the parentheses and it will give us:
50:2:5=
First, we will divide 50:2 and rewrite the exercise:
25:5=5
Option 2 - according to the order of operations:
Division by quotient
It is valid when we need to divide a certain element by the quotient of others.
Rule:
a:(b:c)=a:b⋅c
- This is also valid in algebraic expressions.
We can operate according to the rule: apply the division to the first element inside the parentheses and then apply the multiplication to the second element of the parentheses.
Likewise, we can act according to the order of mathematical operations starting with the parentheses - calculate the quotient and only then divide by it.
For example, in the exercise:
48:(6:2)=
Option 1 - according to the rule:
We will apply division to the first element inside the parentheses and then multiply by the second element of the parentheses.
48:6⋅2=
First, we will divide 48:6 and rewrite the exercise:
8⋅2=16
Option 2 - according to the order of operations:
Examples and exercises with solutions of arithmetic rules
Exercise #1
60:(10×2)=
Video Solution
Step-by-Step Solution
We write the exercise in fraction form:
10×260=
Let's separate the numerator into a multiplication exercise:
10×210×6=
We simplify the 10 in the numerator and denominator, obtaining:
26=3
Answer
Exercise #2
12:(2×2)=
Video Solution
Step-by-Step Solution
According to the order of operations, we first solve the exercise within parentheses:
2×2=4
Now we divide:
12:4=3
Answer
Exercise #3
7−(4+2)=
Video Solution
Step-by-Step Solution
According to the order of operations, we first solve the exercise within parentheses:
4+2=6
Now we solve the rest of the exercise:
7−6=1
Answer
Exercise #4
8−(2+1)=
Video Solution
Step-by-Step Solution
According to the order of operations, we first solve the exercise within parentheses:
2+1=3
Now we solve the rest of the exercise:
8−3=5
Answer
Exercise #5
13−(7+4)=
Video Solution
Step-by-Step Solution
According to the order of operations, we first solve the exercise within parentheses:
7+4=11
Now we subtract:
13−11=2
Answer
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