The Numbers 0 and 1 in Operations - Examples, Exercises and Solutions

Understanding The Numbers 0 and 1 in Operations

Complete explanation with examples

The numbers 0 0 and 1 1 have some special characteristics when performing basic operations like addition, subtraction, multiplication, and division—including combined calculations.

In this article we will learn what they are and why they are important.

Visual explanation of identity elements: Zero is shown as the additive identity with the equations a + 0 = a and a - 0 = a. One is shown as the multiplicative identity with the equations a × 1 = a and a ÷ 1 = a

Detailed explanation

Practice The Numbers 0 and 1 in Operations

Test your knowledge with 19 quizzes

\( \frac{25+25}{10}= \)

Examples with solutions for The Numbers 0 and 1 in Operations

Step-by-step solutions included
Exercise #1

(5×410×2)×(35)= (5\times4-10\times2)\times(3-5)=

Step-by-Step Solution

This simple rule is the order of operations which states that multiplication precedes addition and subtraction, and division precedes all of them,

In the given example, a multiplication occurs between two sets of parentheses, thus we simplify the expressions within each pair of parentheses separately,

We start with simplifying the expression within the parentheses on the left, this is done in accordance with the order of operations mentioned above, meaning that multiplication comes before subtraction, we perform the multiplications in this expression first and then proceed with the subtraction operations within it, in reverse we simplify the expression within the parentheses on the right and perform the subtraction operation within them:

What remains for us is to perform the last multiplication that was deferred, it is the multiplication that occurred between the expressions within the parentheses in the original expression, we perform it while remembering that multiplying any number by 0 will result in 0:

Therefore, the correct answer is answer d.

Answer:

0 0

Video Solution
Exercise #2

8×(5×1)= 8\times(5\times1)=

Step-by-Step Solution

According to the order of operations, we first solve the expression in parentheses:

5×1=5 5\times1=5

Now we multiply:

8×5=40 8\times5=40

Answer:

40

Video Solution
Exercise #3

7×1+12= ? 7\times1+\frac{1}{2}=\text{ ?}

Step-by-Step Solution

According to the order of operations, we first place the multiplication operation inside parenthesis:

(7×1)+12= (7\times1)+\frac{1}{2}=

Then, we perform this operation:

7×1=7 7\times1=7

Finally, we are left with the answer:

7+12=712 7+\frac{1}{2}=7\frac{1}{2}

Answer:

712 7\frac{1}{2}

Video Solution
Exercise #4

63×1= ? \frac{6}{3}\times1=\text{ ?}

Step-by-Step Solution

According to the order of operations, we will solve the exercise from left to right since it only contains multiplication and division operations:

63=2 \frac{6}{3}=2

2×1=2 2\times1=2

Answer:

2 2

Video Solution
Exercise #5

12+3×0= 12+3\times0=

Step-by-Step Solution

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

3×0=0 3\times0=0

12+0=12 12+0=12

Answer:

12

Video Solution

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