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.

Suggested Topics to Practice in Advance

  1. The Order of Basic Operations: Addition, Subtraction, and Multiplication
  2. Order of Operations: Exponents
  3. Order of Operations: Roots
  4. Order of Operations with Parentheses

Practice The Numbers 0 and 1 in Operations

Examples with solutions for The Numbers 0 and 1 in Operations

Exercise #1

8×(5×1)= 8\times(5\times1)=

Video Solution

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

Exercise #2

7×1+12= 7\times1+\frac{1}{2}=

Video Solution

Step-by-Step Solution

According to the order of operations rules, we first insert the multiplication exercise into parentheses:

(7×1)+12= (7\times1)+\frac{1}{2}=

Let's solve the exercise inside the parentheses:

7×1=7 7\times1=7

And now we get the exercise:

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

Answer

712 7\frac{1}{2}

Exercise #3

63×1= \frac{6}{3}\times1=

Video Solution

Step-by-Step Solution

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

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

2×1=2 2\times1=2

Answer

2 2

Exercise #4

Solve the following exercise:

12+30= 12+3\cdot0=

Step-by-Step Solution

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

12+(30)= 12+(3\cdot0)=

3×0=0 3\times0=0

12+0=12 12+0=12

Answer

12 12

Exercise #5

Solve the following exercise:

2+0:3= 2+0:3=

Step-by-Step Solution

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

2+(0:3)= 2+(0:3)=

0:3=0 0:3=0

2+0=2 2+0=2

Answer

2 2

Exercise #6

25+2510= \frac{25+25}{10}=

Video Solution

Step-by-Step Solution

Let's begin by multiplying the numerator:

25+25=50 25+25=50

We obtain the following fraction:

5010 \frac{50}{10}

Finally let's reduce the numerator and denominator by 10 and we are left with the following result:

51=5 \frac{5}{1}=5

Answer

5 5

Exercise #7

0:7+1= 0:7+1=

Video Solution

Step-by-Step Solution

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

0:7=0 0:7=0

0+1=1 0+1=1

Answer

1 1

Exercise #8

12+1+0= 12+1+0=

Video Solution

Step-by-Step Solution

According to the order of operations rules, since the exercise only involves addition operations, we will solve the problem from left to right:

12+1=13 12+1=13

13+0=13 13+0=13

Answer

13

Exercise #9

0+0.2+0.6= 0+0.2+0.6=

Video Solution

Step-by-Step Solution

According to the order of operations rules, since the exercise only involves addition operations, we will solve the problem from left to right:

0+0.2=0.2 0+0.2=0.2

0.2+0.6=0.8 0.2+0.6=0.8

Answer

0.8

Exercise #10

12+0+12= \frac{1}{2}+0+\frac{1}{2}=

Video Solution

Step-by-Step Solution

According to the order of operations, since the exercise only involves addition operations, we will solve the problem from left to right:

12+0=12 \frac{1}{2}+0=\frac{1}{2}

12+12=11=1 \frac{1}{2}+\frac{1}{2}=\frac{1}{1}=1

Answer

1 1

Exercise #11

90+0.5= 9-0+0.5=

Video Solution

Step-by-Step Solution

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

90=9 9-0=9

9+0.5=9.5 9+0.5=9.5

Answer

9.5

Exercise #12

19+10= 19+1-0=

Video Solution

Step-by-Step Solution

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

19+1=20 19+1=20

200=20 20-0=20

Answer

20 20

Exercise #13

2+0:3= 2+0:3=

Video Solution

Step-by-Step Solution

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

0:3=0 0:3=0

2+0=2 2+0=2

Answer

2 2

Exercise #14

12+3×0= 12+3\times0=

Video Solution

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

Exercise #15

1×12:2 1\times\frac{1}{2}:2

Video Solution

Step-by-Step Solution

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

1×12=12 1\times\frac{1}{2}=\frac{1}{2}

12:2=14 \frac{1}{2}:2=\frac{1}{4}

Answer

1/4

Topics learned in later sections

  1. Division and Fraction Bars (Vinculum)
  2. Neutral Element (Identiy Element)
  3. Multiplicative Inverse
  4. The Order of Operations
  5. Order or Hierarchy of Operations with Fractions