Complete The Equation Using Unit Form And Whole Numbers. Write The Quotient In Decimal Form.$\[ 1.3 \div 0.2 = \\]$\[\qquad \text{tenths} \div \qquad \text{tenths} = \\]$\[\qquad \\]$\[\qquad \\]$\[ =

by ADMIN 201 views

Introduction

Division is a fundamental operation in mathematics that involves sharing a certain quantity into equal parts or groups. In this article, we will focus on solving division equations that involve unit form and whole numbers. We will explore how to complete the equation using unit form and whole numbers, and then write the quotient in decimal form.

Understanding Unit Form and Whole Numbers

Before we dive into solving the division equation, let's first understand what unit form and whole numbers are.

  • Unit form: Unit form refers to the way we represent numbers in terms of their place value. For example, the number 12 can be written as 10 + 2, where 10 is the tens place and 2 is the ones place. In unit form, we can represent numbers as a sum of their place values.
  • Whole numbers: Whole numbers are positive integers that do not have any fractional part. Examples of whole numbers include 1, 2, 3, 4, and so on.

Solving the Division Equation

Now that we have a basic understanding of unit form and whole numbers, let's solve the division equation.

{ 1.3 \div 0.2 = \}

To solve this equation, we need to divide 1.3 by 0.2. We can start by converting the decimal numbers to their unit form.

1.3=1+0.3{ 1.3 = 1 + 0.3 }

0.2=0+0.2{ 0.2 = 0 + 0.2 }

Now, we can rewrite the division equation as:

{ (1 + 0.3) \div (0 + 0.2) = \}

To divide the numbers, we can use the following rule:

(a+b)÷(c+d)=(a+b)(c+d){ (a + b) \div (c + d) = \frac{(a + b)}{(c + d)} }

Applying this rule to our equation, we get:

(1+0.3)(0+0.2)=1.30.2{ \frac{(1 + 0.3)}{(0 + 0.2)} = \frac{1.3}{0.2} }

Now, we can simplify the fraction by dividing the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 1.3 and 0.2 is 0.1.

1.30.2=132{ \frac{1.3}{0.2} = \frac{13}{2} }

Therefore, the quotient of 1.3 divided by 0.2 is 6.5.

Writing the Quotient in Decimal Form

Now that we have found the quotient, we need to write it in decimal form. To do this, we can simply divide the numerator and denominator by their GCD.

132=6.5{ \frac{13}{2} = 6.5 }

Therefore, the quotient of 1.3 divided by 0.2 is 6.5.

Conclusion

In this article, we have learned how to solve division equations that involve unit form and whole numbers. We have seen how to convert decimal numbers to their unit form, and then use the rule for dividing numbers to find the quotient. We have also learned how to write the quotient in decimal form by dividing the numerator and denominator by their GCD. With practice and patience, you can become proficient in solving division equations with unit form and whole numbers.

Example Problems

Here are some example problems to help you practice solving division equations with unit form and whole numbers.

Example 1

{ 2.5 \div 0.5 = \}

To solve this equation, we can convert the decimal numbers to their unit form.

2.5=2+0.5{ 2.5 = 2 + 0.5 }

0.5=0+0.5{ 0.5 = 0 + 0.5 }

Now, we can rewrite the division equation as:

{ (2 + 0.5) \div (0 + 0.5) = \}

Applying the rule for dividing numbers, we get:

(2+0.5)(0+0.5)=2.50.5{ \frac{(2 + 0.5)}{(0 + 0.5)} = \frac{2.5}{0.5} }

Simplifying the fraction, we get:

2.50.5=5{ \frac{2.5}{0.5} = 5 }

Therefore, the quotient of 2.5 divided by 0.5 is 5.

Example 2

{ 3.8 \div 0.8 = \}

To solve this equation, we can convert the decimal numbers to their unit form.

3.8=3+0.8{ 3.8 = 3 + 0.8 }

0.8=0+0.8{ 0.8 = 0 + 0.8 }

Now, we can rewrite the division equation as:

{ (3 + 0.8) \div (0 + 0.8) = \}

Applying the rule for dividing numbers, we get:

(3+0.8)(0+0.8)=3.80.8{ \frac{(3 + 0.8)}{(0 + 0.8)} = \frac{3.8}{0.8} }

Simplifying the fraction, we get:

3.80.8=4.75{ \frac{3.8}{0.8} = 4.75 }

Therefore, the quotient of 3.8 divided by 0.8 is 4.75.

Example 3

{ 4.2 \div 0.2 = \}

To solve this equation, we can convert the decimal numbers to their unit form.

4.2=4+0.2{ 4.2 = 4 + 0.2 }

0.2=0+0.2{ 0.2 = 0 + 0.2 }

Now, we can rewrite the division equation as:

{ (4 + 0.2) \div (0 + 0.2) = \}

Applying the rule for dividing numbers, we get:

(4+0.2)(0+0.2)=4.20.2{ \frac{(4 + 0.2)}{(0 + 0.2)} = \frac{4.2}{0.2} }

Simplifying the fraction, we get:

4.20.2=21{ \frac{4.2}{0.2} = 21 }

Therefore, the quotient of 4.2 divided by 0.2 is 21.

Practice Problems

Here are some practice problems to help you reinforce your understanding of solving division equations with unit form and whole numbers.

Problem 1

{ 5.6 \div 0.6 = \}

Problem 2

{ 7.3 \div 0.3 = \}

Problem 3

{ 9.1 \div 0.1 = \}

Answer Key

Here is the answer key for the practice problems.

Problem 1

5.6÷0.6=9.33{ 5.6 \div 0.6 = 9.33 }

Problem 2

7.3÷0.3=23.67{ 7.3 \div 0.3 = 23.67 }

Problem 3

9.1÷0.1=91{ 9.1 \div 0.1 = 91 }

Conclusion

Q: What is unit form in mathematics?

A: Unit form refers to the way we represent numbers in terms of their place value. For example, the number 12 can be written as 10 + 2, where 10 is the tens place and 2 is the ones place.

Q: What are whole numbers?

A: Whole numbers are positive integers that do not have any fractional part. Examples of whole numbers include 1, 2, 3, 4, and so on.

Q: How do I convert decimal numbers to their unit form?

A: To convert a decimal number to its unit form, you can break it down into its place values. For example, the decimal number 2.5 can be written as 2 + 0.5, where 2 is the ones place and 0.5 is the tenths place.

Q: What is the rule for dividing numbers?

A: The rule for dividing numbers is:

(a+b)÷(c+d)=(a+b)(c+d){ (a + b) \div (c + d) = \frac{(a + b)}{(c + d)} }

Q: How do I simplify a fraction?

A: To simplify a fraction, you can divide the numerator and denominator by their greatest common divisor (GCD). For example, the fraction 6/2 can be simplified by dividing both numbers by 2, resulting in 3/1.

Q: What is the greatest common divisor (GCD)?

A: The greatest common divisor (GCD) of two numbers is the largest number that divides both numbers without leaving a remainder. For example, the GCD of 6 and 2 is 2.

Q: How do I write a quotient in decimal form?

A: To write a quotient in decimal form, you can simply divide the numerator and denominator by their GCD. For example, the quotient 6/2 can be written in decimal form as 3.0.

Q: What are some common mistakes to avoid when solving division equations with unit form and whole numbers?

A: Some common mistakes to avoid when solving division equations with unit form and whole numbers include:

  • Not converting decimal numbers to their unit form
  • Not using the rule for dividing numbers
  • Not simplifying fractions
  • Not writing quotients in decimal form

Q: How can I practice solving division equations with unit form and whole numbers?

A: You can practice solving division equations with unit form and whole numbers by working through example problems and practice exercises. You can also try creating your own problems to challenge yourself.

Q: What are some real-world applications of solving division equations with unit form and whole numbers?

A: Solving division equations with unit form and whole numbers has many real-world applications, including:

  • Calculating discounts and sales tax
  • Determining the cost of goods and services
  • Calculating interest rates and investment returns
  • Solving problems in science, technology, engineering, and mathematics (STEM) fields

Conclusion

In this article, we have answered some frequently asked questions about solving division equations with unit form and whole numbers. We have covered topics such as unit form, whole numbers, converting decimal numbers to their unit form, the rule for dividing numbers, simplifying fractions, and writing quotients in decimal form. We have also discussed common mistakes to avoid and provided tips for practicing and applying solving division equations with unit form and whole numbers in real-world scenarios.