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# Lesson 7 Homework Practice Divide Decimals By Whole Numbers

## Lesson 7 Homework Practice Divide Decimals By Whole Numbers

In this lesson, you will learn how to divide decimals by whole numbers using different methods. You will also practice solving some problems that involve dividing decimals by whole numbers.

## What are decimals and whole numbers?

A decimal is a number that has a decimal point and one or more digits after the decimal point. For example, 0.42, 3.14, and 6.8 are decimals. A whole number is a number that does not have a decimal point or any digits after the decimal point. For example, 0, 1, 2, and 10 are whole numbers.

## How to divide decimals by whole numbers?

There are different methods to divide decimals by whole numbers. Here are some of them:

• Method 1: Use place value

To use this method, you need to know the place value of each digit in a decimal number. The place value of a digit tells you how much it is worth based on its position in the number. For example, in the number 0.42, the digit 4 is in the tenths place and it is worth 0.4 or 4/10, and the digit 2 is in the hundredths place and it is worth 0.02 or 2/100.

To divide a decimal by a whole number using place value, you need to do the following steps:

• Write the decimal number as a fraction with a denominator of 10, 100, or 1000 depending on how many digits are after the decimal point. For example, 0.42 can be written as 42/100.

• Divide the numerator and the denominator of the fraction by the whole number. For example, to divide 0.42 by 3, you can divide both 42 and 100 by 3 and get (42/3)/(100/3) = 14/33.

• Write the quotient as a decimal by putting a decimal point in the same place as in the original decimal number. For example, since 0.42 has two digits after the decimal point, you need to put a decimal point after the second digit in 14/33 and get 0.14.

Here is an example of using this method:

Divide 0.36 by 4 using place value.

• Write 0.36 as a fraction with a denominator of 100: 36/100.

• Divide both 36 and 100 by 4: (36/4)/(100/4) = 9/25.

• Write the quotient as a decimal by putting a decimal point after the second digit: 0.09.

• Method 2: Use long division

To use this method, you need to know how to do long division with whole numbers. Long division is a process of dividing a large number by a smaller number using repeated subtraction and multiplication.

To divide a decimal by a whole number using long division, you need to do the following steps:

• Move the decimal point in the dividend (the number being divided) to the right until it becomes a whole number. For example, to divide 0.36 by 4, you need to move the decimal point in 0.36 two places to the right and get 36.

• Move the decimal point in the divisor (the number that divides) the same number of places as in the dividend. For example, since you moved the decimal point in 0.36 two places to the right, you need to move the decimal point in 4 two places to the right and get 400.

• Do long division with the new numbers as if they were whole numbers. For example, to divide 36 by 400, you can use this long division symbol: ``` ____ 400)36 ```

• Bring down the decimal point in the quotient (the answer) to the same place as in the original dividend. For example, since the decimal point in 0.36 was after the second digit, you need to put the decimal point in the quotient after the second digit: ``` 0.09 ____ 400)36 ```

Here is another example of using this method:

Divide 1.2 by 3 using long division.

• Move the decimal point in 1.2 one place to the right and get 12.

• Move the decimal point in 3 one place to the right and get 30.

• Do long division with 12 and 30: ``` 0.4 ____ 30)12 -0 --- 120 -120 ---- 0 ```

• Bring down the decimal point in the quotient to the same place as in 1.2: ``` 0.4 ____ 30)1.2 -0 --- 120 -120 ---- 0 ```

• Method 3: Use a number line

To use this method, you need to know how to use a number line to represent decimals and fractions. A number line is a line that has numbers marked on it at equal intervals. You can use a number line to show how a decimal or a fraction is divided into equal parts.

To divide a decimal by a whole number using a number line, you need to do the following steps:

• Draw a number line and mark the decimal number on it. For example, to divide 0.42 by 3, you can draw a number line from 0 to 0.5 and mark 0.42 on it.

• Divide the number line into equal parts according to the whole number. For example, since you are dividing by 3, you need to divide the number line into three equal parts.

• Find the length of each part by subtracting the endpoints of each part. For example, to find the length of one part, you can subtract 0 from 0.14 and get 0.14.

• Write the quotient as a decimal by using the length of one part as the answer. For example, since one part is 0.14, the quotient is 0.14.

Here is an example of using this method:

Divide 0.42 by 3 using a number line.

``` ------------ ------------ ^ ^ ^ ^ ^ 0 .14 .28 .42 .5 ```

• Draw a number line from 0 to 0.5 and mark 0.42 on it.

• Divide the number line into three equal parts.

• Find the length of one part by subtracting 0 from 0.14 and get 0.14.

• Write the quotient as a decimal by using 0.14 as the answer.

## Practice problems

Now that you have learned how to divide decimals by whole numbers using different methods, you can practice solving some problems that involve dividing decimals by whole numbers. You can use any method that you prefer, but make sure to show your work and explain your reasoning.

• Divide 1.8 by 6 using place value.

Solution:

• Write 1.8 as a fraction with a denominator of 10: 18/10.

• Divide both 18 and 10 by 6 and get (18/6)/(10/6) = 3/5.

• Write the quotient as a decimal by putting a decimal point after the first digit: 0.6.

• Divide 0.75 by 5 using long division.

Solution:

• Move the decimal point in 0.75 two places to the right and get 75.

• Move the decimal point in 5 two places to the right and get 500.

• Do long division with 75 and 500: ``` 0.15 ____ 500)75 -50 --- 250 -250 ---- 0 ```

• Bring down the decimal point in the quotient to the same place as in 0.75: ``` 0.15 ____ 500)0.75 -50 --- 250 -250 ---- 0 ```

• Divide 0.9 by 3 using a number line.

Solution:

• Draw a number line and mark 0.9 on it. You can also mark some other numbers to help you divide the number line into equal parts.

• ``` ------------ ------------ ^ ^ ^ ^ ^ 0 .3 .6 .9 1 ``` Divide the number line into three equal parts.

• ``` ------------ / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / -/--/--/- ^ ^ ^ ^ ^ 0 .3 .6 .9 1 ``` Find the length of one part by subtracting the endpoints of each part. For example, to find the length of one part, you can subtract 0 from 0.3 and get 0.3.

• Write the quotient as a decimal by using the length of one part as the answer. For example, since one part is 0.3, the quotient is 0.3.