Course: 7.9整数除以分数的除法

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整数除以分数的除法
Vanessa is making a game. She has a 40 inch long roll of paper and wants to divide this piece of paper into $\begin{aligned} \frac{1}{2} \end{aligned}$ inch strips. How many strips of paper can Vanessa make?
::Vanessa在玩游戏,她有40英寸长的纸卷想把这张纸分割成12英寸长的条纹

In this concept, you will learn how to divide a whole number by a fraction.
::在这个概念中,你将学会如何将一个整数除以一个小数。

Dividing Whole Numbers by Fractions
::按分数排列的整数

Sometimes you will need to divide a whole number by a fraction. Here is an example.
::有时您需要将整个数字除以一个分数。这里举一个例子。

$\begin{aligned} 1 \div \frac{1}{2} = \underline{} \end{aligned}$

At first glance, you might think that the answer would be one-half. This problem is not asking for $\begin{aligned} \frac{1}{2} \end{aligned}$ of 1. It is asking for how many $\begin{aligned} \frac{1}{2} \end{aligned}$ s are in 1. Here is a diagram of 1 whole.
::乍一看,你可能会认为答案是半分之一。这个问题不是要1分的12秒,而是要1分的12秒。这是1分的图。

Divide the whole into $\begin{aligned} \frac{1}{2} \end{aligned}$ s.
::将整块除以12秒。

There are 2 one-half sections. The answer is 2.
::有2个半部分,答案是2个部分

You learned that when you divide a fraction by a whole number, you instead multiply by the reciprocal of the divisor . The same applies to dividing a whole number by a fraction. Change the operation to multiplication and change the divisor to its reciprocal.
::您知道, 当将一个分数除以整数时, 您反之会乘以差数的对等数。这同样适用于将整数除以一个分数。将操作改为乘法, 并将差数改为对等数。

Here is the division problem again.
::这里又是分裂问题。

$\begin{aligned} 1 \div \frac{1}{2} = \end{aligned}$

First, change the operation to multiplication and $\begin{aligned} \frac{1}{2} \end{aligned}$ to its reciprocal.
::首先,将作业改为乘法,将乘法改为乘法,将乘法改为乘法,将乘法改为乘法。

$\begin{aligned} 1 \div \frac{1}{2} = 1 \times \frac{2}{1} \end{aligned}$

Then, multiply. Remember that any whole number can be written as a fraction, $\begin{aligned} n = \frac{n}{1} \end{aligned}$ . In this example, the identity property of multiplication states that a number multiplied by 1 will be the number itself. $\begin{aligned} \frac{2}{1} \end{aligned}$ is also equal to 2.
::然后,乘。记住, 任何整数都可以以分数, n = n 1 的形式写成。在此示例中, 乘法的身份属性表示, 乘数乘以 1 是数字本身。 2 1 也等于 2 。

$\begin{aligned} 1 \times \frac{2}{1} = 1 \times 2 = 2 \end{aligned}$

The answer is the same as when you used the pictures.
::答案与使用图片时相同。

Examples
::实例

Example 1
::例1

Earlier, you were given a problem about Vanessa and her game.
::早些时候,你得到一个问题关于Vanessa和她的游戏。

Vanessa wants to cut $\begin{aligned} \frac{1}{2} \end{aligned}$ inch strips of paper from a roll of paper that is 40 inches long. Divide 40 by $\begin{aligned} \frac{1}{2} \end{aligned}$ to find the total number of strips of paper she can make.
::Vanessa想从一张40英寸长的纸上剪掉12英寸长的纸条

First, write a division problem.
::首先,写一个分裂问题。

$\begin{aligned} 40 \div \frac{1}{2} = \underline{} \end{aligned}$

Then, change this into a multiplication problem. Multiply by the reciprocal of the divisor.
::然后,把它变成一个乘法问题。乘以断层的对等。

$\begin{aligned} 40 \div \frac{1}{2} = 40 \times \frac{2}{1} strips of paper \end{aligned}$

Next, multiply the fractions. Remember that $\begin{aligned} \frac{2}{1} \end{aligned}$ is also equal to 2.
::下一步, 乘以分数。记住 2 1 也等于 2 。

$\begin{aligned} 40 \times \frac{2}{1} = 40 \times 2 = 80 \end{aligned}$

Vanessa can make 80 strips from a 40 inch long roll of paper.
::Vanessa可以从40英寸长的纸上做80条条

Example 2
::例2

Divide by fraction.
::除以分数。

$\begin{aligned} 25 \div \frac{2}{5} = \underline{} \end{aligned}$

First, change the operation to multiplication and $\begin{aligned} \frac{2}{5} \end{aligned}$ to its reciprocal.
::首先,将作业改为乘法,将2-5改为对等。

$\begin{aligned} 25 \div \frac{2}{5} = 25 \times \frac{5}{2} \end{aligned}$

Then, multiply. Remember that 25 can also be written as $\begin{aligned} \frac{25}{1} \end{aligned}$ .
::那么,乘数。记住25也可以写为25 1。

$\begin{aligned} \frac{25}{1} \times \frac{5}{2} = \frac{125}{2} \end{aligned}$

Next, simplify the fraction. Convert the improper fraction to a mixed number .
::接下来,简化分数。将不适当的分数转换成混合数。

$\begin{aligned} \frac{125}{2} = 62 \frac{1}{2} \end{aligned}$

The answer is $\begin{aligned} 62 \frac{1}{2} \end{aligned}$ .
::答案是6212

Example 3
::例3

Divide by fraction: $\begin{aligned} 4 \div \frac{1}{2} = \underline{} \end{aligned}$ .
::分数除以: 4+1 2 = _ 。

First, change the expression. Multiply by the inverse of the divisor.
::首先,更改表达式。乘以 divisor 的反面。

$\begin{aligned} 4 \div \frac{1}{2} = 4 \times \frac{2}{1} \end{aligned}$

Then, multiply.
::然后,乘数。

$\begin{aligned} 4 \times 2 = 8 \end{aligned}$

The answer is 8.
::答案是8岁

Example 4
::例4

Divide by fraction: $\begin{aligned} 6 \div \frac{1}{3} = \underline{} \end{aligned}$ .
::分数除以: 6 1 3 = _ 。

First, change the expression. Multiply by the inverse of the divisor.
::首先,更改表达式。乘以 divisor 的反面。

$\begin{aligned} 6 \div \frac{1}{3} = 6 \times \frac{3}{1} \end{aligned}$

Then, multiply.
::然后,乘数。

$\begin{aligned} 6 \times 3 = 18 \end{aligned}$

The answer is 18.
::答案是18岁

Example 5
::例5

Divide by fraction: $\begin{aligned} 12 \div \frac{3}{4} = \underline{} \end{aligned}$ .
::分数除以: 12 3 4 = _。

First, change the expression. Multiply by the inverse of the divisor.
::首先,更改表达式。乘以 divisor 的反面。

$\begin{aligned} 12 \div \frac{3}{4} = 12 \times \frac{4}{3} \end{aligned}$

Then, multiply.
::然后,乘数。

$\begin{aligned} 12 \times \frac{4}{3} = \frac{12^{4}}{1} \times \frac{4}{3^{1}} = 16 \end{aligned}$

The answer is 16.

::答案是16岁

Review
::回顾

Divide the following whole numbers and fractions.
::将以下数字和分数除以。

$\begin{aligned} 8 \div \frac{1}{3} = \underline{} \end{aligned}$

$\begin{aligned} 18 \div \frac{1}{2} = \underline{} \end{aligned}$

$\begin{aligned} 28 \div \frac{1}{4} = \underline{} \end{aligned}$

$\begin{aligned} 14 \div \frac{1}{7} = \underline{} \end{aligned}$

$\begin{aligned} 16 \div \frac{2}{3} = \underline{} \end{aligned}$

$\begin{aligned} 22 \div \frac{1}{2} = \underline{} \end{aligned}$

$\begin{aligned} 24 \div \frac{2}{5} = \underline{} \end{aligned}$

$\begin{aligned} 36 \div \frac{2}{3} = \underline{} \end{aligned}$

$\begin{aligned} 40 \div \frac{3}{10} = \underline{} \end{aligned}$

$\begin{aligned} 60 \div \frac{1}{3} = \underline{} \end{aligned}$

$\begin{aligned} 12 \div \frac{3}{4} = \underline{} \end{aligned}$

$\begin{aligned} 48 \div \frac{2}{12} = \underline{} \end{aligned}$

$\begin{aligned} 18 \div \frac{1}{6} = \underline{} \end{aligned}$

$\begin{aligned} 30 \div \frac{2}{5} = \underline{} \end{aligned}$

$\begin{aligned} 45 \div \frac{5}{9} = \underline{} \end{aligned}$

Review (Answers)
::回顾(答复)

Click to see the answer key or go to the Table of Contents and click on the Answer Key under the 'Other Versions' option.
::单击可查看答题键, 或转到目录中, 单击“ 其他版本” 选项下的答题键。

Resources
::资源

Section outline

General

整数除以分数的除法

Dividing Whole Numbers by Fractions ::按分数排列的整数

Examples ::实例

Example 1 ::例1

Example 2 ::例2

Example 3 ::例3

Example 4 ::例4

Example 5 ::例5

Review ::回顾

Review (Answers) ::回顾(答复)

Resources ::资源

Dividing Whole Numbers by Fractions
::按分数排列的整数

Examples
::实例

Example 1
::例1

Example 2
::例2

Example 3
::例3

Example 4
::例4

Example 5
::例5

Review
::回顾

Review (Answers)
::回顾(答复)

Resources
::资源