Section: 混合数商 | 7.12混合数商

Section outline

Keith loves snakes. Last summer, he found a $\begin{aligned} 2 \frac{1}{4} \end{aligned}$ foot garter snake in his backyard. Keith read that the average anaconda is between 12 and 18 feet long. In the book, there was a picture of a $\begin{aligned} 13 \frac{1}{2} \end{aligned}$ feet long anaconda. How many garter snakes would it take to equal that anaconda?
::Keith喜欢蛇。去年夏天,他在后院发现了一条24英尺长的吊带蛇。 Keith读到,平均的Anaconda在12至18英尺之间。在这本书中,有一张长1312英尺长的Anaconda的照片。需要多少条吊带蛇才能等同那条吊带蛇?

In this concept, you will learn how to divide mixed numbers.
::在这个概念中,你们将学会如何分化混合数字。

Dividing Mixed Numbers
::混合数字

You can divide a mixed number by another mixed number. This means that you are looking for how many groups and parts of groups can be made from another whole and part. This seems complicated, but if you follow a few simple steps, you can figure it out.
::您可以将混合数字除以另一个混合数字。这意味着您正在寻找从另一个整体和部分中可以组成多少组和组的一部分。这似乎很复杂, 但如果您遵循几个简单的步骤, 您可以找到答案。

These are the rules for dividing a mixed number by a fraction.
::这些是混合数除以分数的规则。

Convert the mixed number to an improper fraction .
::将混合数字转换成不适当的部分。

Change the division to its inverse, multiplication, and multiply by the reciprocal of the divisor .
::将除法改变为反向、倍增和乘以断层的对等。

Multiply and simplify to find the quotient .
::乘以和简化以找到商数。

Here is a division problem.
::这是一个分裂问题。

$\begin{aligned} 3 \frac{1}{2} \div 1 \frac{1}{4} = \underline{} \end{aligned}$

The first step to dividing a mixed number by another mixed number is to convert both mixed numbers to improper fractions.
::将混合数除以另一个混合数的第一步是将混合数转换为不适当的分数。

$\begin{aligned} 3 \frac{1}{2} & = \frac{7}{2} \\ 1 \frac{1}{4} & = \frac{5}{4} \end{aligned}$

Next, rewrite the problem with the improper fractions.
::接下来,重写问题与不适当的分数。

$\begin{aligned} \frac{7}{2} \div \frac{5}{4} = \underline{} \end{aligned}$

Then, change the operation to multiplication and multiply by the reciprocal.
::然后,将操作改为乘以乘以乘以乘以对等。

$\begin{aligned} \frac{7}{2} \div \frac{5}{4} = \frac{7}{2} \times \frac{4}{5} \end{aligned}$

Next, multiply the fractions and simplify the answer.
::下一步,乘以分数并简化答案。

$\begin{aligned} \frac{7 \times 4}{2 \times 5} = \frac{28}{10} = 2 \frac{8^{4}}{10^{5}} = 2 \frac{4}{5} \end{aligned}$

The quotient is $\begin{aligned} 2 \frac{4}{5} \end{aligned}$ . Therefore, $\begin{aligned} 1 \frac{1}{4} \end{aligned}$ can divide into $\begin{aligned} 3 \frac{1}{2} \end{aligned}$ a total of $\begin{aligned} 2 \frac{4}{5} \end{aligned}$ times.
::商数是2 4 5 。因此, 1 14 可以分为3 1 2, 总共2 4 5 次。

Examples
::实例

Example 1
::例1

Earlier, you were given a problem about Keith and the garter snake.
::早些时候,你被问及基思和吊带蛇的问题

Keith wrote a division problem to find out how many $\begin{aligned} 2 \frac{1}{4} \end{aligned}$ feet long garter snakes would equal the length of a $\begin{aligned} 13 \frac{1}{2} \end{aligned}$ feet long anaconda. Divide the length of the anaconda by the length of the garter snake.
::Keith写了个分裂问题,以了解有多少长2,14英尺长的吊带蛇将等于长13,12英尺长的Anaconda。将Anaconda的长度除以吊带蛇的长度。

$\begin{aligned} 13 \frac{1}{2} \div 2 \frac{1}{4} & = \underline{} \end{aligned}$

First, convert both mixed numbers to improper fractions.
::首先,将两个混合数字转换为不适当的分数。

$\begin{aligned} 13 \frac{1}{2} \div 2 \frac{1}{4} = \frac{27}{2} \div \frac{9}{4} \end{aligned}$

Then, change the operation to multiplication and multiply by th reciprocal.
::然后,将操作改为乘以乘以乘以乘以乘以乘以乘以乘以乘以乘以乘以乘以乘以乘以乘以乘以。

$\begin{aligned} \frac{27}{2} \div \frac{9}{4} = \frac{27}{2} \times \frac{4}{9} \end{aligned}$

Next, multiply the fractions and simplify the answer. You can cross simplify before multiplying the fractions.
::下一步,乘以分数并简化答案。您可以在乘以分数之前交叉简化。

$\begin{aligned} \frac{27^{3}}{2^{1}} \times \frac{4^{2}}{9^{1}} = \frac{3 \times 2}{1 \times 1} = \frac{6}{1} = 6 \end{aligned}$

It would take 6 garter snakes to equal the length of the one anaconda in Keith's book.
::需要6条吊带蛇才能和基思的书里那条Anaconda一样长

Example 2
::例2

Divide the mixed number: $\begin{aligned} 12 \frac{1}{2} \div 2 \frac{1}{3} = \underline{} \end{aligned}$ . Answer in simplest form .
::除以混合数字: 12 1 2 + 2 1 3 = _。回答最简单。

First, convert both mixed numbers to improper fractions.
::首先,将两个混合数字转换为不适当的分数。

$\begin{aligned} 12 \frac{1}{2} = \frac{25}{2} \\ 2 \frac{1}{3} = \frac{7}{3} \end{aligned}$

Rewrite the problem with the improper fractions.
::用不适当的分数重写问题。

$\begin{aligned} \frac{25}{2} \div \frac{7}{3} = \underline{} \end{aligned}$

Then, change the operation to multiplication and multiply by the reciprocal.
::然后,将操作改为乘以乘以乘以乘以对等。

$\begin{aligned} \frac{25}{2} \div \frac{7}{3} = \frac{25}{2} \times \frac{3}{7} \end{aligned}$

Next, multiply the fractions and simplify the answer.
::下一步,乘以分数并简化答案。

$\begin{aligned} \frac{25 \times 3}{2 \times 7} = \frac{75}{14} = 5 \frac{5}{14} \end{aligned}$

The quotient is $\begin{aligned} 5 \frac{5}{14} \end{aligned}$ .
::商数是5 5 14

Example 3
::例3

Divide the mixed number: $\begin{aligned} 2 \frac{1}{4} \div 1 \frac{1}{2} = \underline{} \end{aligned}$ . Answer in simplest form.
::除以混合数字: 2,1,4,1,1,2 =_。回答最简单。

First, convert both mixed numbers to improper fractions.
::首先,将两个混合数字转换为不适当的分数。

$\begin{aligned} 2 \frac{2}{3} \end{aligned}$

Then, change the operation to multiplication and multiply by the reciprocal.
::然后,将操作改为乘以乘以乘以乘以对等。

$\begin{aligned} \frac{9}{4} \div \frac{3}{2} = \frac{9}{4} \times \frac{2}{3} \end{aligned}$

Next, multiply the fractions and simplify the answer.
::下一步,乘以分数并简化答案。

$\begin{aligned} \frac{9 \times 2}{4 \times 3} = \frac{18^{3}}{12^{2}} = 1 \frac{1}{2} \end{aligned}$

The quotient is $\begin{aligned} 1 \frac{1}{2} \end{aligned}$ .
::商数是1112

Example 4
::例4

Divide the mixed number: $\begin{aligned} 3 \frac{1}{3} \div 1 \frac{1}{4} = \underline{} \end{aligned}$ . Answer in simplest form.
::除以混合数: 3, 1, 3 + 1, 1 4 = _。回答最简单。

First, convert both mixed numbers to improper fractions.
::首先,将两个混合数字转换为不适当的分数。

$\begin{aligned} 3 \frac{1}{3} \div 1 \frac{1}{4} = \frac{10}{3} \div \frac{5}{4} \end{aligned}$

Then, change the operation to multiplication and multiply by the reciprocal.
::然后,将操作改为乘以乘以乘以乘以对等。

$\begin{aligned} \frac{10}{3} \div \frac{5}{4} = \frac{10}{3} \times \frac{4}{5} \end{aligned}$

Next, multiply the fractions and simplify the answer.
::下一步,乘以分数并简化答案。

$\begin{aligned} \frac{10 \times 4}{3 \times 5} = \frac{40^{8}}{15^{3}} = 2 \frac{2}{3} \end{aligned}$

The quotient is $\begin{aligned} 2 \frac{2}{3} \end{aligned}$ .
::商数是2 2 3

Example 5
::例5

Divide the mixed number: $\begin{aligned} 2 \frac{1}{5} \div 1 \frac{1}{2} = \underline{} \end{aligned}$ . Answer in simplest form.
::除以混合数字: 2,1,5,1,1,2 =_。回答最简单。

First, convert both mixed numbers to improper fractions.
::首先,将两个混合数字转换为不适当的分数。

$\begin{aligned} 2 \frac{1}{5} \div 1 \frac{1}{2} = \frac{11}{5} \div \frac{3}{2} \end{aligned}$

Then, change the operation to multiplication and multiply by the reciprocal.
::然后,将操作改为乘以乘以乘以乘以对等。

$\begin{aligned} \frac{11}{5} \div \frac{3}{2} = \frac{11}{5} \times \frac{2}{3} \end{aligned}$

Next, multiply the fractions and simplify the answer.
::下一步,乘以分数并简化答案。

$\begin{aligned} \frac{11 \times 2}{5 \times 3} = \frac{22}{15} = 1 \frac{7}{15} \end{aligned}$

The quotient is $\begin{aligned} 1 \frac{7}{15} \end{aligned}$ .

::商数是1715

Review
::回顾

Divide the mixed number. Answer in simplest form.
::除以混合数字。回答最简单。

$\begin{aligned} 2 \frac{1}{2} \div 1 \frac{1}{3} = \underline{} \end{aligned}$

$\begin{aligned} 1 \frac{1}{4} \div 3 \frac{1}{3} = \underline{} \end{aligned}$

$\begin{aligned} 1 \frac{1}{6} \div 1 \frac{1}{2} = \underline{} \end{aligned}$

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

$\begin{aligned} 5 \frac{1}{2} \div 1 \frac{1}{2} = \underline{} \end{aligned}$

$\begin{aligned} 3 \frac{1}{4} \div 1 \frac{1}{3} = \underline{} \end{aligned}$

$\begin{aligned} 4 \frac{1}{2} \div 5 \frac{1}{2} = \underline{} \end{aligned}$

$\begin{aligned} 6 \frac{1}{2} \div 2 \frac{1}{4} = \underline{} \end{aligned}$

$\begin{aligned} 5 \frac{1}{3} \div 2 \frac{1}{2} = \underline{} \end{aligned}$

$\begin{aligned} 3 \frac{1}{2} \div 3 \frac{1}{2} = \underline{} \end{aligned}$

$\begin{aligned} 6 \frac{2}{3} \div 1 \frac{1}{2} = \underline{} \end{aligned}$

$\begin{aligned} 8 \frac{2}{5} \div 1 \frac{1}{3} = \underline{} \end{aligned}$

$\begin{aligned} 12 \frac{1}{2} \div 2 \frac{1}{4} = \underline{} \end{aligned}$

$\begin{aligned} 6 \frac{5}{6} \div 2 \frac{1}{2} = \underline{} \end{aligned}$

$\begin{aligned} 8 \frac{3}{4} \div 2 \frac{1}{2} = \underline{} \end{aligned}$

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

Dividing Mixed Numbers ::混合数字

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 Mixed Numbers
::混合数字

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