节: 分数与带分数比较 | 5.16分数与带分数比较

章节大纲

Keith and his sister were assigned the task of cleaning up after a party. Keith took all of the leftover tuna sandwiches and his sister took all of the left over ham sandwiches.
::Keith和他的妹妹在聚会后被指派清理工作,基思拿走了所有剩下的金枪鱼三明治,他姐姐把剩下的所有三明治都拿走了火腿三明治。

Keith has $\begin{aligned} \frac{15}{2} \end{aligned}$ of tuna sandwiches.
::Keith有15 2个金枪鱼三明治。

His sister has $\begin{aligned} 6 \frac{3}{4} \end{aligned}$ of ham sandwiches. Who has more sandwiches?
::他姐姐有6 3 4个火腿三明治谁还有三明治?

In this concept, you will learn how to compare and order improper fractions and mixed numbers.
::在这个概念中,你将学会如何比较和排序不适当的分数和混合数字。

Comparing Improper Fractions and Mixed Numbers
::比较不适当分数和混合数字

An improper fraction is a fraction where the numerator is larger than the denominator .
::当分子大于分母时,不适当的分数是一个分数。

A mixed number is composed of a whole number and a fraction.
::混合数由整数和小数组成。

To compare a mixed number and an improper fraction, first make sure that they are in the same form. Convert the improper fraction to a mixed number or the mixed number to an improper fraction, then compare.
::要比较混合数字和不适当分数,首先要确保它们以相同形式出现。将不当分数转换成混合数字或混合数字,然后进行比较。

$\begin{aligned} 6 \frac{1}{2} \underline{} \frac{15}{4} \end{aligned}$

Convert $\begin{aligned} \frac{15}{4} \end{aligned}$ into a mixed number. Divide 15 by 4 and write the quotient as a whole number and a fraction.
::将 15 4 转换为混合数。除以 15 乘 4 , 将商数作为整数和小数来写。

$\begin{aligned} \frac{15}{4} = 3 \frac{3}{4} \end{aligned}$

Compare the numbers.
::比较数字。

$\begin{aligned} 6 \frac{1}{2} > 3 \frac{3}{4} \end{aligned}$

$\begin{aligned} 6 \frac{1}{2} \end{aligned}$ is greater than $\begin{aligned} \frac{15}{4} \end{aligned}$ .
::6 1 2 大于 15 4 。

If the whole number is the same, compare the fractions. You may have to convert the fractions using the lowest common denominator .
::如果整数相同, 请比较分数。您可能需要使用最小的公分母转换分数。

You can order improper fractions and mixed numbers in the same way. Convert them all to the same form and then write them in order.
::您可以以同样的方式订购不适当的分数和混合数字。把它们都转换成相同的格式, 然后按顺序写。

Order these fractions from least to greatest.
::将这些分数从最小排序到最大排序。

$\begin{aligned} 4 \frac{1}{2}, \frac{10}{6}, \frac{4}{3}, 7 \frac{1}{9} \end{aligned}$

First, change the fractions so that they are all in the same form. Let’s change them all to mixed numbers. Simplify if you can.
::首先,改变分数,使它们都以同样的形式出现。让我们把它们都换成混合数字。如果可以,请简化。

$\begin{aligned} \frac{10}{6} = \frac{5}{3} = 1 \frac{2}{3} \end{aligned}$

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

Now you can write them in order from least to greatest.
::现在你可以写成从最少到最伟大的。

$\begin{aligned} \frac{4}{3}, \frac{10}{6}, 4 \frac{1}{2}, 7 \frac{1}{9} \end{aligned}$

Examples
::实例

Example 1
::例1

Earlier, you were given a problem about Keith and the sandwiches.
::早些时候,你被问及基思和三明治的问题

Keith has $\begin{aligned} \frac{15}{2} \end{aligned}$ tuna sandwiches and his sister has $\begin{aligned} 6 \frac{3}{4} \end{aligned}$ ham sandwiches. Compare the fractions to see who has more sandwiches.
::Keith有15 2个金枪鱼三明治,他妹妹有6 3 4个火腿三明治。比较一下,看看谁有更多的三明治。

First, convert the improper fraction to a mixed number.
::首先,把不当的分数转换成混合数。

$\begin{aligned} \frac{15}{2} = 7 \frac{1}{2} \end{aligned}$

Then, compare the two quantities.
::然后,比较这两个数量。

$\begin{aligned} 7 \frac{1}{2} > 6 \frac{3}{4} \end{aligned}$

Keith has more sandwiches.
::基斯有更多的三明治。

For the following examples, compare the fractions.
::以下示例比较分数。

Example 2
::例2

$\begin{aligned} \frac{29}{3} \underline{} 7 \frac{1}{3} \end{aligned}$

First, convert the improper fraction to a mixed number.
::首先,把不当的分数转换成混合数。

$\begin{aligned} \frac{29}{3} = 9 \frac{2}{3} \end{aligned}$

Compare the numbers.
::比较数字。

$\begin{aligned} 9 \frac{2}{3} > 7 \frac{1}{3} \end{aligned}$

$\begin{aligned} \frac{29}{3} \end{aligned}$ is greater than $\begin{aligned} 7 \frac{1}{3} \end{aligned}$ .
::29 3大于7 1 3。

Example 3
::例3

$\begin{aligned} 4 \frac{1}{2} \underline{} \frac{12}{5} \end{aligned}$

First, change the improper fraction to a mixed number
::首先,将不当分数改变为混合数

$\begin{aligned} \frac{12}{5} = 2 \frac{2}{5} \end{aligned}$

Then, compare the numbers.
::然后,比较数字。

$\begin{aligned} 4 \frac{1}{2} > 2 \frac{2}{5} \end{aligned}$

$\begin{aligned} 4 \frac{1}{2} \end{aligned}$ is greater than $\begin{aligned} \frac{12}{5} \end{aligned}$ .
::4 1 2 大于 12 5 。

Example 4
::例4

$\begin{aligned} \frac{16}{3} \underline{} \frac{22}{5} \end{aligned}$

Both fractions are improper. Let’s try comparing the fractions using the lowest common denominator of 3 and 5. The LCD is 15.
::这两种分数都是不恰当的。让我们尝试用3和5的最低公分母来比较分数。液晶分数是15。

First, find the equivalent fraction for each with the denominator of 15.
::首先,找到每个分母的等同分数,分母为15。

$\begin{aligned} \frac{16}{3} = \frac{80}{15} \end{aligned}$

$\begin{aligned} \frac{22}{5} = \frac{66}{15} \end{aligned}$

Then, compare the fractions.
::然后,比较分数。

$\begin{aligned} \frac{80}{15} > \frac{66}{15} \end{aligned}$

$\begin{aligned} \frac{16}{3} \end{aligned}$ is greater than $\begin{aligned} \frac{22}{5} \end{aligned}$ .
::16 3大于22 5。

Example 5
::例5

$\begin{aligned} \frac{17}{4} \underline{} 4 \frac{1}{4} \end{aligned}$

First, convert the mixed fraction to an improper fraction. Multiply the whole number by the denominator and add the numerator. Write it as a fraction over 4.
::首先, 将混合分数转换为不适当的分数。将整数乘以分母, 并添加分子。将其写成分数 4 以上 4 。

$\begin{aligned} 4 \times 4 + 1 = 17 \end{aligned}$

$\begin{aligned} 4 \frac{1}{4} = \frac{17}{4} \end{aligned}$

Then, compare the fractions.
::然后,比较分数。

$\begin{aligned} \frac{17}{4} = \frac{17}{4} \end{aligned}$

$\begin{aligned} \frac{17}{4} \end{aligned}$ is equal to $\begin{aligned} 4 \frac{1}{4} \end{aligned}$ .
::17 4等于4 1 4。

Review
::回顾

Compare each set of values using <, > or =.
::使用 < 、 > 或 = 比较每组数值。

$\begin{aligned} \frac{12}{5} \underline{} 2 \frac{1}{4} \end{aligned}$

$\begin{aligned} \frac{16}{5} \underline{} 3 \frac{1}{2} \end{aligned}$

$\begin{aligned} \frac{44}{9} \underline{} 6 \frac{1}{3} \end{aligned}$

$\begin{aligned} \frac{45}{7} \underline{} 6 \frac{1}{2} \end{aligned}$

$\begin{aligned} \frac{19}{4} \underline{} 4 \frac{3}{4} \end{aligned}$

$\begin{aligned} \frac{16}{8} \underline{} 2 \end{aligned}$

$\begin{aligned} \frac{49}{5} \underline{} 6 \frac{2}{3} \end{aligned}$

$\begin{aligned} \frac{99}{10} \underline{} 10 \end{aligned}$

$\begin{aligned} \frac{69}{4} \underline{} 8 \frac{2}{5} \end{aligned}$

$\begin{aligned} \frac{70}{3} \underline{} 10 \frac{4}{7} \end{aligned}$

$\begin{aligned} \frac{80}{8} \underline{} \frac{40}{4} \end{aligned}$

$\begin{aligned} \frac{75}{3} \underline{} 25 \end{aligned}$

$\begin{aligned} \frac{18}{3} \underline{} \frac{24}{6} \end{aligned}$

$\begin{aligned} \frac{99}{3} \underline{} \frac{33}{11} \end{aligned}$

$\begin{aligned} \frac{78}{4} \underline{} 10 \frac{8}{9} \end{aligned}$

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

章节大纲

Comparing Improper Fractions and Mixed Numbers ::比较不适当分数和混合数字

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

Comparing Improper Fractions and Mixed Numbers
::比较不适当分数和混合数字

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