节: 分数减法 | 3.7分数减法

章节大纲

Sarah and her mom just got back from the fabric store. They bought $\begin{aligned} 7 \frac{3}{4} \end{aligned}$ yards of a beautiful fabric. Sarah is excited because she is planning to make a dress with the fabric. Her mom liked the fabric so much she wants to make a decorative pillow with it too. To make the pillow, Sarah's mom needs $\begin{aligned} 1 \frac{1}{2} \end{aligned}$ yards of the fabric. After her mom makes the pillow, how much fabric will Sarah have left to make her dress? If the pattern for her dress says she will need 5 yards of fabric, will she have enough?
::Sarah和她的妈妈刚从布料店回来,他们买了734码漂亮的布料。Sarah很兴奋,因为她正计划用布料做衣服。她妈妈非常喜欢布料,所以也想用它做一个装饰性枕头。做枕头,Sarah的妈妈需要12码的布料。在她妈妈做枕头后,Sarah要留下多少布料来做衣服?如果她服装的布料显示她需要5码的布料,她会有足够的吗?

In this concept, you will learn how to subtract fractions and mixed numbers.
::在这个概念中,你会学会如何减去分数和混合数字。

Subtracting Fractions and Mixed Numbers
::减法分数和混合数字

Subtracting fractions is very similar to adding fractions. The key is to make sure that the fractions that you are subtracting have the same denominator . If they don't, you will need to rewrite one or both fractions before subtracting.
::减法分数与增加分数非常相似。关键是要确保您所减分数的分数具有相同的分母。如果它们没有, 您就需要在减法之前重写一个或两个分数。

To subtract fractions:
::减去分数 :

Rewrite each fraction as an equivalent fraction so that the denominators are the same.
::将每一分数重写为相等的分数,以便分母相同。

Subtract the numerators of the . Keep the denominator the same.
::减号数。保持分母不变。

Simplify your answer.
::简化您的答案。

Here is an example.
::举一个例子。

Subtract $\begin{aligned} \frac{2}{3} - \frac{2}{9} \end{aligned}$ .
::减号2 3 - 2 9

First, find a common denominator . You are looking for a number that is a multiple of both 3 and 9. 9 is the least common multiple of 3 and 9.
::首先,找到一个共同的分母。您正在寻找一个数字,它是一个3和9的倍数,9是3和9中最不常见的 3和9的倍数。

Now, rewrite each fraction as an equivalent fraction with a denominator of 9. $\begin{aligned} \frac{2}{9} \end{aligned}$ already has a denominator of 9 so it will not change.
::现在,将每一分数重写为相等的分数, 分母为9. 2 9, 分母为9. 9, 分母为9. 9, 所以不会改变。

$\begin{aligned} \begin{array}{rcl} \frac{2}{3} & = & \frac{2 \times 3}{3 \times 3} = \frac{6}{9} \\ \frac{2}{9} & = & \frac{2}{9} \end{array} \end{aligned}$

Next, subtract the equivalent fractions. You will subtract the numerators and keep the denominator the same.
::下一步,减去相等的分数。您将减去分子数,并将分母保持原样。

$\begin{aligned} \frac{6}{9} - \frac{2}{9} = \frac{4}{9} \end{aligned}$

Finally, check to make sure your answer is in simplest form . $\begin{aligned} \frac{4}{9} \end{aligned}$ is in simplest form because 4 and 9 do not have any common factors besides 1.
::最后,检查以确保您的答复最简单。 4 9 最简单, 因为 4 和 9 除了 1 以外没有任何共同因素。

The answer is $\begin{aligned} \frac{2}{3} - \frac{2}{9} = \frac{4}{9} \end{aligned}$ .
::答案是2 3 - 2 9 = 4 9 。

You can also subtract mixed numbers. The easiest way to subtract mixed numbers is to convert them to improper fractions before subtracting. Then, you can subtract them just like any other fractions.
::您也可以减去混合数字。最容易减少混合数字的方法是在减去之前将其转换为不适当的分数。然后, 您可以把它们与其他分数一样去掉。

To subtract mixed numbers:
::要减去混合数字:

Rewrite the fractional part of each mixed number as an equivalent fraction so that the denominators are the same.
::将每个混合数的分数部分重写为相等的分数,以便分母相同。

Convert each mixed number to an improper fraction. To get the numerator of the improper fraction, multiply the whole number with the denominator and add the original numerator. The denominator of the improper fraction will be the same as the original denominator.
::将每个混合数转换成不适当的分数。要获取不适当的分数的分子, 请将整数乘以分母并添加原数。不当分数的分数将与原始分数相同。

Subtract the numerators of the fractions. Keep the denominator the same.
::减去分数的分子。保持分母不变。

Simplify your answer. Rewrite as a mixed number.
::简化您的回答。重写为混合数字。

Here is an example.
::举一个例子。

Subtract $\begin{aligned} 3 \frac{1}{2} - 1 \frac{3}{4} \end{aligned}$ .
::减号3 1 2 - 1 3 4

First, find a common denominator for the fractional parts of the mixed numbers. You are looking for a number that is a multiple of both 2 and 4. 4 is the least common multiple of 2 and 4.
::首先,为混合数字的分数部分找到一个共同的分母。您正在寻找一个数字, 该数字是2和4的倍数, 2和4的倍数, 4是2和4中最不常见的倍数。

Now, rewrite each fractional part as an equivalent fraction with a denominator of 4. $\begin{aligned} \frac{3}{4} \end{aligned}$ already has a denominator of 4 so it will not change.
::现在,将每个分部分重写为等效分数,分母为4. 3 4 分母已经有一个分母为4 分母,所以它不会改变。

$\begin{aligned} \begin{array}{rcl} \frac{1}{2} & = & \frac{1 \times 2}{2 \times 2} = \frac{2}{4} \\ \frac{3}{4} & = & \frac{3}{4} \end{array} \end{aligned}$

Next, rewrite the problem with the equivalent fractions.
::下一步, 重写问题, 重写相应的分数。

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

Now, rewrite each mixed number as an improper fraction. Multiply each denominator by the whole number and add the original numerator to get the numerator of the improper fraction.
::现在, 重写每个混合数字为不适当的分数。将每个分数乘以整数, 并添加原始的分子来获取不适当的分数的分子。

$\begin{aligned} \begin{array}{rcl} 3 \frac{2}{4} & = & \frac{(4 \times 3) + 2}{4} = \frac{14}{4} \\ 1 \frac{3}{4} & = & \frac{(4 \times 1) + 3}{4} = \frac{7}{4} \end{array} \end{aligned}$

Next, subtract the improper fractions. You will subtract the numerators and keep the denominator the same.
::下一步, 减去不适当的分数。您将减去分子数, 并保持分母不变。

$\begin{aligned} \frac{14}{4} - \frac{7}{4} = \frac{7}{4} \end{aligned}$

Finally, convert your answer back to a mixed number and check to make sure it is in simplest form.
::最后,将您的答复转换为混合数字,并检查是否最简单。

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

The answer is $\begin{aligned} 3 \frac{1}{2} - 1 \frac{3}{4} = 1 \frac{3}{4} \end{aligned}$ .
::答案是3 1 2 - 1 3 4 = 1 3 4 。

Examples
::实例

Example 1
::例1

Earlier, you were given a problem about Sarah and her fabric.
::早些时候,你得到一个问题关于莎拉和她的布料。

She bought $\begin{aligned} 7 \frac{3}{4} \end{aligned}$ yards of fabric at the store with her mom. Her mom will use $\begin{aligned} 1 \frac{1}{2} \end{aligned}$ yards of the fabric to make a pillow. Sarah wants to figure out how much fabric will be left after her mom makes the pillow. Sarah is planning to make a dress and needs 5 yards of fabric to do that, so she wants to make sure she has enough.
::她和妈妈在店里买了7 3 4码的布料。她妈妈用12码的布料做枕头。莎拉想弄清楚在她妈妈做枕头之后,会留下多少布料。莎拉正计划做一件衣服,需要5码的布料来做,所以她想确保自己有足够的。

In order to figure out how much fabric Sarah will have left, she will need to subtract.
::为了弄清楚莎拉还剩下多少织物她需要减去

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

First, she should find a common denominator for the fractional parts of the mixed numbers. 4 is the least common multiple of 4 and 2.
::首先,她应该为混合数字的分部分找到一个共同的分母。 4是4和2中最不常见的倍数。

Now, Sarah should rewrite each fractional part as an equivalent fraction with a denominator of 4.
::现在,莎拉应该重新写下每个分部分的分数, 以等值的分数, 分母为4。

$\begin{aligned} \begin{array}{rcl} \frac{3}{4} & = & \frac{3}{4} \\ \frac{1}{2} & = & \frac{1 \times 2}{2 \times 2} = \frac{2}{4} \end{array} \end{aligned}$

Next, she should rewrite the problem with the equivalent fractions.
::接下来,她应该用同等的分数重写问题。

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

Now, Sarah should rewrite each mixed number as an improper fraction.
::现在,莎拉应该把每一个混合数字都改写为不适当的分数。

$\begin{aligned} 7 \frac{3}{4} = \frac{(4 \times 7) + 3}{4} = \frac{31}{4} \\ 1 \frac{2}{4} = \frac{(4 \times 1) + 2}{4} = \frac{6}{4} \end{aligned}$

Next, Sarah should subtract the improper fractions.
::接下来,莎拉应该减去不适当的分数。

$\begin{aligned} \frac{31}{4} - \frac{6}{4} = \frac{25}{4} \end{aligned}$

Finally, she should convert her answer back to a mixed number and check to make sure it is in simplest form.
::最后,她应将其回答转换成混合数字,并检查是否最简单。

$\begin{aligned} \frac{25}{4} = 6 \frac{1}{4} \end{aligned}$

The answer is Sarah will have $\begin{aligned} 6 \frac{1}{4} \end{aligned}$ yards of fabric left to make her dress. If she only needs 5 yards of fabric to make the dress, she should have enough!
::答案是Sarah还有614码的织物来做衣服如果她只需要5码的织物来做衣服,她应该有足够的!

Example 2
::例2

Benito works in a bakery and has baked the world's longest loaf of cinnamon bread. His loaf measures $\begin{aligned} 11 \frac{5}{8} \end{aligned}$ feet. He cuts a piece of bread that is $\begin{aligned} 2 \frac{2}{3} \end{aligned}$ feet long for his friend Serena. How long is his loaf of bread now?
::贝尼托在一家面包店工作,烤了世界上最长的肉桂面包,他的面包是11,5,8英尺。他切了一块面包,对于他的朋友瑟琳娜来说是2,2,3英尺长。他的面包是多久?

In order to figure out how much bread Benito has left, you will need to subtract.
::为了弄清楚贝尼托剩下多少面包,你需要减去。

$\begin{aligned} 11 \frac{5}{8} - 2 \frac{2}{3} \end{aligned}$

First, find a common denominator for the fractional parts of the mixed numbers. You are looking for a number that is a multiple of both 8 and 3. 24 is the least common multiple of 8 and 3.
::首先,为混合数字的分数部分找到一个共同的分母。您正在寻找一个数字, 这个数字是8和3的倍数, 24是8和3的最不常见的倍数。

Now, rewrite each fractional part as an equivalent fraction with a denominator of 8.
::现在,将每个分部分重写为相等的分数,分母为8。

$\begin{aligned} \frac{5}{8} = \frac{5 \times 3}{8 \times 3} = \frac{15}{24} \\ \frac{2}{3} = \frac{2 \times 8}{3 \times 8} = \frac{16}{24} \end{aligned}$

Next, rewrite the problem with the equivalent fractions.
::下一步, 重写问题, 重写相应的分数。

$\begin{aligned} 11 \frac{15}{24} - 2 \frac{16}{24} \end{aligned}$

Now, rewrite each mixed number as an improper fraction.
::现在,重写每个混合数字,作为一个不适当的分数。

$\begin{aligned} 11 \frac{15}{24} = \frac{(24 \times 11) + 15}{24} = \frac{279}{24} \\ 2 \frac{16}{24} = \frac{(24 \times 2) + 16}{24} = \frac{64}{24} \end{aligned}$

Next, subtract the improper fractions. You will subtract the numerators and keep the denominator the same.
::下一步, 减去不适当的分数。您将减去分子数, 并保持分母不变。

$\begin{aligned} \frac{279}{24} - \frac{64}{24} = \frac{215}{24} \end{aligned}$

Finally, convert your answer back to a mixed number and check to make sure it is in simplest form.
::最后,将您的答复转换为混合数字,并检查是否最简单。

$\begin{aligned} \frac{215}{24} = 8 \frac{23}{24} \end{aligned}$

The answer is Benito's loaf is now $\begin{aligned} 8 \frac{23}{24} \end{aligned}$ feet long.
::答案是贝尼托的面包长82324英尺

Example 3
::例3

Subtract $\begin{aligned} \frac{10}{12} - \frac{6}{12} \end{aligned}$ .
::减号10 12 - 6 12

First, notice that these fractions already have a common denominator of 12. Subtract the fractions. You will subtract the numerators and keep the denominator the same.
::首先,请注意这些分数已经有一个共同的分母 12 。减减这些分数。您会减去分子, 并保持分母不变。

$\begin{aligned} \frac{10}{12} - \frac{6}{12} = \frac{4}{12} \end{aligned}$

Finally, check to make sure your answer is in simplest form. To rewrite $\begin{aligned} \frac{4}{12} \end{aligned}$ in simplest form, divide both the numerator and the denominator by 4.
::最后, 请检查以确保您的回答以最简单的形式出现。要以最简单的形式重写 4 12, 将分子和分母除以 4 。

$\begin{aligned} \frac{4 \div 4}{12 \div 4} = \frac{1}{3} \end{aligned}$

The answer is $\begin{aligned} \frac{10}{12} - \frac{6}{12} = \frac{1}{3} \end{aligned}$ .
::答案是10 12 - 6 12 = 1 3。

Example 4
::例4

Subtract $\begin{aligned} \frac{6}{7} - \frac{3}{4} \end{aligned}$ .
::减 6 7 - 3 4

First, find a common denominator. You are looking for a number that is a multiple of both 7 and 4. 28 is the least common multiple of 7 and 4.
::首先,找到一个共同的分母。您正在寻找一个数字,它是一个7和4的倍数,28是7和4的最不常见的倍数。

Now, rewrite each fraction as an equivalent fraction with a denominator of 28.
::现在,将每一分数重写为等效分数,分母为28。

$\begin{aligned} \frac{6}{7} = \frac{6 \times 4}{7 \times 4} = \frac{24}{28} \\ \frac{3}{4} = \frac{3 \times 7}{4 \times 7} = \frac{21}{28} \end{aligned}$

Next, subtract the equivalent fractions. You will subtract the numerators and keep the denominator the same.
::下一步,减去相等的分数。您将减去分子数,并将分母保持原样。

$\begin{aligned} \frac{24}{28} - \frac{21}{28} = \frac{3}{28} \end{aligned}$

Finally, check to make sure your answer is in simplest form. $\begin{aligned} \frac{3}{28} \end{aligned}$ is in simplest form because 3 and 28 do not have any common factors besides 1.
::最后,检查以确保您的答复最简单。 3 28 最简单, 因为 3 和 28 除了1 以外没有任何共同因素。

The answer is $\begin{aligned} \frac{6}{7} - \frac{3}{4} = \frac{3}{28} \end{aligned}$ .
::答案是6 7 - 3 4 = 3 28。

Example 5
::例5

Subtract $\begin{aligned} 4 \frac{1}{4} - \frac{3}{4} \end{aligned}$ .
::减号4 1 4 - 3 4

First, notice that the fractional parts of the numbers already have a common denominator. Rewrite the mixed number as an improper fraction.
::首先, 请注意数字的分数部分已经有一个共同的分母。重写混合数作为不适当的分数。

$\begin{aligned} \begin{array}{rcl} 4 \frac{1}{4} & = & \frac{(4 \times 4) + 1}{4} = \frac{17}{4} \\ \frac{3}{4} & = & \frac{3}{4} \end{array} \end{aligned}$

Next, subtract the fractions.
::接下来,减去分数。

$\begin{aligned} \frac{17}{4} - \frac{3}{4} = \frac{14}{4} \end{aligned}$

Finally, convert your answer back to a mixed number. Rewrite the fractional part of the mixed number so that it is in simplest form by dividing both the numerator and the denominator by 2.
::最后,将您的答复转换为混合数。重写混合数的分数部分,以便通过将分子和分母除以 2 来使其最简单化。

$\begin{aligned} \frac{14}{4} = 3 \frac{2}{4} = 3 \frac{1}{2} \end{aligned}$

The answer is $\begin{aligned} 4 \frac{1}{4} - \frac{3}{4} = 3 \frac{1}{2} \end{aligned}$ .
::答案是4 1 4 - 3 4 = 3 1 2 。

Review
::回顾

Subtract.
::减。

$\begin{aligned} \frac{7}{10} - \frac{1}{4} \end{aligned}$

$\begin{aligned} \frac{4}{8} - \frac{1}{2} \end{aligned}$

$\begin{aligned} \frac{4}{7} - \frac{1}{21} \end{aligned}$

$\begin{aligned} \frac{3}{4} - \frac{1}{8} \end{aligned}$

$\begin{aligned} 3 \frac{1}{10} - \frac{1}{5} \end{aligned}$

$\begin{aligned} 4 \frac{3}{8} - 3 \frac{1}{4} \end{aligned}$

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

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

Estimate the difference.
::估计差异。

$\begin{aligned} \frac{14}{16} - \frac{1}{11} \end{aligned}$

$\begin{aligned} \frac{28}{60} - \frac{6}{13} \end{aligned}$

$\begin{aligned} \frac{6}{7} - \frac{2}{145} \end{aligned}$

$\begin{aligned} \frac{22}{33} - \frac{5}{12} \end{aligned}$

$\begin{aligned} 14 \frac{20}{21} - 3 \frac{18}{19} \end{aligned}$

$\begin{aligned} 2 \frac{1}{49} - 1 \frac{13}{14} \end{aligned}$

$\begin{aligned} 3 \frac{2}{21} - 2 \frac{6}{11} \end{aligned}$

$\begin{aligned} 4 \frac{8}{17} - \frac{71}{73} \end{aligned}$

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

Subtracting Fractions and Mixed Numbers ::减法分数和混合数字

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

Subtracting Fractions and Mixed Numbers
::减法分数和混合数字

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