Section: 混合数表达式求值 | 6.12混合数表达式求值

Section outline

Trevor is running some errands today. He walks $\begin{aligned} 5 \frac{1}{3} \end{aligned}$ blocks to the post office. Then he walks $\begin{aligned} 6 \frac{1}{2} \end{aligned}$ blocks to the grocery store. After the grocery store, he walks $\begin{aligned} 2 \frac{1}{3} \end{aligned}$ blocks home. How many blocks did Trevor walk today?
::Trevor今天去办点事,他走513个街区到邮局,然后走612个街区到杂货店,在杂货店之后,他走23个街区回家,Trevor今天走多少个街区?

In this concept, you will learn how to evaluate numerical expressions involving mixed numbers.
::在此概念中,您将学会如何评价混杂数字的数字表达式。

Evaluating Expressions with Mixed Numbers
::混合数字评价表达式

A numerical expression can have both addition and subtraction in them. When this happens, follow the order of operations. Resolve the operations with parentheses first, and then add or subtract the mixed numbers going from left to right.
::数字表达式可以在其中添加和减法。当发生这种情况时,要遵循操作的顺序。先用括号解决操作,然后加上或减去从左到右的混合数字。

Here is a numerical expression.
::这里是一个数字表达式。

$\begin{aligned} 4 \frac{1}{6} + 3 \frac{4}{6} - 1 \frac{4}{6} = \underline{} \end{aligned}$

This problem has two operations, addition and subtraction. The fractions have the same denominators so you can start by adding the first two fractions. Add the fractions before adding the whole numbers .
::此问题有两个操作、添加和减法。分数具有相同的分母, 这样您可以开始添加前两个分数。在添加整数之前添加分数。

$\begin{aligned} 4 \frac{1}{6} + 3 \frac{4}{6} = 7 \frac{5}{6} \end{aligned}$

Then, take the sum and subtract the third fraction. Subtract the fractions before subtracting the whole numbers.
::然后,取整数再减去第三分数。在减去整数之前,减去这些分数。

$\begin{aligned} 7 \frac{5}{6} - 1 \frac{4}{6} = 6 \frac{1}{6} \end{aligned}$

Remember to write the fraction in simplest form . In this example, the fraction is in simplest form.
::记住要以最简单的形式写入分数。在此示例中, 分数以最简单的形式出现。

The value of the expression is $\begin{aligned} 6 \frac{1}{6} \end{aligned}$ .
::表达式的值为 616 。

Here is another numerical expression.
::下面是另一个数字表达式。

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

The denominators of these fractions are not all alike. Before evaluating the expression, rewrite the fractions with one common denominator . The lowest common denominator is 6. The first two fractions are already in sixths. Rewrite the third fraction in sixths.
::这些分母的分母不完全相同。在评价表达式之前, 用一个共同分母重写分母。最小共同分母是 6 。前两个分母已经是六分之六。将第三个分母重写为六分之六。

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

$\begin{aligned} 2 \frac{4}{6} + 1 \frac{1}{6} - 1 \frac{3}{6} = \underline{} \end{aligned}$

Then, add the first two fractions. Add the fractions before adding the whole numbers.
::然后添加前两个分数。在添加整个数字之前添加分数。

$\begin{aligned} 2 \frac{4}{6} + 1 \frac{1}{6} = 3 \frac{5}{6} \end{aligned}$

Next, take the sum and subtract the third mixed number . Subtract the fractions before subtracting the whole numbers.
::接下来,拿下总和,然后减去第三个混合数字。在减去整个数字之前,先减去分数。

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

Finally, write the fraction in simplest form. Simplify the fraction with the (GCF) of 6 and 2. The GCF is 2.
::最后,以最简单的形式写出分数。将分数简化为6和2的(GCF)和2。全球合作框架为2。

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

The value of the expression is $\begin{aligned} 2 \frac{1}{3} \end{aligned}$ .
::表达式的值为 2 1 3 。

Examples
::实例

Example 1
::例1

Earlier, you were given a problem about Trevor, who is running some errands.
::早些时候,你曾听说特雷弗有问题,他正在处理一些事情。

Trevor is running some errands and walks $\begin{aligned} 5 \frac{1}{3} \end{aligned}$ blocks to the post office, $\begin{aligned} 6 \frac{1}{2} \end{aligned}$ blocks to the grocery store, and $\begin{aligned} 2 \frac{1}{3} \end{aligned}$ b
::Trevor正在办一些杂事,走513个街区到邮局,走612个街区到杂货店,走213个街区到邮局,走612个街区到杂货店,走213个b

locks back home. Find the sum of the mixed numbers to get the total number of blocks Trevor walked that day.
::找到混合数字的总和来获得特雷弗那天走过的街区的总数

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

First, rewrite the fraction with the common denominator of 6.
::首先,用6的公分母重写分数。

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

Then, add or subtract the mixed numbers in the order from left to right.
::然后,增加或减去混合数,依顺序从左到右。

$\begin{aligned} 5 \frac{2}{6} + 6 \frac{3}{6} = 11 \frac{5}{6} + 2 \frac{2}{6} = 13 \frac{7}{6} \end{aligned}$

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

$\begin{aligned} \frac{7}{6} = 1 \frac{1}{6} \\ 13 + 1 \frac{1}{6} = 14 \frac{1}{6} \end{aligned}$

Trevor walked a total of $\begin{aligned} 14 \frac{1}{6} \end{aligned}$ blocks.
::特雷弗共走过1416个街区

Example 2
::例2

Evaluate the expression.
::评估表达方式。

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

The fractions have different denominators. Before evaluating the expression, rewrite the fractions with a common denominator.
::分数有不同的分母。在评价表达式之前, 用共同分母重写分母。

$\begin{aligned} 3 \frac{3}{4} = 3 \frac{6}{8} 2 \frac{1}{2} = 2 \frac{4}{8} \\ 2 \frac{1}{8} + 3 \frac{3}{4} - 2 \frac{1}{2} = 2 \frac{1}{8} + 3 \frac{6}{8} - 2 \frac{4}{8} \end{aligned}$

Then, evaluate the expression starting in order from left to right. Add the first set of fractions, then subtract the third fraction from the sum.
::然后按照从左到右的顺序对表达式进行评价。添加第一组分数,然后从总和中减去第三组分数。

$\begin{aligned} 2 \frac{1}{8} + 3 \frac{6}{8} = 5 \frac{7}{8} - 2 \frac{4}{8} = 3 \frac{3}{8} \end{aligned}$

The fraction is in simplest form.
::分数以最简单的形式出现。

The value of the expression is $\begin{aligned} 3 \frac{3}{8} \end{aligned}$ .
::表达式的值为 3 3 8 。

Example 3
::例3

Evaluate the expression: $\begin{aligned} 6 \frac{4}{8} + 2 \frac{2}{8} - 1 \frac{1}{8} = \underline{} \end{aligned}$ . Answer in simplest form.
::评价表达式: 6 4 8 + 2 2 8 - 1 1 8 = _. 回答最简单。

Add or subtract the mixed numbers in the order from left to right.
::添加或减去从左到右顺序的混合数字。

$\begin{aligned} 6 \frac{4}{8} + 2 \frac{2}{8} = 8 \frac{6}{8} - 1 \frac{1}{8} = 7 \frac{5}{8} \end{aligned}$

The value of the expression is $\begin{aligned} 7 \frac{5}{8} \end{aligned}$ .
::表达式的值为 7 5 8 。

Example 4
::例4

Evaluate the expression: $\begin{aligned} 4 \frac{3}{9} + 2 \frac{1}{3} - 1 \frac{2}{9} = \underline{} \end{aligned}$ . Answer in simplest form.
::评价表达式:4 3 9+2 1 3 - 1 2 9 =_。回答最简单。

First, rewrite the fractions using a common denominator of 9.
::首先,使用9的公分母重写分数。

$\begin{aligned} 2 \frac{1}{3} = 2 \frac{3}{9} \\ 4 \frac{3}{9} + 2 \frac{1}{3} - 1 \frac{2}{9} = 4 \frac{3}{9} + 2 \frac{3}{9} - 1 \frac{2}{9} \end{aligned}$

Then, add or subtract the mixed numbers in the order from left to right.
::然后,增加或减去混合数,依顺序从左到右。

$\begin{aligned} 4 \frac{3}{9} + 2 \frac{3}{9} = 6 \frac{6}{9} - 1 \frac{2}{9} = 5 \frac{4}{9} \end{aligned}$

The value of the expression is $\begin{aligned} 5 \frac{4}{9} \end{aligned}$ .
::表达式的值为 5 4 9 。

Example 5
::例5

Evaluate the expression: $\begin{aligned} 2 \frac{1}{3} + 5 \frac{1}{3} - 6 \frac{1}{4} = \underline{} \end{aligned}$ . Answer in simplest form.
::评价表达式:2,1,3+5,1,3-6,1,4=_。回答最简单。

First, rewrite the fractions using a common denominator of 12.
::首先,使用12的公分母重写分数。

$\begin{aligned} 2 \frac{1}{3} = 2 \frac{4}{12} 5 \frac{1}{3} = 5 \frac{4}{12} 6 \frac{1}{4} = 6 \frac{3}{12} \\ 2 \frac{1}{3} + 5 \frac{1}{3} - 6 \frac{1}{4} = 2 \frac{4}{12} + 5 \frac{4}{12} - 6 \frac{3}{12} \end{aligned}$

Then, add or subtract the mixed numbers in the order from left to right.
::然后,增加或减去混合数,依顺序从左到右。

$\begin{aligned} 2 \frac{4}{12} + 5 \frac{4}{12} = 7 \frac{8}{12} - 6 \frac{3}{12} = 1 \frac{5}{12} \end{aligned}$

The value of the expression is $\begin{aligned} 1 \frac{5}{12} \end{aligned}$ .

::表达式的值为 1 5 12 。

Review
::回顾

Evaluate the following expressions. Answer in simplest form.
::评估以下表达式。以最简单的形式回答。

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

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

$\begin{aligned} 7 \frac{3}{9} + 8 \frac{1}{9} - 1 \frac{2}{9} = \underline{} \end{aligned}$

$\begin{aligned} 8 \frac{3}{10} + 2 \frac{5}{10} - 6 \frac{4}{10} = \underline{} \end{aligned}$

$\begin{aligned} 6 \frac{1}{5} + 2 \frac{3}{5} - 1 \frac{1}{5} = \underline{} \end{aligned}$

$\begin{aligned} 9 \frac{4}{9} + 2 \frac{4}{9} - 3 \frac{5}{9} = \underline{} \end{aligned}$

$\begin{aligned} 6 \frac{9}{12} + 3 \frac{2}{12} - 8 \frac{4}{12} = \underline{} \end{aligned}$

$\begin{aligned} 7 \frac{8}{9} - 1 \frac{1}{9} + 1 \frac{3}{9} = \underline{} \end{aligned}$

$\begin{aligned} 6 \frac{4}{8} + 3 \frac{4}{8} - 6 \frac{6}{8} = \underline{} \end{aligned}$

$\begin{aligned} 14 \frac{2}{3} - 2 \frac{1}{3} + 1 \frac{1}{3} = \underline{} \end{aligned}$

$\begin{aligned} 12 \frac{6}{9} + 12 \frac{8}{9} - 10 \frac{7}{9} = \underline{} \end{aligned}$

$\begin{aligned} 9 \frac{1}{7} + 12 \frac{3}{7} + 1 \frac{2}{7} = \underline{} \end{aligned}$

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

$\begin{aligned} 18 \frac{6}{15} + 2 \frac{3}{15} - 4 \frac{2}{15} = \underline{} \end{aligned}$

$\begin{aligned} 12 \frac{1}{9} + 2 \frac{1}{3} - 1 \frac{1}{6} = \underline{} \end{aligned}$

Review (Answers)
::回顾(答复)

Section outline

Evaluating Expressions with Mixed Numbers ::混合数字评价表达式

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)

Evaluating Expressions with Mixed Numbers
::混合数字评价表达式

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)