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  • 前端估计

    Brandon saves pennies for over a year. His sister does the same. At the end of the year, he has saved 1357 pennies, and his sister has saved 2122 pennies. Their mother tells them that they can estimate their combined number of pennies using  front-end estimation . About how many pennies do Brandon and his sister have?
    ::布兰登节省了1年多的便士。他的姐姐也这样。到了年底,他节省了1357个便士,他的姐姐节省了2122个便士。他们的母亲告诉他们,他们可以用前端估计来估计他们的总便士数。关于布兰登和他的妹妹有多少便士呢?

    In this concept, you will learn how to use front-end estimation.

    ::在这个概念中,你将学会如何使用前端估计。

    Sums and Differences Using Front-End Estimation
    ::使用前期估算法计算总和和和差异

    Front–end  estimation  is a method of estimating used when adding or subtracting numbers that are greater than 1000.
    ::前端估计是在增加或减去超过1000个数字时使用的估算方法。

    Here are the steps for front–end estimation.
    ::以下是前端估算的步骤。

    1. Keep the digits of the two highest place values in the number.
      ::在数字中保留两个最高位数的数字。
    2. Insert zeros for the other place values.
      ::插入其他位置值的零。

    Let's look at an example.

    ::让我们举个例子。

    Estimate 4597 + 3865 = _____
    ::估计数4597+3865=______

    Follow the rules for front–end estimation since each number is over 1000.
    ::遵循前端估算规则, 因为每个数字都超过1000。

    4597 becomes 4500. The 4 and 5 are the digits of the two highest place values and you filled in zeros for the rest of the places.
    ::4597成为4500。4和5是两个最高值的位数,其余的位数以零填充。

    3865 becomes 3800. The 3 and 8 are the digits of two highest place values and you filled in zeros for the rest of the places.
    ::3865变成3800。 3和8是两个最高位数的位数, 其余位数的位数以零填充 。

    Now rewrite the problem.
    ::现在重写问题。

    4500 + 3800 = 8300

    The answer is that 4597 + 3865 is approximately 8300.
    ::答案是,4597+3865是大约8300。

    Let's look at another example.

    ::让我们再举一个例子。

    Estimate 4496 - 745 = _____
    ::估计数4496 - 745 = __

    Notice that one of the numbers is over 1000 and the other is not over 1000. Use front-end estimation for the number that is over 1000 and  round  to the nearest hundred for the number that is under 1000.
    ::请注意其中一位数字超过1000, 而另一位数字不超过1000。 使用前端估计值为1000以上, 圆到最接近的100, 数字低于1000 。

    4496 becomes 4400 using front–end estimation.
    ::根据前端估计,4496成为4400。

    745 becomes 700 by  rounding  to the nearest hundred.
    ::通过四舍五入到最接近的100,745变成700。

    4400 - 700 = 3700

    The answer is that 4496 - 745 is approximately 3700.
    ::答案是4496 - 745大约是3 700。

    When using front–end estimation and decimals, figure out how to keep the wholes separate from the parts and then combine them together. Here are the steps to front–end estimation with decimals.
    ::当使用前端-端估计值和小数点时,请找出如何将整件与部件分开,然后将它们合并起来。 这是前端-端估计值和小数点。 这是前方-小数点-以小数点计算。

    1. Add the front digits of the numbers being added or subtracted.
      ::添加要加或减的数字的前位数字。
    2. Round off the decimals of the numbers being added or subtracted.
      ::舍入所加或减数字的十进制舍入。
    3. Combine or subtract the results.
      ::合并或减去结果。

    2.10 + 3.79 = _____

    Start with the front digits of the numbers being added. That means add 2 + 3 = 5. Next, round the decimal part of each number. 0.10 stays 0.10 and 0.79 becomes 0.80.
    ::以添加数字的前位数开始。 这意味着增加 2+ 3 = 5 。 接下来, 将每个数字的小数部分四舍五入。 0. 10 保持0. 10, 0. 79 变成 0. 80 。

    0.10 + 0.80 = 0.90

    Now add the two estimates together.
    ::现在将这两个估计数加在一起。

    5 + 0.90 = 5.90

    The answer is that 2.10 + 3.79 is approximately 5.90.
    ::答案是2.10+3.79约为5.90。

    Examples
    ::实例

    Example 1
    ::例1

    Earlier, you were given a problem about Brandon and his sister.
    ::之前,你得到一个问题 关于布兰登和他的妹妹。

    Brandon has 1357 pennies and his sister has 2122. Estimate their combined number of pennies using front-end estimation.
    ::Brandon有1357便士,他妹妹有2122。

    First, check to make sure that both numbers are greater than 1000.
    ::首先,检查以确保这两个数字都大于1000。

    Yes
    ::是 是

    Next, keep the digits of the two highest place values in the number.
    ::接下来,保留数字中两个最高位数的位数。

    1357 becomes 1300
    ::1357变成1300

    2122 becomes 2100
    ::2122 成为 2100

    Then, calculate the  sum .
    ::然后,计算总和。

    1300 + 2100 = 3400

    The answer is that 1357 + 2122 is approximately 3400.
    ::答案是,1357+2122约为3400。

    Example 2
    ::例2

    Estimate 16.79 + 14.12 = _____ using front-end estimation.
    ::利用前端估计,估计16.79+14.12=____。

    First, add the front digits of the numbers.
    ::首先,添加数字的前位数字。

    16 + 14 = 30

    Next, round the decimals and add them.
    ::接下来,四舍五入小数点并添加它们。

    0.8 + 0.1 = 0.9

    Then combine the results.
    ::然后把结果合并起来

    30 + 0.9 = 30.9

    The answer is that 16.79 + 14.12 is approximately 30.9.
    ::答案是16.79+14.12大约为30.9。

    Example 3
    ::例3

    Estimate 5674 + 1256 = _____ using front-end estimation.
    ::使用前端估计值估算的估计数5674+1256=____。

    First, check to make sure that both numbers are greater than 1000.
    ::首先,检查以确保这两个数字都大于1000。

    Yes
    ::是 是

    Next, keep the digits of the two highest place values in the number.
    ::接下来,保留数字中两个最高位数的位数。

    5674 becomes 5600
    ::5674变成5600

    1256 becomes 1200
    ::1256 变成 1200

    Then, calculate the sum.
    ::然后,计算总和。

    5600 + 1200 = 6800

    The answer is that 5674 + 1256 is approximately 6800.
    ::答案是,5674+1256大约是6800。

    Example 4
    ::例4

    Estimate 4632 - 576 = _____ using front-end estimation.
    ::根据前端估计,估计4632 - 576 = 。

    First, check to make sure that both numbers are greater than 1000.
    ::首先,检查以确保这两个数字都大于1000。

    No, one number is greater than 1000 and the other is less than 1000.
    ::不,一个数字大于1000,另一个小于1000。

    Next, keep the digits of the two highest place values in the number that is over 1000 and round the number that is less than 1000 to the nearest hundred.
    ::接下来,将数字1000以上两个最高位数的位数位数保留在数字1000以上,并将不到1000到最接近的百位数四舍五入。

    4632 becomes 4600
    ::4632变成4600

    576 becomes 600
    ::576变成600

    Then, calculate the  difference .
    ::然后计算差额。

    4600 - 600 = 4000

    The answer is that 4632 - 576 is approximately 4000.
    ::答案是4632 - 576大约是4,000。

    Example 5
    ::例5

    Estimate 8.93 + 1.44 = _____ using front-end estimation.
    ::8.93 + 1.44 = = 使用前端估计。

    First, add the front digits of the numbers.
    ::首先,添加数字的前位数字。

    8 + 1 = 9

    Next, round the decimals and add them.
    ::接下来,四舍五入小数点并添加它们。

    0.9 + 0.4 = 1.3

    Then combine the results.
    ::然后把结果合并起来

    9 + 1.3 = 10.3

    The answer is that 8.93 + 1.44 is approximately 10.3.
    ::答案是8.93+1.44大约为10.3。

    Review
    ::回顾

    Estimate using front–end estimation.
    ::使用前端估计估算值估算。

    1. 34.66 + 11.12 = _____
    2. 43.18 + 16.75 = _____
    3. 2.34 + 1.56 = _____
    4. 7.89 + 5.79 = _____
    5. 8.90 + 3.21 = _____
    6. 7.18 - 3.13 = _____
    7. 12.65 - 7.23 = _____
    8. 15.70 - 11.10 = _____
    9. 25.67 - 18.40 = _____
    10. 78.46 - 55.21 = _____
    11. 88.12 - 34.06 = _____
    12. 87.43 - 80.11 = _____
    13. 94.12 - 7.08 = _____
    14. 98.10 - 6.01 = _____
    15. 145.90 + 18.12 = _____