1.1 Rearrange The Following In Descending Order:1.1.1 ${$0.402; , \frac{21}{50}; , 0.375; , 1.2; , 85%$}$1.1.2 { \frac{3}{4}; , \frac{1}{2}; , \frac{4}{5}; , \frac{3}{8}$}$
In mathematics, comparing and ordering fractions and decimals is a fundamental concept that is essential for various mathematical operations and problem-solving techniques. When dealing with fractions and decimals, it is crucial to understand how to compare and order them in ascending or descending order. In this article, we will focus on rearranging the given fractions and decimals in descending order.
Rearranging the First Set of Numbers
The first set of numbers includes decimals and percentages. To rearrange these numbers in descending order, we need to convert them into a comparable format. Let's start by converting the decimals into fractions.
1.1.1 Rearranging Decimals and Percentages
- 0.402: This decimal can be converted into a fraction by dividing the numerator by the denominator. In this case, 0.402 is equal to 402/1000, which can be simplified to 201/500.
- 0.375: This decimal can be converted into a fraction by dividing the numerator by the denominator. In this case, 0.375 is equal to 375/1000, which can be simplified to 15/40.
- 85%: This percentage can be converted into a decimal by dividing the numerator by 100. In this case, 85% is equal to 85/100, which can be simplified to 17/20.
- 1.2: This decimal can be converted into a fraction by dividing the numerator by the denominator. In this case, 1.2 is equal to 12/10, which can be simplified to 6/5.
- 21/50: This fraction is already in its simplest form.
Now that we have converted all the decimals and percentages into fractions, we can compare and order them in descending order.
| Fraction | Simplified Fraction |
|---|---|
| 201/500 | 201/500 |
| 17/20 | 17/20 |
| 6/5 | 6/5 |
| 15/40 | 3/8 |
| 21/50 | 21/50 |
To compare these fractions, we need to find a common denominator. The least common multiple (LCM) of 500, 20, 5, 40, and 50 is 2000. Now, let's convert each fraction to have a denominator of 2000.
| Fraction | Simplified Fraction | Equivalent Fraction (2000 denominator) |
|---|---|---|
| 201/500 | 201/500 | 804/2000 |
| 17/20 | 17/20 | 1700/2000 |
| 6/5 | 6/5 | 1200/2000 |
| 3/8 | 3/8 | 750/2000 |
| 21/50 | 21/50 | 840/2000 |
Now that we have a common denominator, we can compare the fractions in descending order.
- 1700/2000 (17/20)
- 1200/2000 (6/5)
- 840/2000 (21/50)
- 804/2000 (201/500)
- 750/2000 (3/8)
Therefore, the rearranged list in descending order is:
- 0.85 (85%)
- 1.2 (6/5)
- 0.84 (21/50)
- 0.402 (201/500)
- 0.375 (15/40)
Rearranging the Second Set of Numbers
The second set of numbers includes fractions. To rearrange these fractions in descending order, we need to compare their values.
1.1.2 Rearranging Fractions
- 3/4: This fraction is already in its simplest form.
- 1/2: This fraction is already in its simplest form.
- 4/5: This fraction is already in its simplest form.
- 3/8: This fraction is already in its simplest form.
To compare these fractions, we need to find a common denominator. The least common multiple (LCM) of 4, 2, 5, and 8 is 40. Now, let's convert each fraction to have a denominator of 40.
| Fraction | Simplified Fraction | Equivalent Fraction (40 denominator) |
|---|---|---|
| 3/4 | 3/4 | 30/40 |
| 1/2 | 1/2 | 20/40 |
| 4/5 | 4/5 | 32/40 |
| 3/8 | 3/8 | 15/40 |
Now that we have a common denominator, we can compare the fractions in descending order.
- 32/40 (4/5)
- 30/40 (3/4)
- 20/40 (1/2)
- 15/40 (3/8)
Therefore, the rearranged list in descending order is:
- 4/5
- 3/4
- 1/2
- 3/8
In this section, we will address some of the most common questions related to rearranging fractions and decimals in descending order.
Q: What is the first step in rearranging fractions and decimals in descending order?
A: The first step in rearranging fractions and decimals in descending order is to convert them into a comparable format. This can be done by converting decimals into fractions or percentages into decimals.
Q: How do I convert a decimal into a fraction?
A: To convert a decimal into a fraction, you can divide the numerator by the denominator. For example, to convert 0.402 into a fraction, you can divide 402 by 1000, which gives you 201/500.
Q: What is the least common multiple (LCM) and how do I find it?
A: The least common multiple (LCM) is the smallest number that is a multiple of two or more numbers. To find the LCM, you can list the multiples of each number and find the smallest number that appears in all the lists. Alternatively, you can use a calculator or a formula to find the LCM.
Q: How do I compare fractions with different denominators?
A: To compare fractions with different denominators, you need to find a common denominator. This can be done by finding the least common multiple (LCM) of the two denominators. Once you have a common denominator, you can compare the fractions by comparing their numerators.
Q: What is the difference between ascending and descending order?
A: Ascending order refers to the order in which numbers or fractions are arranged from smallest to largest. Descending order, on the other hand, refers to the order in which numbers or fractions are arranged from largest to smallest.
Q: Can I use a calculator to find the LCM and compare fractions?
A: Yes, you can use a calculator to find the LCM and compare fractions. Many calculators have built-in functions for finding the LCM and comparing fractions.
Q: What are some common mistakes to avoid when rearranging fractions and decimals in descending order?
A: Some common mistakes to avoid when rearranging fractions and decimals in descending order include:
- Not converting decimals into fractions or percentages into decimals
- Not finding a common denominator when comparing fractions with different denominators
- Not comparing the numerators when fractions have a common denominator
- Not using a calculator or formula to find the LCM
Q: How can I practice rearranging fractions and decimals in descending order?
A: You can practice rearranging fractions and decimals in descending order by working through examples and exercises. You can also use online resources and calculators to help you practice.
Q: What are some real-world applications of rearranging fractions and decimals in descending order?
A: Rearranging fractions and decimals in descending order has many real-world applications, including:
- Calculating percentages and proportions
- Comparing and ordering data
- Solving mathematical problems and equations
- Working with financial and scientific data
In conclusion, rearranging fractions and decimals in descending order is an essential skill that has many real-world applications. By following the steps outlined in this article and practicing regularly, you can become proficient in rearranging fractions and decimals in descending order.