Is 87 Over 21 Equivalent To 168 Over 43

Are 87/21 and 168/43 Equivalent Fractions? Unraveling the Mystery

Fractions represent parts of a whole. Understanding if two fractions are equivalent is crucial in various fields, from baking and sewing to engineering and finance. This article explores whether 87/21 and 168/43 represent the same portion of a whole, demystifying the process of comparing and simplifying fractions.

1. Understanding Equivalent Fractions

Equivalent fractions represent the same value, even though they look different. Imagine slicing a pizza: one-half (1/2) is the same as two-quarters (2/4) or four-eighths (4/8). They all represent half the pizza. The key to finding equivalent fractions lies in multiplying or dividing both the numerator (top number) and the denominator (bottom number) by the same non-zero number. This is because we're essentially multiplying or dividing the fraction by 1 (e.g., 2/2 = 1, 5/5 = 1).

2. Method 1: Simplifying Fractions to their Lowest Terms

The simplest way to check if two fractions are equivalent is to reduce each fraction to its simplest form. This involves finding the greatest common divisor (GCD) – the largest number that divides both the numerator and denominator without leaving a remainder. Let's apply this to our fractions:

87/21: The GCD of 87 and 21 is 3. Dividing both the numerator and denominator by 3, we get 29/7.

168/43: This fraction cannot be simplified further because 168 and 43 have no common divisors other than 1. Their GCD is 1.

Since 29/7 and 168/43 are different in their simplest forms, the original fractions, 87/21 and 168/43, are not equivalent.

3. Method 2: Cross-Multiplication

Another method to determine if two fractions are equivalent is cross-multiplication. This involves multiplying the numerator of one fraction by the denominator of the other, and vice versa. If the products are equal, the fractions are equivalent.

Let's apply this to 87/21 and 168/43:

87 x 43 = 3741
21 x 168 = 3528

Since 3741 ≠ 3528, the fractions 87/21 and 168/43 are not equivalent.

4. Practical Example: Recipe Scaling

Imagine you have a recipe that calls for 87 grams of flour and 21 grams of sugar (87/21 ratio). You want to scale the recipe up, but you only have a measuring tool that uses 43 grams as its base unit. Can you accurately scale the recipe based on a 168/43 ratio? Based on our analysis, the answer is no. Using a 168/43 ratio would result in a different flour-to-sugar proportion than the original recipe.

5. Visual Representation

Visualizing fractions can also help understand equivalence. Imagine two identical rectangles. Divide one into 21 equal parts and shade 87 of them. Divide the other into 43 equal parts and shade 168 of them. The shaded areas would not be equal, visually demonstrating that the fractions are not equivalent.

Key Takeaways

Equivalent fractions represent the same value, even with different numerators and denominators.
Simplifying fractions to their lowest terms is a straightforward way to check for equivalence.
Cross-multiplication offers another effective method to compare fractions.
Understanding equivalent fractions is essential for various applications, including scaling recipes, solving equations, and working with proportions.

Frequently Asked Questions (FAQs)

1. What if I get a decimal when simplifying a fraction? If you obtain a decimal after simplifying, it means the fractions are likely not equivalent. However, always check for rounding errors during calculations.

2. Can I use a calculator to check for equivalent fractions? Yes, you can use a calculator to perform the cross-multiplication or to simplify fractions to their lowest terms.

3. Why is finding the greatest common divisor (GCD) important? The GCD helps reduce fractions to their simplest form, making it easier to compare and work with them.

4. Are there other methods to determine equivalent fractions? Yes, you can also use the concept of ratios and proportions to solve for equivalent fractions.

5. What if one fraction is a mixed number? Convert the mixed number to an improper fraction before applying any of the methods mentioned above. For example, convert 2 1/2 to 5/2 before comparison.

Search Results:

台式机的CPU温度经常80至90摄氏度，可能造成损害吗? - 知乎 而对于最大工作温度Tjmax和Tcmax，往往设定较高（80°C~100°C都有，目前的CPU大都在90°C以上），接近或超出最大工作温度，则会因电子迁移效应导致CPU寿命缩短。而目前电 …

67、71、78、84、87、98、104、108位键盘的有多少不同？ 罗技（G）1适配攻击鲨M86无线机械键盘 84键相较于87键，设计更为紧凑。（减少的键位各家不太一样）

Eaanticheatservice not launching Error 87 : The parameter is … 11 Jun 2024 · I am having the same problem. In my case, I have change the service to start automatically but it doesn´t work, even if I restart the computer it comes back to manual start, …

知乎 - 有问题，就会有答案 知乎，中文互联网高质量的问答社区和创作者聚集的原创内容平台，于 2011 年 1 月正式上线，以「让人们更好的分享知识、经验和见解，找到自己的解答」为品牌使命。知乎凭借认真、专业 …

VPN (IKEv2) connection failure 87 the parameter is incorrect ... This VPN had worked fine a couple of weeks ago before I upgraded the system to the latest release. Now is Win 10 Pro Version 1809 Build 17763.195 Today I use the same VPN, and a …

以ftp开头的网址怎么打开? - 知乎 FTP开头的网址可以通过浏览器、FTP客户端或命令行工具打开。

女性文胸杯型尺寸尺码对照表？ - 知乎 Q：某位妹纸下胸围76，上胸围87，请问她的罩杯是什么？ A：87-76=11 11在10到12.5之间，建议选择B罩杯~ TIPS: 1.如果脂肪偏多：量出上下围之差为某个杯级时，罩杯的级数应该选大一级 …

【实测月更】2025年机械键盘选购指南，入坑必看！玩游戏、码 … 5 Feb 2025 · 目前 87 配列的卷王产品，三模 gasket 结构单键开槽设计，ixpe 轴下垫加上 pet 声优垫的设计，让 F87 在200元以内声音无敌，轴体方面灰木 V3 属于类银轴适合打游戏用，灵动 …

哪位大神知道这种键盘没有num lock键怎么解锁的啊 - 知乎 14 Dec 2022 · 你现在的情况就是因为 numlock 锁住了。因为你没有小键盘所以自然是没有这个按键的。有些电脑可以通过快捷键，比如三星电脑FN+F11就是numlock键。不过你挨个试成功 …