Content

• Steps
• Method 1 of 2: Evaluating fractions in your head
• Method 2 of 2: Visually evaluating fractions
• Tips
• Warnings

Estimate (or an educated guess) can be very helpful when it comes to fractions. If you are trying to figure out certain proportions without the data or time to find the exact value, the correct estimate will allow you to make the right decision. However, there is a fine line between judgment and guesswork. Consider these values ​​to improve the accuracy of your estimate.

Steps

Method 1 of 2: Evaluating fractions in your head

1. 1 Determine if you want to evaluate fractions. By evaluating a fraction, you can determine its approximate value, but most likely you will not find the exact value. Evaluate the fraction to get an approximate value, and use the appropriate measurements to solve the equation to find the exact value. A correct estimate will allow you to quickly find an approximate value, which is in no way accurate.
   • For example, a correct assessment can be useful in the following cases: when planning random events (to find the amount of materials needed), when expressing an idea (without the small details), when cooking some dishes (such as stews, where the exact amount of ingredients is not so important).
2. 2 Simplify the fraction if possible. It is much easier to evaluate a fraction in your head if you simplify it to the minimum value. For example, 4/8 can be simplified to 2/4 or 1/2. The last two fractions are equal to the original. If possible, simplify the fraction to make it easier to evaluate. Find the number that divides (entirely) both the numerator and the denominator of the fraction. If you divide the numerator and denominator by the same number, the fraction will be simplified, but its meaning will not change.
   • It is generally easier to work with smaller numbers than larger ones. If fractions have a common denominator, they can be divided by several numbers to bring them to a common denominator. For example, the fractions 4/16 and 6/8 can be divided by 4 and 2, respectively. You will get fractions 1/4 and 3/4.
   • Remember: if both the numerator and the denominator have an even number, the numerator and denominator can be divided by 2. The numerator and denominator will halve, but the value of the fraction will not change.
   • Make sure that when you divide the numerator and denominator by some number, you get whole numbers. Remember that if a fraction contains a fraction, it is very difficult to work with it.
3. 3 Round off the fraction. Do this to make it easier to evaluate the fraction.If the fraction cannot be simplified, round the numerator and / or denominator up or down to make it easier to estimate due to the exact value. The rounding of a fraction depends on many factors, in particular the number of very specific fractions and the number of parts that must be accounted for.
   • Rounding a fraction is rounding the numerator and / or denominator up or down to simplify the fraction. For example, the fraction 7/16 is quite difficult to evaluate in your head, but if you round it to 8/16 and then reduce it to 1/2, you get half a whole (that is, half of some value).
4. 4 Decide on the number of rounding options. If a fraction needs to be judged mentally, try rounding it in a way that makes it easier to work with. Since the skills of evaluating quantities (in particular fractions) in the mind depend on the person, you can round the fraction up or down. The simplest fractions need to be rounded to 0, 1/2, or 1, while more complex fractions need several rounding options.
   • Rounding a fraction to smaller parts (for example, eighths or sixteenths) is a difficult process that depends on the skill of the person, but in this case the result will be closer to the exact value.
5. 5 Select a rounding option for each fraction. In most cases, the original fraction will be closer to one rounding option than others. For example, 7/8 is closer to 1 (8/8) than 1/2 (4/8). But in some cases, the value of the original fraction is somewhere in the middle between the rounding options. For example, 65/100 can be rounded down to 60/100 or up to 70/100. Choose the rounding option that best matches the data presented. The number line will help you to clearly determine which rounding option the fraction is closer to.
   • Recall that you do not need to do something with fractions that fall into one of the rounding options.
6. 6 Remember the original and rounded fractions. Rounding a fraction up and down makes it easier to judge, but you shouldn't think of a rounded fraction as a real proportion. Therefore, be sure to remember the original fraction. Having memorized both fractions, you can easily work with them and, if necessary, support the conclusions with accurate data.
7. 7 Compare the rounded (and simplified) fraction with the original. Do this to refine the estimate based on the size of the original fraction. That is, in this way you can determine how much the estimate differs from the exact value. The estimated value is useful for visualizing or quickly making sense of the data presented, but you need to think about the difference between the estimate and the exact value.
   • 7/16 can be rounded to 8/16 or 1/2. 7/16 is pretty close to half a whole, but remember that the simplified fraction is slightly larger than the original. Mathematically, it can be written like this: (1/2 - 1/16).

Method 2 of 2: Visually evaluating fractions

1. 1 Determine the need for a visual assessment. A visual representation of a fraction will help depict proportions and make it easier for others to understand, especially if they are not good at math. A visual assessment is useful when comparing two fractions. The human eye easily compares and measures objects, even if the person has no mathematical experience. Visualizing something allows the brain to free itself from abstract thinking based on numbers. It is also recommended to use visual assessments to solve problems from everyday life.
   • For example, at first glance, the fraction 12/16 is larger than the fraction 7/8, but if you depict these fractions in a visual form, it turns out that the second fraction is larger than the first.
   • To represent fractions in a visual form, graphs are used in the form of lines and circles. Straight lines are better for displaying fractions, and circles (more precisely, pie charts) are better for displaying proportions.
2. 2 Choose a visual model. Different visual models correspond to different people.If you want to use a pie chart, rectangle, chart, or other visual model to depict proportions, it will not only simplify the estimation process, but also work with fractions in general.
   • Different proportions can be indicated by different shades or colors. For example, two (out of three) shaded sectors of a pie chart represent 2/3.
   • It is recommended to apply different visual models to the same fractions. So you can understand how different models depict the same proportions.
3. 3 Illustrate the fraction with physical objects. Using pieces of chocolate, baby cubes, or even pebbles, you can evaluate the fraction by combining different pieces into groups. If the whole value has 50 parts, the fractions 17/50 and 33/50 can be illustrated by dividing the 50 parts into two groups. Thus, you can visually determine how fractions relate to each other.
   • By illustrating two or more fractions next to each other, you can easily figure out which fraction is greater (or less). The human eye quickly detects size differences, so this is a great way to compare multiple fractions.
4. 4 Place the proportions next to each other. In everyday life, fractions are found at every turn, and we often make choices based on their assessment, without even thinking about it. To practice visualizing fractions, place two objects of different heights next to each other. Now try to determine which part of the larger object matches the smaller one.
   • To check your answer, measure items with a ruler.
5. 5 Create a pie chart. A pie chart is a great visual model that allows you to depict proportions. If you have a better visual mind, depict the rounded fractions as circles. Now evaluate the fractions; there is no need to rely on rounded numbers, which can lead to inaccurate results. Unlike charts (which tend to be based on accurate data), a pie chart is a way to quickly display data. As a rule, it is easier to visually analyze the sectors of a circle because it represents an integer value.

Tips

• The more often you evaluate fractions, the more accurate the evaluation becomes. If you run into problems at first, keep trying and checking the answers wherever you can. This will help you understand if estimates are becoming more accurate.
• A common fraction cannot be greater than 1. It must be greater than 0, but less than 1.

Warnings

• The estimate is in no way a substitute for the exact value. If an accurate result is needed, do not rely on the estimated value.