How to Estimate Fractions
Decide if estimation is appropriate., Simplify the fractions where possible.Fractions will always be easier to deal with mentally if you simply them to their lowest common denominators., Round the fractions.Rounding fractions makes them easier to...
Step-by-Step Guide
-
Step 1: Decide if estimation is appropriate.
Estimating a fraction will give you the gist of the fraction.
However, you'll seldom guess the exact answer with it.
If you only need a general idea of the answer, estimations are helpful.
However, if you need to give an exact answer, solve your equation with exact measurements.
A good estimation will convey the general idea across quickly, and won't attempt to pass itself off as an exact answer.
Examples of situations that favour estimations include planning casual events (roughly gauging supplies needed), expressing an idea verbally (getting the idea across without the nitty-gritty details) or some cooking situations like stews, where exact measurements aren't needed in the final product. -
Step 2: Simplify the fractions where possible.Fractions will always be easier to deal with mentally if you simply them to their lowest common denominators.
A fraction listed as 4/8, for example, can be expressed as 2/4 or 1/2.
These are different ways of expressing the exact same fraction.
It's a good idea to simplify your fractions however possible in order to make your estimating easier.
Find a number you can divide the top and bottom half of a fraction by equally.
Dividing them by the same number will reduce the size of the numbers, while keeping the proportions intact.
Smaller numbers are generally easier to work with than big numbers.
If all of the numbers included share a common denominator, it's possible to divide them by that root accordingly.
For example, 4/16 and 6/8 could be divided by 4 and 2 respectively.
This would result in 1/4 and 3/4.Generally speaking, if both the top and bottom of your fraction are even, you can divide both sides by
2.
Both sides will be only half as big as before, and the proportion will remain the same.
Make sure you keep both sides of your fraction whole while dividing.
Making fractions out of fractions by dividing denominators improperly will make your fraction much more frustrating to deal with. , If you have a fraction that can't be simplified as is, moving it slightly up or down can allow you to simplify at the cost of the "exact" answer.
Rounding fractions up or down will depend on a lot of things, specifically whether you're dealing with a lot of very specific fractions, and whether there are few enough parts to still make sense. "Rounding" a fraction means bringing it slightly up or down so that the fraction may be simplified.
For example, 7/16 may be a tricky fraction to visualize mentally, but if you round it up slightly to 8/16, it becomes exactly half (1/2) of the whole. , If you're intent on using mental math, it's a good idea to try to round your fractions down to proportions you're most comfortable with.
Because personal skills with mental math will depend on the individual, you can make the rounding as big or small as you'd like.
Rounding to halves (0, 1/2, 1) only makes sense for the simplest fractions, while more complex proportions will benefit from a greater number of rounding options.
Rounding your fractions into smaller portions (like eighths or sixteenths) may be more difficult depending on your level of skill, but you'll find your answer is closer to the real answer., Most of the time, a fraction will be closer to one of its adjacent rounding options than the other. 7/8, for example, is closer to 1 (8/8) than 1/2 (4/8).
In some cases however, it may lie somewhere in the middle.
A fraction like 65/100 can be rounded up or down to 60/100 or 70/100.
You can make a decision on which you think best represents the data given.
Mapping out a number line will help indicate visually what rounding option a fraction is closest to.Although it may go without saying, you won't need to do anything to fractions that already fall on one of your rounding options. , Although rounding fractions up and down could be helpful for the sake of estimating, it's important that you don't take these new proportions as an accurate report of the real proportions.Keep the original, precise fractions at hand.
Having both the exact and estimated versions available is useful, because you'll be able to communicate the idea easily, as well as back it up with the hard data when needed. , Once you have a rounded, simplified estimation you're comfortable with, you can sharpen your estimation further by propping it up against the original fraction.
This way, you can identify how your estimate might vary from the real number.
While an estimate is a great way to visualize or think broadly about the data, you should reflect on how close your fraction really is.
A 7/16 fraction could be rounded up to 8/16 (or 1/2). 7/16 may still be seen roughly as a half, but you should remember that the simplified version is slightly more than the real number.
A mathematical way of expressing this would be: (1/2
- 1/16). -
Step 3: Round the fractions.Rounding fractions makes them easier to deal with.
-
Step 4: Choose a suitable number of rounding options.
-
Step 5: Choose a rounding option for each of your fractions.
-
Step 6: Keep your rounding changes in mind.
-
Step 7: Compare your estimation with the precise fractions.
Detailed Guide
Estimating a fraction will give you the gist of the fraction.
However, you'll seldom guess the exact answer with it.
If you only need a general idea of the answer, estimations are helpful.
However, if you need to give an exact answer, solve your equation with exact measurements.
A good estimation will convey the general idea across quickly, and won't attempt to pass itself off as an exact answer.
Examples of situations that favour estimations include planning casual events (roughly gauging supplies needed), expressing an idea verbally (getting the idea across without the nitty-gritty details) or some cooking situations like stews, where exact measurements aren't needed in the final product.
A fraction listed as 4/8, for example, can be expressed as 2/4 or 1/2.
These are different ways of expressing the exact same fraction.
It's a good idea to simplify your fractions however possible in order to make your estimating easier.
Find a number you can divide the top and bottom half of a fraction by equally.
Dividing them by the same number will reduce the size of the numbers, while keeping the proportions intact.
Smaller numbers are generally easier to work with than big numbers.
If all of the numbers included share a common denominator, it's possible to divide them by that root accordingly.
For example, 4/16 and 6/8 could be divided by 4 and 2 respectively.
This would result in 1/4 and 3/4.Generally speaking, if both the top and bottom of your fraction are even, you can divide both sides by
2.
Both sides will be only half as big as before, and the proportion will remain the same.
Make sure you keep both sides of your fraction whole while dividing.
Making fractions out of fractions by dividing denominators improperly will make your fraction much more frustrating to deal with. , If you have a fraction that can't be simplified as is, moving it slightly up or down can allow you to simplify at the cost of the "exact" answer.
Rounding fractions up or down will depend on a lot of things, specifically whether you're dealing with a lot of very specific fractions, and whether there are few enough parts to still make sense. "Rounding" a fraction means bringing it slightly up or down so that the fraction may be simplified.
For example, 7/16 may be a tricky fraction to visualize mentally, but if you round it up slightly to 8/16, it becomes exactly half (1/2) of the whole. , If you're intent on using mental math, it's a good idea to try to round your fractions down to proportions you're most comfortable with.
Because personal skills with mental math will depend on the individual, you can make the rounding as big or small as you'd like.
Rounding to halves (0, 1/2, 1) only makes sense for the simplest fractions, while more complex proportions will benefit from a greater number of rounding options.
Rounding your fractions into smaller portions (like eighths or sixteenths) may be more difficult depending on your level of skill, but you'll find your answer is closer to the real answer., Most of the time, a fraction will be closer to one of its adjacent rounding options than the other. 7/8, for example, is closer to 1 (8/8) than 1/2 (4/8).
In some cases however, it may lie somewhere in the middle.
A fraction like 65/100 can be rounded up or down to 60/100 or 70/100.
You can make a decision on which you think best represents the data given.
Mapping out a number line will help indicate visually what rounding option a fraction is closest to.Although it may go without saying, you won't need to do anything to fractions that already fall on one of your rounding options. , Although rounding fractions up and down could be helpful for the sake of estimating, it's important that you don't take these new proportions as an accurate report of the real proportions.Keep the original, precise fractions at hand.
Having both the exact and estimated versions available is useful, because you'll be able to communicate the idea easily, as well as back it up with the hard data when needed. , Once you have a rounded, simplified estimation you're comfortable with, you can sharpen your estimation further by propping it up against the original fraction.
This way, you can identify how your estimate might vary from the real number.
While an estimate is a great way to visualize or think broadly about the data, you should reflect on how close your fraction really is.
A 7/16 fraction could be rounded up to 8/16 (or 1/2). 7/16 may still be seen roughly as a half, but you should remember that the simplified version is slightly more than the real number.
A mathematical way of expressing this would be: (1/2
- 1/16).
About the Author
Rachel Richardson
Dedicated to helping readers learn new skills in lifestyle and beyond.
Rate This Guide
How helpful was this guide? Click to rate: