You are watching: Fractions closer to 1 than to 0

Although a number line diagram is not provided, numerous students may choose to draw one; teachers might suggest doing for this reason if a student is struggling through the problem. For plenty of students, developing a number line will help them acknowledge that $frac45$ is only $frac15$ indigenous 1 and also that $frac54$ is just $frac14$ from 1 even though the loved one size that the fountain is similar and the 2 fractions space plotted on various sides of 1 top top the number line. Some students may select to develop two number lines, for this reason they deserve to partition one right into fourths and also one into fifths, and then compare them.

It is feasible to fix this trouble using typical denominators. While not technically incorrect, that equipment is not shown due to the fact that first, students perform not occupational with usual denominators until fourth grade, and also second, also when lock know how to find usual denominators, they must recognize in a instance like this the straight-forward reasoning around the relative sizes the unit fountain is more efficient.

Below is a list of related rememberingsomer.com in this set in bespeak of sophistication:

Locating Fractions much less than One top top the Number LineLocating Fractions higher than One ~ above the Number LineClosest to $frac12$Find 1Find $frac23$Which is Closer come 1?## Solutions

Solution:3.NF.2 Plot Points to Compare

Many student will sketch something like the complying with number line diagram:

Fifths room closer with each other than fourths. $frac45$ is $frac15$ from 1. $frac54$ is $frac14$ indigenous 1. For this reason $frac45$ is closer come 1 보다 $frac54$.

Solution:3.NF.2 Recognize and also Reason

A couple of students might simply reason in the following means (stated in student language rather than the much more formal language supplied here):

If we division the segment native 0 to 1 in 4 equal-length segments(so each has a size of $frac14$), and we likewise divide the segment from 0 to 1 into 5 equal-length segment (so each has a size of $frac15$), the segments of size $frac14$ will certainly be much longer than the segments of length $frac15$ since there space fewer of them.

The distance between $frac45$ and also 1 is $frac15$, and also the distance between $frac54$ and 1 is $frac14$.

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so $frac45$ is closer to 1 than $frac54$

A correct systems does require that the student explain how that or she figured out that $frac45$ is closer come 1.