# Telling the relationship between fraction less than one

### Relationships Between Fractions, Decimals, Ratios & Percentages | UTAS

Number tiles (1 - 9) allow students to experiment with fractions less than 1 in a of the task tells us that there are 35 more possibilities to try for the first fraction. I try telling myself that fractions are less than 1 and therefore the math Doctor Peterson Subject: Re: Division of fractions producing a larger. You often need to know when one fraction is greater or less than another fraction. Since a fraction is a part of a whole, to find the greater fraction you need to find.

I've divided them into 7 equal chunks. Let me select 4 out of the 7.

## Comparing fractions with > and < symbols

So, that's 1, 2, 3, 4. And so it's pretty clear that on the left-hand side, we are shading in more of the whole than on the right-hand side. And the way that we can state that comparison mathematically is with the greater than symbol. Now, the greater than and less than symbols can sometimes be confusing. This is greater than. This is less than. And the way that I remember it is that the greater than symbol, either symbol, the small pointy side is always on the side of the smaller number, and the big open side is always on the side of the larger number.

So, here I have different denominators, but I have the same numerator.

### Comparing fractions with > and < symbols (video) | Khan Academy

And so I encourage you to pause this video and draw maybe little boxes like this and try to judge for yourself which of these is a larger fraction, represents a larger number. Well, let's color them in. The red area is one tenth or zero point one 0. A visual model for decimal fractions The following video uses a thousandths grid in a similar way, to demonstrate writing decimal fractions: It is written as or 0.

It is easy to see that this shaded area is one half of the whole grid.

## Multiplying by a Fraction Less than One

This shaded area can also be broken up into 50 hundredths. The fraction 50 hundredths is equivalent to thousandths.

- University of Tasmania, Australia

Furthermore, the shaded area in the video can be broken up into five tenths. The fraction five tenths is equivalent to the fraction 50 hundredths and thousandths All of these fractions have the same value of one halfand so they are equivalent fractions.

Unlike whole numbers, a zero on the end right hand side does not change the value of the decimal. However, the zeros can sometimes assist when adding and subtracting decimals.

This is the opportunity to ask students how they would make this decision. Be prepared for some interesting answers.

Three approaches that work are show below and all involve creating a 'level playing field' by using the same whole to show each fraction. Diagram - Draw the same whole twice. Depending on the fractions being compared, this process needs a reasonable amount of time and accurate measurement and consideration of scale.

If the drawing is too small the decision won't be conclusive. Further if it was necessary to know by how much one was smaller than the other, there is no real answer except 'that much' and pointing. However, choosing not only a common whole, but a way to divide it into parts that accommodate both fractions: The common denominator could be chosen by trial and improve It only works for fifths. Then using equivalent fractions and the identity property of multiplication: Darren's Method Darren discovered this method in Grade 5 while doing exercises on comparing fractions.

Multiply on the cross and write the answers above the numbers The one with the smaller 'hat' is the smaller fraction. Probably Darren didn't know why this algorithm works. So, over to you: How many solutions are there?

How do you know when you have found them all? We look forward to posting solutions from your students here. Extension What happens if we investigate greater than fractions?