Is 5 8 Bigger Than 1 3? The 199 New Answer

I recently read the book Beyond Pizzas & Pies: 10 Essential Strategies for Supporting Fraction Sense by Julie McNamara and Meghan Shaughnessy.

I posted the following image on Twitter while reading during my daughter’s swim class.

My colleague Hedge replied that he was challenged by a middle school teacher on this very subject.

I let them know that a few years ago, when I was a digital curriculum developer, I was also challenged for this idea. The argument I heard at the time was that using context to check the correctness of fractional comparisons would be against the fact that fractions are numbers. Therefore, 1/2 is always greater than 1/3, regardless of context. I wondered about that at the time, but I still felt it was important to show context.

Jump ahead and I’ve been thinking about this idea all day. I think I finally understand why we need to be careful about what we say about the role of context when comparing fractions. I may be completely off the mark, but I’ll still share my thoughts and let you decide in the comments whether you want to challenge my thoughts or share an alternative point of view.

Let’s start with whole numbers. If I told you to compare 3 and 6, you would probably say “3 is less than 6” or “6 is greater than 3”. This is how the numbers 3 and 6 are related.

Now what if I showed you these two pictures of 3 and 6: (As illustrated by my daughter’s toys.)

Technically the 3 dolls are bigger and therefore make up more stuff, but does that really mean that 3 is now bigger than 6? In the end, my daughter has fewer dolls (3) than figures (6). The context does not fundamentally change the relationship between the numbers 3 and 6.

In this case I don’t even know how to justify that she has more when I refer to the dolls. Sure, they’re bigger, but she might prefer to have more things to play with, and chooses the 6 figures even though they’re smaller overall.

Let’s continue by looking at this from a fractional perspective. Now I take 1/3 of the dolls and 1/2 of the figures.

Consistent with the idea that context should determine when one number is larger than another, I should be confident that 1/3 of the puppets is larger than 1/2 of the figures because 1 puppet is so much larger than the 3 characters. Oh wait, or should I be thinking that 1/2 of the figures is larger than 1/3 of the dolls because I ended up with 3 figures, which is a larger number of things than 1 doll? It’s not that clear cut, even if I try to let the context dictate how to interpret the fractions.

It boils down to breaks representing a relationship. When I think about the relationships each fraction represents, 1/2 is always greater than 1/3 no matter how I try to rotate it. Looking back at my examples, taking 1/2 of the figurine group means I’m taking a larger proportion of that group (this whole) than if I take 1/3 of the puppet group (a different whole, but still a whole) . The size of things in my group (total) doesn’t matter because the relationship represented by 1/2 is larger than the relationship represented by 1/3.

Does this mean that we should ignore contexts altogether? no There’s still a lot of debate about who ate more pizza when one person eats half of a small pizza and another person eats a third of a large pizza. Context is still interesting to discuss and helps students use math to interpret the world around them. However, if our goal is to compare fractions, then 1/2 is greater than 1/3 every time.

That’s the argument I came up with today, trying to understand the criticism I’ve heard. Now that you’ve read it, what do you think?

It can be difficult to remember which inequality sign or symbol to use in a number comparison, but we have a simple memory trick that can help!

Notice how the inequality symbol has a wide end and a narrow end?

The wide end opens to the larger value and the narrow end points to the smaller value. If we describe the image below from left to right, it reads that all spider people are bigger (or taller) than just a spider ham.

If we flip things around, we can still read it left-to-right, but now it reads like one Spider-Ham is smaller (or smaller) than all of the Spider People.

wide end

open for

larger number

How do we find the larger number? 🕵🏿‍♀️

The larger digit is farther from 0 on the number line. When we compare numbers, we compare place values ​​from left to right. The number that has the first place value with a on the number line. The number furthest to the right on the number line is the larger number. − 4 − 3 − 2 − 1 0 1 2 3 4 Move left Move right Remember that numbers are larger further to the right, by imagining a phone’s signal bars – the bars get bigger and stronger the further we go go right. This also means that any positive number is greater than any negative number 💡. Why is a larger negative number smaller than a smaller negative number? 🤔 Remember that as we move right on the number line, the numbers get bigger. For negative numbers, you can think of “greater than” as meaning “which number is less negative (or more positive)”. − 7 − 2 0 − 2 > − 7 Since −2 is further to the right than −7, −2 is greater than −7. Calculator Calculator Lesson Practice Practice Check out our or the and sections to learn more about comparing numbers, fractions and decimals and test your understanding. Explore Calculator

We can apply the same concept to comparing numbers. The sign should always be that

Question:

How many 1/3 cups do you need to make 1/2 cup?

Divide fractions:

When we have a number that is divided by a fraction, we need to multiply by the inverse of the fraction. This means that when we divide by 2/7, we are actually multiplying by 7/2 to get our result. The product of the multiplication can then often be reduced by factoring both numbers.

Answer and explanation: 1

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Welcome to the Smartick Blog! In this week’s post, we’ll learn how to calculate halves, thirds, and quarters. These expressions are used not only in mathematical problems but also in everyday life.

do you know what they are Do you know how to calculate them? In this post you will see how easy it is to calculate halves, thirds and quarters.

halves

One half equals the fraction: 1/2. Therefore it is half of any amount. Half is calculated by dividing by 2.

For example:

One half of 10 = ½ of 10 = 10/2 = 5.

One half of 34 = ½ of 34 = 34/2 = 17.

Three halves of 14 = 3/2 of 14 = 3 x 14/2 = 3 x 7 = 21.

one-third

A third equals the fraction: 1/3. So it’s a third of the amount. Thirds are calculated by dividing by 3.

For example:

A third of 24 = 1/3 of 24 = 24/3 = 8.

A third of 33 = 1/3 of 33 = 33/3 = 11.

Five thirds of 15 = 5/3 of 15 = 5 x 15/3 = 5 x 5 = 25.

Quarter

A quarter equals the fraction: 1/4. So it’s a quarter of the amount. Quarters are calculated by dividing by 4.

For example:

A quarter of 20 = ¼ of 20 = 20/4 = 5.

A quarter of 28 = ¼ of 28 = 28/4 = 7.

Seven quarters of 8 = 7/4 of 8 = 7 x 8/4 = 7 x 2 = 14.

Did you learn about halves, thirds and quarters? Feel free to share this post with your friends and colleagues so they can learn too. And remember, the best way to learn these calculations and more is to sign up for Smartick and try it for free!

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If we want to compare two fractions, we must have the same denominator. So we need the LCM (least common multiple) of #4# and #3#, which is #12#. So we need to multiply 4 by #3# and 3 by #4#

Remember that whatever you do below must be done above.

For #3/4# we multiply 3 down (denominator), so we need to multiply #3# up (numerator).

For #2/3# we multiply #4# down, so we need to multiply #4# up.

#(3xx3)/(4xx3)=9/12# and #(2xx4)/(3xx4)=8/12#

Now just look at the counts of the two answers. #9# is bigger than #8#, so #9/12# is bigger! #9/12# was originally #3/4# .

So #3/4# is greater than #2/3# .

I hope you understood this and my source is my knowledge!

When comparing two fractions, the denominator of the first fraction must be equal to the denominator of the second fraction. In this case, the two denominators are different, resulting in fractions and unequals. The first step is to find the lowest common denominator (LCD) for both fractions and .

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Stay up to date with Quantitative Aptitude Questions and Answers with Testbook. Learn more about simplification and learn about the concept of fractions.