Key Concepts
- Use models to compare fractions: Same Denominator
- Use models to compare fractions: Same Numerator
Introduction:
The same denominator method
- The denominator is the bottom number in a fraction.
- It shows how many equal parts the item is divided.
When two fractions have the same denominator, they are easy to compare:
For instance, 4/9 is less than, 5/9 (because 4 < 5)
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5954.png)
4/9 is 4 times the unit fraction 1/9
5/9 is 5 times the unit fraction 1/9
Draw 𝟏/𝟗 strips,
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/10/image-22.png)
Here, we can observe that denominators are the same in both fractions.
So, we must compare numerators.
Numerator 4 is less than 5 (4 < 5)
∴4/9 is less than 5/9
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/10/image-20.png)
Comparison using symbols: 4/9 < 5/9
Example
Which is greater, 3/6 or 2/6 ?
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5955-1024x487.png)
3/6 is 3 of the unit fraction 1/6
2/6 is 2 of the unit fraction 1/6
So, 3/6 is greater than 2/6
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/10/image-21.png)
Comparison using symbols: 3/6 > 2/6
Real-life Example
A Pizza was divided into three equal parts (slices).
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5956.png)
In the diagram, the whole is represented with the fraction 3/3
If you take out one part, the remaining portion represents 2/3
In this example, both denominators are the same, so we must compare numerators.
The numerator 3 is greater than 2.
∴ 3/3 is greater than 2/3.
Using 𝟏/𝟑 strips:
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5957-1024x487.png)
Comparison using symbols: 3/3 > 2/3
13.4 Use models to compare fractions: Same Numerator
Look at the models
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5958-1024x336.png)
They each have 1 piece shaded in. So, all we have to compare is the size of each piece
Which pie has the largest shaded part?
- The pie which is partitioned into halves
- The denominator with the smallest number gives you the biggest size pieces
Comparison using symbols:
1/2 > 1/4 > 1/6
What happens to the denominator as your pieces get smaller?
- The number in the denominator gets bigger
- The same numerator is equal to the same number of pieces being referred to
- So, if the fractions refer to the same whole, and the numerators are the same, then the number of pieces being compared is the same.
Example
Tom and Jerry each made a pie. The pies were the same size. Tom cut his pie into 8 slices; Jerry cut his into 6 slices. They each ate 2 slices of their own pie. Who ate more?
Draw a model. Write the fraction that each ate
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5959.png)
Did they eat the same number of pieces?
Are the numerators the same?
We use fraction strips to compare the size of the pieces or compare the denominators.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5960.png)
Sixths are bigger than eighths, so
2/6 is bigger than 2/8.
So, Jerry ate more pie.
Comparison using symbols: 2/6 > 2/8
Exercise:
- Rani reads 1/6 of a book in the morning; she reads 4/6 of the book in the afternoon. What fraction of the book does she read?
- What is the equivalent fraction of 3/4 with denominator 20?
- Raj has 26 toffees. He gave one-half to his friend. How many toffees did he give to his friend?
- Write two comparison statements about the fractions shown below.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5972.png)
5. Which is greater ¼ or 1/6 ? Draw fraction strips to complete the diagram and answer the question.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5973.png)
6. Maria and Nina each ordered a small pizza. Maria ate 3/8 of her pizza. Nina ate 3/6 of her pizza. Who ate more pizza?
7. Explain Why is 1/6 greater than 1/8 but less than 1/3?
8. Two pizzas were each cut into sixths. Ashraf, Drew, and Katie shared the pizzas equally. How many sixths did each friend get?
9. Eric and Frank want to share 4/3 feet of rope equally. What length of rope should each friend get? Explain how to use a drawing to help solve the problem.
10. Ronald spent the day making a painting for his friend. At the end of the day, Ronald finished ¼ of the painting. If he is able to finish as much of a painting each day he works, how long will it take Ronald to make 2 whole paintings?
What we have learned:
- How to compare fractions that refer to the same-sized whole and have the same denominator by comparing their numerators
- How to compare fractions that refer to the same-sized whole and have the same numerator by comparing their denominators
- How to use symbols (>, <, =) to compare fractions with different numerators and denominators
- Recognize that to compare two fractions both must refer to the same whole
- How to draw area models to compare two fractions
- How to compare fractions that refer to the same-sized whole and have the same denominator by comparing their numerators
- How to compare fractions that refer to the same-sized whole and have the same numerator by comparing their denominators
- How to use symbols (>, <, =) to compare fractions with different numerators and denominators
- Recognize that to compare two fractions both must refer to the same whole
- How to draw area models to compare two fractions
Concept Map
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5974.png)
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5975.png)
![Same Numerator and Denominator Method](/_next/image?url=https%3A%2F%2Fwww.turito.com%2Flearn-internal%2Fwp-content%2Fuploads%2F2022%2F09%2FSame-Numerator-and-Denominator-Method.png&w=1920&q=50)
![demo](https://a.storyblok.com/f/128066/544x376/641160f2e6/learn_toast.webp)
Comments: