Equivalent Fractions and Comparing Fractions

Use Models to Compare Fractions: Same Denominator

Prior Knowledge:

Identify and recognize the following fractions:

1. Which nation’s flag is ¼ red?

2. Compare which is greater 2/3 or 1/3 = ?

3. How many fractions lie between 0 and 1?

Answers:

1. The fourth nation’s (Mexico) flag is ¼ red.

2. Both fractions have equal denominators 3, and the numerators are 2 > 1.

      Therefore,  2/3 >1/3

3. There would be infinite fractions between 0 and 1.

 Example: 1/2,1/3,2/3 ……., infinity.

Introduction:

The same denominator method

When two fractions have the same denominator, they are easy to compare:

For instance, 4/9 is less than, 5/9  (because 4 < 5)

 4/9 is 4 times the unit fraction 1/9   

 5/9 is 5 times the unit fraction 1/9

Draw 1/9 strips, 

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

If two fractions have the same denominator, the fraction with the smaller numerator is the smaller fraction.

Comparison Using Symbols:  4/9<5/9

Example

Which is greater, 3/6 or 2/6 ?

 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

If two fractions have the same denominator, the fraction with the greater numerator is the greater fraction.

Comparison Using Symbols:  3/6 > 2/6

Real-life Example

A Pizza was divided into three equal parts (slices).

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:  

Comparison Using Symbols:  3/3>2/3

Use Models to Compare Fractions: Same Numerator

Look at the models

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?

Comparison Using Symbols: 

                    1/2 >1/4 > 1/6

What happens to the denominator as your pieces get smaller?

Example

Tom and Jerry each made a pie. The pies were the same size. Tom cut his pie into 8 slices; Jerry cut him into 6 slices. They each ate 2 slices of their own pie. Who ate more?

Draw a model. Write the fraction that each ate

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 the denominators.

Sixths are bigger than eighth, so 2/6 is bigger than 2/8.
So, Jerry ate more pie.

Comparison Using Symbols:  2/6  > 2/8

Exercise:

1. 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?
2. What is the equivalent fraction of 3/4 with denominator 20?
3. Raj has 26 toffees. He gave one-half to his friend. How many toffees did he give to his friend?
4. Write two comparison statements about the fractions shown below.

5. Which is greater ¼  or 1/6?  Draw fraction strips to complete the diagram and answer the question.

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 do fractions that refer to the same-sized whole and have the same denominator compare their numerators?
• How do 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 do draw area models to compare two fractions?

Concept Map: