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Comparing and Ordering Fractions

Word of the Day: Biography- a written history of a person’s life.

Page 47 in JBHM binder (DOK 3) Bell Ringer: Page 47 in JBHM binder (DOK 3)

Focus/Introduction: Friday, we began talking about fractions and the need for them. What is a proper fraction? What is an improper fraction? What is a mixed number? How do you change an improper fraction to a mixed number and vice versa. Today, we will be comparing and ordering fractions

Guided Practice: (DOK 1) Comparing and Ordering Fractions Sometimes we have fractions that we need to compare and order. This can be a little tricky, especially if the fractions are not some of our benchmark fractions or common fractions that we use every day.

Remember the comparison symbols > (greater than), < (less than), and = (equal to). These will be used to compare fractions just as they were to compare whole numbers and decimals. In the cookie example, it can be noted that the fraction with the larger denominator actually represents the smaller part of the whole or fraction. This comparison of the two pieces from our cookie example can be expressed using mathematical terms and symbols. Show them that 1/16 is less than 1/8.

Exploring Fractions on a Number Line  

Comparing Fractions It is quite simple to compare fractions when the denominator is the same. These are called like fractions. To compare them, simply compare the numerators. is less than

When comparing fractions with unlike denominators, there is more involved. Often, pictures are helpful to compare fractions. Draw a rectangle and shade in one-half. Draw another rectangle and shade in one-third.

This strategy can often be deceiving as it is difficult to draw pictures that accurately represent fractional parts. Also, it gets quite difficult when working with fractions involving higher numbers like 21/43.

There is another strategy that will always work and is quite simple There is another strategy that will always work and is quite simple. It will be referred to as criss-cross.

Strategy 1: Criss-cross This tells us which one is greater than (>) or less than (<). To do this, multiply the numerator in the first fraction by the denominator in the second fraction (2 x 4). Write the product above or below the first fraction. Then multiply the numerator in the second fraction by the denominator of the first fraction (3 x 3). Write the product above or below the second fraction. Compare the products (8 and 9). The result is the answer to comparing the fractions.

Compare:

Compare:

Compare:

Ordering Fractions Sometimes we are given more than two fractions to order from least to greatest or vice versa. When given this challenge, we can try a little math magic to make it fun and easy!

Multiply the 1st Numerator x 2nd Denominator x 3rd Denominator Multiply the 1st Numerator x 2nd Denominator x 3rd Denominator 2 x 4 x 2 = 16 This product is assigned to the fraction with the numerator that was used. Multiply the 2nd Numerator x the 3rd Denominator x 1st Denominator 1 x 2 x 3 = 6 Multiply the 3rd Numerator x 1st Denominator x 2nd Denominator 1 x 3 x 4 = 12

   

Example:  

 

Independent Practice: (DOK 1 and 2) Take Handout #2 from your JBHM binders. You will begin to work this in class and will finish this for homework. It is practice on comparing and ordering fractions.

Closure: NO. 1a Compare and order integers, decimals to the nearest ten-thousandths, like and unlike fractions, and mixed numbers using <, >, and =. (DOK 1) Remember to finish handout #2 for homework.