Multiplying Mixed Numbers

Week 6 Notes

Monday, 9-28-15

Multiplying Mixed Numbers

Students will practice multiplying fractions, including mixed numbers. Mixed numbers are whole numbers with fractions.

An example of a mixed number would be 12 34 . Students must first change their mixed number into an improper fraction by multiplying the denominator with the whole number and then adding the numerator to the answer (product). The denominator will stay the same. So, the improper fraction for 12 34 would be 514 (4*12=48, 48+3=51).

Once your fraction is in the ab format, then you can multiply the numerator and multiply the denominator. If your answer is an improper fraction, I would like for it to be changed to a mixed number by dividing. This is a skill that was taught in 5th grade as well.

Example:

To change 125 to a mixed number, you divide 12 by 5, how many 5’s go into 12? 2….2 times 5 equals 10….12-10=2 this remainder 2 becomes the numerator of the final answer and the 5 will be the denominator in the final answer. The whole number will be 2. The final answer is 225.

If you multiply a whole number with a fraction or mixed number, the whole number is put into a fraction by writing it over 1. For example, 7 equals 71 .

Tuesday, 9-29-15

Dividing Fractions

Before we dive into dividing fraction, let’s review parts of the division problem. I found this on the internet (http://www.ducksters.com/kidsmath/division_basics.php) and thought it was worth reviewing:

Signs for Division
There are a number of signs that people may use to indicate division. The most common one is ÷, but the backslash / is also used. Sometimes people will write one number on top of another with a line between them. This is also called a fraction.
Example signs for "a divided by b":
a ÷ b
a/b
a
b
Dividend, Divisor, and Quotient
Each part of a division equation has a name. The three main names are the dividend, the divisor, and the quotient.

·  Dividend - The dividend is the number you are dividing up

·  Divisor - The divisor is the number you are dividing by

·  Quotient - The quotient is the answer

Dividend ÷ Divisor = Quotient
Example:
In the problem 20 ÷ 4 = 5
Dividend = 20
Divisor = 4
Quotient = 5

When you divide either a fraction by a fraction or a whole number by a fraction, the result will be an answer that is larger than the dividend.

EXAMPLE:

34 ÷ 18

In this problem, you are asking, “How many groups of 18 are in 34 ?”

You can find the answer by getting the reciprocal (switching the numerator and denominator) of the 2nd fraction and then multiplying the numerators and the denominators.

34 ÷ 81 = 244

The next step is to divide, to get either a whole number or mixed number as a final answer. 4 goes into 24 six times, therefore, 6 is the final answer.

So, there are 6 groups of 18 in 34.

Wednesday, 9-30-14

Dividing Mixed Numbers

Students will learn how to divide mixed numbers. Mixed numbers are whole numbers with fractions. Dividing by a fraction is equivalent to multiplying by its reciprocal. You can use the fact to divide mixed numbers.

First, rewrite the mixed number as fractions greater than 1, and then multiply the first fraction by the reciprocal of the second fraction.

EXAMPLE:

You have 2 ½ cups of rice and will use ¼ of cup of rice for each sushi roll. How many sushi rolls can you make?

2 ½ ÷ ¼

Change the 2 ½ to an improper fraction… 52

Find the reciprocal of ¼

It is 41

Multiply

52 * 41 = 202

Change the improper fraction by dividing…..2 goes into 20 ten times, so 10 is the final answer. You can make 10 sushi rolls.

Review of reciprocals:

2 is the reciprocal of ½, because 21 is 2.

3 is the reciprocal of 1/3, because 31 is 3.

5/12 is the reciprocal of 12/5

337 is the reciprocal of 724….first you have to change the mixed number to an improper and then switch the denominator and numerator.