6.4Introduction to representations of multiplying and dividing fractions

.

IntroductionBoxes can be split into all kinds of sections.

Can you tell what fraction is shaded in each box?

To multiply, put together like this!Vertical is first, Horizontal is last!

Order does not matter with multiplication, but it sure does with division! So we are going to always do it like this.

2/3 x 1/2

Now Watch!

TADA! THE PRODUCT IS 2/6 OR 1/3!

THE DENOMINATOR IS ALL THE SECTIONS

AND THE NUMERATOR IS THE OVERLAP!

Try these!

¼ x 3/5

We can check this! ¼ x 3/5 is 1 x 3= 3 4 x 5= 20The product is 3/20

Do you think you can?5/6 x 1/4

5 x 1 = 56 x 4 = 24The product is 5/24

Try another?5/8 x 7/12

Check! 5 x 7 = 358 x 12 = 96The product is 35/96

Try another?1/4 x 1/2

Check! 1 x 1 = 14 x 2 = 8The product is 1/8

Now for

DIVISION!

2/3 ÷ 1/2

The numerator is the sections made on the VERTICAL The denominator is the sections made on the HORIZONTAL

4/3

4

3

Try with patterns!

½ ÷ ¼

You can check this by flipping the second fraction (reciprocal) and then multiplying.

½ x 4/1 = 4/2

4

2

Try with patterns!1/4 ÷ 3/4

You can check this by flipping the second fraction (reciprocal) and then multiplying.

1/4 x 4/3 = 4/12 or 1/3

4

12

Now it’s time to set up our notebook and practice!

6.4The student will demonstrate multiple representations of multiplication and

division of fractions

Pg 13

6.4 DirectionsFirst fraction square is vertical. Overlap the second fraction square horizontally.

Multiplication- 1. count all the sections once squares are

overlapped. This is the denominator. 2. Count the sections where the colors or

patterns combine. This is the numerator.

Example- ½ x ¼

1 section overlaps8 sections totalProduct is 1/8

Check- ½ x ¼ =1/8

Vocabulary 6.4 pg. 14SOL 6.4/6.6additionThe act or process of combining numerical values, so as to find their sumsumAn amount obtained as a result of adding numbers EX 2+2=4 4 is the sumsubtractionThe arithmetic operation of finding the difference between two quantities or numbersdifferenceAn amount obtained as a result of subtracting numbers EX 5-3=2 2 is the differencereciprocalAny two numbers whose product is 1.Example: ½ and 2 are reciprocals because ½ X 2 = 1productAn amount obtained as a result of multiplying numbersdivisionThe operation of determining how many times one quantity is contained in another; the inverse of multiplication.quotientAn amount obtained as a result of dividing numbers EX-12 ÷ 2= 6 six is the quotientnumeratorThe expression written above the line in a fraction EX- ½ One is the numeratordenominatorThe expression written below the line in a fraction that indicates the number of parts into which one whole is divided. EX- ½ 2 is the denominatorimproper fractionA fraction in which the numerator is larger than or equal to the denominator. The value of an improper fraction is greater than or equal to one. EX- 14/5mixed numberA numerical value that combines a whole number and a fraction EX- 2 ¾

simplest formA fraction is in simplest form when the greatest common factor of the numerator and denominator is 1.simplifyTo reduce the numerator and the denominator in a fraction to the smallest form possible. To divide the numerator and denominator by the GCF is simplifying a fraction.LCDThe least common multiple of the denominators of two or more fractions. Example: 6 is the least common denominator of 2/3 and 1/6.estimateTo make an approximate or rough calculation, often based on rounding

Pg 16

6.4 DirectionsFirst fraction square is vertical. Overlap the second fraction square horizontally.

Division- 1. count the shaded HORIZONTAL sections

once squares are overlapped. This is the denominator.

2. Count the shaded VERTICAL sections. This is the numerator.

Example- ½ ÷ ¼

Vertical section cut into 4Horizontal section cut into 2Quotient is 4/2

Check- ½ ÷ ¼ FLIP ½ x 4/1 = 4/2

Pg 15 Practice

Draw a box. When you shade use stripes.

Split vertically into 3 sections. Shade 1 section.

Split horizontally into 2 sections. Shade one.

This is 1/3 x ½.OR 1/3 ÷ 1/2.