Section 3.4 Multiplying Fractions

3.4 MultiplyingFractions3.4 MultiplyingFractions

Ex: Indicate the fraction of the shaded region:

These 3 fractions areequal because they coverthe same area

II) Unit Square

Each side of an unit square is 1 unit long

The area of an unit square is 1unit2

If you cut each side in half, and shade only ½ the columnsand ½ the rows, the overlapping area will be the product

Overlapping Area

The overlapping area

is ¼ of the unit square

Link to Fraction Applet

Rules for Multiplying with Manipulatives:

•The denominators indicate how many rows orcolumns to split each side into

•The numerators indicate how many rows or columnsto shade in

•The product will be the fraction of overlappingboxes

Ex: Multiply

Split the unit box into

8 columns and 6 rows

7 columns are shaded

5 rows are shaded

35 out of 48 boxes

overlapp

Link to Fraction Applet

Practice: Multiply the followingfractions using manipulatives

9 columns and8 rows

4 columns areshaded

6 rows areshaded

The overlapping piecescan be shifted to reduce

the number of cuts

10 columns and9 rows

3 columns areshaded

5 rows areshaded

Rearrange the pieces toto reduce the numberof cuts

Link to Fraction Applet

Ex: Write the equation for the followingmultiplication

Link to Fraction Applet

Ex: Jason spent 2/3 of his money on books. Hethen spent ¼ of the rest on shoes. Whatpercentage of his savings does he have?

Take 2/3 away from the unit square

1/3 of his money is left

Take away ¼ of the money left

3 out of 12 units left

Jason has still 25% of his savings

Link to Fraction Applet

Mandy bought some donuts and left it in the staffroom. One hour later, 3/5 of the donuts were eaten.When she returned another hour later, 2/3 of theremaining donuts were gone and four donuts wereleft. How Mandy donuts did Mandy buy?

Take 3/5 away from the unit square

2/3 of the remaining donuts were gone

2 out of 15 boxes are left

If 4 donuts are left, then each yellowbox represents 2 donuts

Mandy bought 30 donuts

Link to Fraction Applet

Simplifying Fractions

The common factor is 4

Put the boxes intogroups of 4

The common factor is 6

The common factor is 7

Reduce the cuts bygrouping every 2 column

The greatest common

factor is 14

Multiplying Fractions

•Simplify each fraction by cancelling out commonfactors

•Multiply the numerators (Top) together and then thedenominators (bottom) together

•Check your answer by estimating

Ex: Multiply the following fractions

Simplify each fraction

Multiply the tops together

Multiply the bottomstogether

Simplify, if possible

Practice: Multiply

Simplify each fraction

Multiply the tops together

Multiply the bottomstogether

Simplify, if possible

Simplify each fraction

Multiply the tops together

Multiply the bottomstogether

Simplify, if possible

Ex: 5/8 of a class have black hair. 4/9 of thestudents with black hair are girls. What fractionof the students are girls and have black hair?

The box represent the whole class

5/8 of this class have black hair

4/9 of this group are girls

Divide the grid into 9 rows

Take only 4 out of the 9 rows

20 out of 72: (REDUCE)

5 out of 18 students are girls andhave black hair

Sara bought a box of cookies at ate 1/8 of it.Jack came and ate 2/7 of what was left. Tomthen ate 2/5 of the leftovers. What fractionof the original box is left?

The box represent all the cookies

1/8 of the cookies were eaten by Sara