cross reducing

A Shortcut

Using Cross-Division to put our multiplication answers into

simplest form quickly.

Simplifying Fractions

• Start with a multiplication statement that looks like it will need to be simplified.

2 3

3 5=ﾴ

Cross Reducing

• Normally, you would multiply the top numbers and then the top.

• Then check to see if your fraction is in simplest form.

2 3

3 5=ﾴ

2 3 6 3 2

3 5 15 3 5

ﾴ ﾸ= =

ﾴ ﾸ

Cross Simplifying

• Now let’s look to see if we can cross reduce.

• First check the upper left and lower right corner.

• Is there any number that can divide evenly into 2 or 5?

2 3

3 5=ﾴ

Nope!

Cross Simplifying

• Now let’s look to see if we can cross reduce the other pair.

• Check the upper right and lower left corners.

• Is there any number that can divide evenly into 3 or 3?

2 3

3 5=ﾴ

Yes! 3

Let’s divide

• Since we can divide three into three at the top and do the same at the bottom, we do it right in the problem.

2 3

3 5=ﾴ

Cross out• Cross out the 3’s

• Divide the bottom left number by 3.

• Replace the three with a one.

• Divide the top right number by 3.

• Replace the three with a one.

2 3

3 5=ﾴ

1

1

New Problem

• Multiply the top numbers.

• Multiply the bottom numbers.

• It will often be in simplest form after cross reducing and multiplying.

2 3

3 5=ﾴ

1

1

2 1 2

1 5 5=ﾴ

Watch one• Cross out the numbers divisible by 5.

• Divide the bottom left number by 5.

• Replace the five with a one.

• Divide the top right number by 5.

• Replace the ten with a two.

2 10

5 11=ﾴ

1

2

New Problem

• Now proceed with the newly formed problem.

2 10

5 11=ﾴ

1

2

2 2

1 11=ﾴ4

11

Try these two.

16

2=ﾴ

7 15

10 16ﾴ

Try these two.

• Divide the 10 and 15 by 5

• Make the 6 a fraction.

• Divide the 2 and 6 by 2.

16

2=ﾴ

7 15

10 16ﾴ

1 6

2 1=ﾴ

3

2

21

32=

3

1

3

2=

Make a mixed number.

2 31

-2

1

112

=

Work on Worksheet F4