Transcript 9-5 PPT

5 Minute Check
Find the LCM for the following.
1. 6, 15
2. 7, 9
3. 11, 5
4. 9, 12, 15
5 Minute Check
Find the LCM for the following.
1. 6, 15
6; 6, 12, 18, 24, 30, 36……
15; 15, 30, 45……..
5 Minute Check
Find the LCM for the following.
2. 7, 9
5 Minute Check
Find the LCM for the following.
2. 7, 9
7; 7, 14, 21, 28, 35, 42, 49, 56, 63, 70 ……
9; 9, 18, 27, 36, 45, 54, 63, 72……..
5 Minute Check
Find the LCM for the following.
3. 11, 5
5 Minute Check
Find the LCM for the following.
3. 11, 5
Since both numbers are prime the LCM is
the product. 11 x 5 = 55
5 Minute Check
Find the LCM for the following.
4. 9, 12, 15
5 Minute Check
Find the LCM for the following.
4. 9, 12, 15
3
/
9
x
\
3
/
12
\
2 x 6
I
/ \
2 x 2 x 3
15
/ \
3 x 5
5 Minute Check
Find the LCM for the following.
4. 9, 12, 15
3 x 5 x 2 x 2 x 3 = 180
9
3
5
3
12
2
2
15
Thursday, Sept 5
Lesson 1.2
Ratios
Ratios
Objective: To express ratios and rates as
fractions.
Ratios
Ratios
A ratio is a comparison of two quantities by
division.
Ratios
A ratio of 2 red paper clips to 6 blue paper
clips can be written 3 different ways.
2 to 6
2:6
2
6
As with fractions, ratios are often expressed
in simplest form.
Ratios
Write the ratio in simplest form that compares the numbers
of black dots to the number of white dots. Then explain
the meaning.
(Write this in your notes)
Ratios
Write the ratio in simplest form that compares the numbers
of black dots to the number of white dots. Then explain
the meaning.
When determining ratios, the order of objects in the
question is the same order as the ratio.
Since we are comparing black dots to white dots, black dots
come first in the question. How many black dots are
there?
Ratios
Write the ratio in simplest form that compares the numbers
of black dots to the number of white dots. Then explain
the meaning.
How many black dots are there? 3
How many white dots are there?
Ratios
Write the ratio in simplest form that compares the numbers
of black dots to the number of white dots. Then explain
the meaning.
How many black dots are there? 3
How many white dots are there? 6
How do we express this as a fraction?
Ratios
Write the ratio in simplest form that compares the numbers
of black dots to the number of white dots. Then explain
the meaning.
How do we express this as a fraction?
black dots
white dots
3
6
(Write this in your notes)
Ratios
Write the ratio in simplest form that compares the numbers of
black dots to the number of white dots. Then explain the
meaning.
To reduce a fraction we can convert it to prime factors.
black dots
white dots
3
6
=
3
2·3
Ratios
Write the ratio in simplest form that compares the numbers
of black dots to the number of white dots. Then explain
the meaning.
Cancel a number if it appears on top and bottom of the
fraction.
black dots
white dots
3
6
=
3
2·3
=
1
2
Remember 3 = 3 x 1, when we cancel 3 on top a 1 remains.
Ratios
Write the ratio in simplest form that compares the numbers
of black dots to the number of white dots. Then explain
the meaning.
black dots
white dots
What does this mean?
3
6
=
3
2·3
=
1
2
Ratios
Write the ratio in simplest form that compares the numbers
of black dots to the number of white dots. Then explain
the meaning.
black dots
white dots
3
6
=
3
2·3
=
1
2
What does this mean?
It means the ratio of black dots to white dots is 1/2, 1:2 or 1
to 2. This means there is 1 black dot for every 2 white
dots.
Ratios
Write the ratio in simplest form that compares the numbers
of red dots to the number of yellow dots. Then explain
the meaning.
(Do this on your own)
Ratios
Write the ratio in simplest form that compares the numbers
of red dots to the number of yellow dots. Then explain
the meaning.
red dots
yellow dots
4
6
=
2·2
2·3
=
2
3
The ratio of red dots to yellow dots is 2/3, 2:3 or 2 to 3.
This means there are 2 red dots for every 3 yellow dots.
Ratios
Several students named their favorite flavor of gum. Write
the ratio that compares the number of who chose fruit to
the total number of students.
Ratios
Several students named their favorite flavor of gum. Write
the ratio that compares the number of who chose fruit to
the total number of students.
How many student chose fruit?
(It is important you ask in the same
order it appears in the question)
Ratios
Several students named their favorite flavor of gum. Write
the ratio that compares the number of who chose fruit to
the total number of students.
How many student chose fruit? 3
How many students are there?
Ratios
Several students named their favorite flavor of gum. Write
the ratio that compares the number of who chose fruit to
the total number of students.
How many student chose fruit? 3
How many students are there? 21
(9 + 8 + 3 + 1)
Ratios
Several students named their favorite flavor of gum. Write
the ratio that compares the number of who chose fruit to
the total number of students.
How many student chose fruit? 3
How many students are there? 21
(9 + 8 + 3 + 1)
What is the fraction?
Ratios
Several students named their favorite flavor of gum. Write
the ratio that compares the number of who chose fruit to
the total number of students.
What is the fraction?
Fruit
3
Total
21
Can we reduce?
Ratios
Several students named their favorite flavor of gum. Write
the ratio that compares the number of who chose fruit to
the total number of students.
What is the fraction?
Fruit
3
3
Total
21
3·7
=
What does this mean?
=
1
7
Ratios
Several students named their favorite flavor of gum. Write
the ratio that compares the number of who chose fruit to
the total number of students.
What is the fraction?
Fruit
3
3
Total
21
3·7
=
=
1
7
What does this mean?
1 out of every 7 students chose fruit gum.
Ratios
Write the ratio of pennies to dimes.
(Do this on your own.)
Ratios
Write the ratio of pennies to dimes.
Pennies
Dimes
3
9
=
3
3·3
=
1
3
For every 1 penny there are 3 dimes.
Ratios
Monday’s yogurt sales are recorded on the table. Write the
ratio that compares the sales of strawberry yogurt to the
total sales. Then explain the meaning.
(Do this on your own.)
Ratios
Monday’s yogurt sales are recorded on the table. Write the
ratio that compares the sales of strawberry yogurt to the
total sales. Then explain the meaning.
Strawberry
Total
8
24
=
2·2·2
2·2·2·3
=
1
3
1 out of every 3students chose strawberry yogurt.
Ratios
Create three different drawings showing a number of circles
and triangles in which the ratio of circles to triangles is 2:3.
Ratios
Create three different drawings showing a number of circles
and triangles in which the ratio of circles to triangles is 2:3.
2:3
4:6
6: 9
OAA Review
OAA Review
What are we looking for?
OAA Review
What are we looking for? The GCF.
OAA Review
12: 1, 2, 3, 4, 6, 12
30: 1, 2, 3, 5, 6, 10, 15, 30
OAA Review
OAA Review
35:1, 5, 7, 35
56:1, 2, 4, 7, 8, 14, 28, 56
84:1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
OAA Review
OAA Review
Dramas
Action
8
6
=
2·2·2
2·3
2·2 4
=3 =3
4:3 (In ratios, we keep fractions as improper)
Ratios
Agenda Notes
Homework –
Homework Practice 1-2
Due Friday, Sept 6
On your homework – please circle the
fraction in simplest form.