5 Minute Check
Complete in your notebook.
1.
2.
3.
4.
9
3
10 + 5
3
1
4 + 5
7
2
3
9
7
8
-3
1
7
-
2
5
6
5 Minute Check
Complete in your notebook.
1.
9
3
10 + 5
5 Minute Check
Complete in your notebook.
1.
9
10
3
5
+ =
9
10
6
10
+ =
15
10
=1
1
2
5 Minute Check
Complete in your notebook.
2.
3
1
4 + 5
5 Minute Check
Complete in your notebook.
2.
3
4
+
1
5
=
15
20
+
4
20
=
19
20
5 Minute Check
Complete in your notebook.
3.
7
2
3
-3
1
7
5 Minute Check
Complete in your notebook.
3.
7
2
3
-3 = 1
7
23
3
161
21 -
7 x 23
7 x 3
22
7
22 x 3
7 x 3
66
21
=
95
21
=4
11
21
5 Minute Check
Complete in your notebook.
4.
9
7
8
-
2
5
6
5 Minute Check
Complete in your notebook.
4.
9
7
8
-
2
5
6
=
79
8
3 x 79
3 x 8
237
24
-
17
6
-
17 x 4
6 x 4
-
68
24
=
169
24
1
24
=7
Video
Thursday, Oct 2
Lesson 6.4.2
Multiply Fractions and Whole Numbers
Multiply Fractions and Whole Numbers
Lesson 6.4.1 is estimation and will be
incorporated into 6.4.2, 6.4.3 and 6.4.4.
Multiply Fractions and Whole Numbers
Objective: To understand how to estimate
and multiply fractions and whole numbers.
Multiply Fractions and Whole Numbers
To multiply fractions, multiply the numerators
and multiply the denominators, then simplify if
needed.
Example x
=
3
2
6
4
5
20
x
=
x
=
=
3
10
Multiply Fractions and Whole Numbers
To multiply fractions, multiply the numerators
and multiply the denominators, then simplify if
needed.
Example x
=
3
2
6
4
5
20
x
=
x
=
=
3
10
Multiply Fractions and Whole Numbers
To multiply a fraction and whole number,
convert the whole number to a fraction, then
multiply as normal.
What is
14 as a fraction?
Multiply Fractions and Whole Numbers
To multiply a fraction and whole number,
convert the whole number to a fraction, then
multiply as normal.
Example
14 =
14
1
Multiply Fractions and Whole Numbers
To multiply a fraction and whole number,
convert the whole number to a fraction, then
multiply as before.
Example 1
5
x 14
1
5
x
x
x
14
1
=
14
5
4
5
= =2
=
1
5
Multiply Fractions and Whole Numbers
x 14
When estimating the product of a fraction and
whole number, make a multiples list for the
smaller of either the whole number or the
denominator.
1
5
Multiply Fractions and Whole Numbers
x 14
When estimating the product of a fraction and
whole number, make a multiples list for the
smaller of either the whole number or the
denominator.
5: 5, 10, 15, 20…..
1
5
Multiply Fractions and Whole Numbers
x 14
Use a comparable number for the larger
number that is in the multiples list.
5: 5, 10, 15, 20…..
1
5
Multiply Fractions and Whole Numbers
x 14
Use a comparable number for the larger
number that is in the multiples list.
5: 5, 10, 15, 20…..
1
5
Multiply Fractions and Whole Numbers
x 14
Use a comparable number for the larger
number that is in the multiples list.
5: 5, 10, 15, 20…..
1
5
x 15
1
5
Multiply Fractions and Whole Numbers
x 14
Use a comparable number for the larger
number that is in the multiples list.
5: 5, 10, 15, 20…..
1
5
15
5
x 15 = = 3
Multiply Fractions and Whole Numbers
Estimate and Multiply.
2
5
2x =
Estimate?
Which number is smaller, 2 or 5?
Multiply Fractions and Whole Numbers
Estimate and Multiply.
2
5
2x =
Which number is smaller, 2 or 5? 2
Multiply Fractions and Whole Numbers
Estimate and Multiply.
2
5
What is a comparable number for 5 that is in
the multiples list of 2?
2: 2, 4, 6, 8,…..
2x =
Multiply Fractions and Whole Numbers
Estimate and Multiply.
2
5
What is a comparable number for 5 that is in
the multiples list of 2?
2: 2, 4, 6, 8,…..
2x =
Multiply Fractions and Whole Numbers
Estimate and Multiply.
2
5
What is a comparable number for 5 that is in
the multiples list of 2?
2: 2, 4, 6, 8,…..
2x =
2
4
4
4
2 x = =1
Multiply Fractions and Whole Numbers
Estimate and Multiply.
2
5
2x =
Actual Product?
Multiply Fractions and Whole Numbers
Estimate and Multiply.
2
5
2x =
Actual Product?
2
1
x
2
5
=
4
5
Is this a reasonable answer?
Multiply Fractions and Whole Numbers
Estimate and Multiply.
2
5
2x =
Actual Product?
2
1
x
2
5
=
4
5
4
Is this a reasonable answer? 5
≈1
Multiply Fractions and Whole Numbers
Estimate and Multiply.
2
5
2x =
4
5
A model can be used to represent this
equation. Remember,
2x
2
2
5 is the same as 5
+
2
5
Multiply Fractions and Whole Numbers
Estimate and Multiply.
2
5
2x =
4
5
A model can be used to represent this
equation.
+
=
Multiply Fractions and Whole Numbers
When multiplying a fraction by a whole
number, the order of the factors does not
change the product. This is true for any
numbers and is an example of the
Commutative Property.
Example
2
5
2x =
2
5
x2
Multiply Fractions and Whole Numbers
2
5
2x
Is the same as
2
5
x2
Which is asking
2
What is 5 of
2?
Multiply Fractions and Whole Numbers
Estimate and Multiply.
2
3
6x =
Estimate?
Multiply Fractions and Whole Numbers
Estimate and Multiply.
2
3
6x =
Estimate?
Since 3 and 6 are in the same multiples list the
estimate and actual product will be the same.
Actual Product?
Multiply Fractions and Whole Numbers
Estimate and Multiply.
2
3
6x =
Actual Product?
6
1
x
2
3
12
3
= =4
Multiply Fractions and Whole Numbers
Estimate and Multiply.
4x
3
5
Do this on your own.
Multiply Fractions and Whole Numbers
Estimate and Multiply.
3
5
4 x ≈3
4
1
x
3
5
12
5
= =2
Work done in my head:
2
5
4:4, 8, 12…….
4
3
1 X 4
12
4
= =3
Multiply Fractions and Whole Numbers
If the numerators and denominators have a
common factor you can simplify before
multiplying.
Multiply Fractions and Whole Numbers
If the numerators and denominators have a
common factor you can simplify before
multiplying.
To simplify before multiplying, convert all
numbers to prime factors.
Multiply Fractions and Whole Numbers
If the numerators and denominators have a
common factor you can simplify before
multiplying.
Example
5
3
x
9
10
=
Convert all numbers are prime factors (which
means they have no factors other than one and
itself).
Multiply Fractions
If the numerators and denominators have a
common factor you can simplify before
multiplying.
Example
5
3
x
9
10
=
5
3x3
3
2x5
Are there any factors that appear in the
numerator and denominator?
x
=
Multiply Fractions
If the numerators and denominators have a
common factor you can simplify before
multiplying.
Example
5
3
x
9
10
=
5
3x3
3
3
2x5
2
Are there any factors that appear in the
numerator and denominator?
x
=
Multiply Fractions
If the numerators and denominators have a
common factor you can simplify before
multiplying.
Example
5
3
5
3
x
9
10
x
=
3x3
2x5
=
3
2
1
2
=1
We can prove this by multiplying the original.
Multiply Fractions
If the numerators and denominators have a
common factor you can simplify before
multiplying.
Example
5
3
5
3
x
9
10
x
= 30 = 2 =12
3x3
2x5
45
=
3
3
2
1
1
2
=1
We can prove this by multiplying the original.
Multiply Fractions and Whole Numbers
Estimate and Multiply.
3
4
x 14
Do this on your own.
Multiply Fractions and Whole Numbers
Estimate and Multiply.
3
4
3
2x2
x 14 ≈ 9
x
2x7
1
21
2
= =10
1
2
Multiply Fractions and Whole Numbers
Estimate and Multiply.
1
3
x9
Do this on your own.
Multiply Fractions and Whole Numbers
Estimate and Multiply.
1
3
1
3
x9≈3
x
3x3
1
= 3
Multiply Fractions and Whole Numbers
Estimate and Multiply.
2
5
x 15
Do this on your own.
Multiply Fractions and Whole Numbers
Estimate and Multiply.
2
5
2
5
x 15 ≈ 6
x
3x5
1
6
1
= =6
Multiply Fractions and Whole Numbers
Estimate and Multiply.
1
7
x8
Do this on your own
Multiply Fractions and Whole Numbers
Estimate and Multiply.
1
7
1
7
x8≈1
x
8
1
8
7
1
= = 17
Multiply Fractions and Whole Numbers
Estimate and Multiply.
3
8
x 11
Do this on your own
Multiply Fractions and Whole Numbers
Estimate and Multiply.
3
8
3
8
x 11 ≈ 3
x
11
1
33
8
1
= = 48
Multiply Fractions and Whole Numbers
Estimate and Multiply.
2
3
x 10
Multiply Fractions and Whole Numbers
Estimate and Multiply.
2
3
2
3
x 10 ≈ 6
x
10
1
20
3
2
= = 63
Multiply Fractions and Whole Numbers
4
A sloth spends 5 of it’s life asleep. If a
sloth lives to be 28 years old, how many
years does it spend asleep?
(Do this on your own)
Multiply Fractions and Whole Numbers
4
A sloth spends 5 of it’s life asleep. If a
sloth lives to be 28 years old, how many
years does it spend asleep?
4
5
4
5
x 28 ≈ 24
x
28
1
=
112
5
2
= 225
Multiply Fractions and Whole Numbers
One evening, 2/3 of Mrs. Thorne’s students watched a
reality TV show. Of Mrs. Lombardo’s students, 4/5
watched the same reality show. Which teacher had
more students watch the show?
(Do this on your own)
Multiply Fractions and Whole Numbers
One evening, 2/3 of Mrs. Thorne’s students watched a
reality TV show. Of Mrs. Lombardo’s students, 4/5
watched the same reality show. Which teacher had
more students watch the show?
Mrs. T
2
3
x
Mrs. L
4
5
2x2x3x3
1
5x6
1
x =
=
24
1
24
1
=24
= 24
Multiply Fractions and Whole Numbers
Natalie multiplied 2/3 by 123 and got
156. Is this a reasonable answer?
Multiply Fractions and Whole Numbers
Natalie multiplied 2/3 by 123 and got
156. Is this a reasonable answer?
No, because if you multiply a whole
number by a fraction the answer will
always be less than the whole number.
Multiply Fractions and Whole Numbers
The male Cuban tree frog is about 2/5 the
size of the female. The average size of the
female is shown below. What is the size of the
average male?
Do this on your own.
Multiply Fractions and Whole Numbers
The male Cuban tree frog is about 2/5 the
size of the female. The average size of the
female is shown below. What is the size of the
average male?
2 12
2
5
5
5
6 x = =2
Multiply Fractions and Whole Numbers
Write a problem involving the multiplication of
a whole number and fraction with a product
that is between 8 and 10.
Do this on your own.
Multiply Fractions and Whole Numbers
Write a problem involving the multiplication of
a whole number and fraction with a product
that is between 8 and 10.
Sample:
3 36
4
4
12 x = =9
Multiply Fractions and Whole Numbers
Find Noah’s mistake and
correct it.
Multiply Fractions and Whole Numbers
Find Noah’s mistake and
correct it.
He multiplied both top and
bottom by 8.
3
4
24
4
x 8= =6
Multiply Fractions and Whole Numbers
Agenda Notes
Homework –
Homework Practice 6.4.2
Show all work
Due Friday, Oct 3
Mid-Chapter 6.4 Quiz
Wednesday, Oct 8