More partial products

1
More partial products
Recall that we can use a drawing of a rectangle
to help us with calculating products. The
rectangle is divided into regions and we
determine partial products which are then added
to find the total.
2
More partial products
Recall that we can use a drawing of a rectangle
to help us with calculating products. The
rectangle is divided into regions and we
determine partial products which are then added
to find the total.
Example 1
7
3
Blue 3 5 15 Yellow 3
2 6 Total 21
3
More partial products
Example 2 The total number of squares can be
found from 54 23. One of the ways to
calculate 54 23 is to divide the rectangle into
4 regions Orange 50 x 20 1000
Yellow 4 x 20 80 White
50 x 3 150 Blue 4 x 3
12 Total
1242 So 54 23 1242
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More partial products
Example 3
So 2.1 x 4.7 81.40.40.07 9.87
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More partial products
Now we are going to explore this technique of
partial products with fractions. Draw a rectangle
and label the sides with 2 and 4 ½ Can you make
two regions in the rectangle and label the sides?
6
More partial products
Now we are going to explore this technique of
partial products with fractions. Draw a rectangle
and label the sides with 2 and 4 ½ Can you make
two regions in the rectangle and label the sides?
7
More partial products
Now we are going to explore this technique of
partial products with fractions. Draw a rectangle
and label the sides with 2 and 4 ½ Can you make
two regions in the rectangle and label the sides?
So we have Yellow 2 4 8 Pink 2 ½
1 So 2 4 ½ 9 Were you expecting 9?
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More partial products
What if we needed to find 2 1/3 x 4 ½ Can you
extend the rectangle underneath?
9
More partial products
What if we needed to find 2 1/3 x 4 ½ Can you
extend the rectangle underneath?
10
So now we have 4 partial products
11
So now we have 4 partial products
So 2 1/3 x 4 1/2 Can be found by adding 8 1
1 1/3 1/6 10 ½
12

• We can also consider lower and upper bounds to
  check our answers.

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2 1/3 x 4 ½
14
(No Transcript)
15
Lower bound 2 x 4 8
16
Lower bound 8
So we know that our answer (to 2 1/3 x 4 ½) lies
between 8 and 15.