Video Transcript
Multiplying Two-Digit Numbers by
One-Digit Numbers Using Partial Products
In this video, we will learn how to
multiply two-digit numbers by one-digit numbers by calculating partial products and
using expanded column multiplication. Let’s imagine we’ve been asked to
multiply 32 by three. We’ve modeled three lots of 32
using base ten blocks. Here’s one group of 32, two groups
of 32, and three groups of 32. 32 is a two-digit number. We can break it apart into its tens
part and its ones parts. 32 has two ones and three 10s,
which are worth 30.
Now that we’ve broken our number
apart, we can multiply each part by three. We need to start with the ones. We have to multiply our two ones by
three, which is the same as saying two multiplied by three. And we know that two times three is
six. Next, we need to multiply the tens
part of the number. We have to multiply three 10s by
three. And we know that three 10s are
worth 30. We know that three multiplied by
three is nine, so three 10s multiplied by three equals nine 10s. And we know that nine 10s are worth
90. So two ones multiplied by three
gives us a total of six ones, and three 10s multiplied by three gives us a total of
nine 10s or 90.
Now all we need to do is add our
two products, our ones product and our tens product. 90 plus six equals 96. 32 multiplied by three is 96. So, to calculate 32 multiplied by
three, first we multiplied the ones. Two times three is six. Next, we multiplied the tens part
of the number. Three 10s or 30 multiplied by
three. The tens product is 90. Finally, we had to add the two
products together. Six ones plus no ones gives us a
total of six ones, and we only have nine 10s to add in the tens column. 90 plus six is 96. Let’s try some practice questions
now where we need to multiply two-digit numbers by one-digit numbers using partial
products.
Calculate 32 multiplied by two.
In this question, we’re being asked
to multiply a two-digit number by a one-digit number. Our two-digit number is the number
32. And we have to multiply it by
two. We can model the number 32 using
three tens blocks and two ones blocks. And we’ve got two lots of 32
because we’re multiplying by two. We can break the number 32
apart. The two is worth two ones, and the
three is worth three 10s or 30. Let’s start by multiplying the ones
part of the number. Two ones multiplied by two gives us
four ones. Next, we need to multiply the tens
part of the number. We’ve got three 10s, and we need to
multiply them by two. Three 10s multiplied by two gives
us six 10s. And we know that six 10s are
60. 30 times two is 60.
Now, all we need to do is add our
two partial products. Four ones and no ones gives us a
total of four. And we only have six 10s in our
tens column. 32 multiplied by two is 64. To calculate 32 multiplied by two,
first we broke the number apart. 30 [32] has two ones and
three 10s worth 30. First, we multiplied the ones. Two times two is four. Then we multiplied the tens. Three 10s multiplied by two gives
us a total of six 10s or 60. Finally, we added our two partial
products together. Four plus 60 equals 64. 32 times two is 64.
Calculate the following: 75
multiplied by six.
In this question, we’re multiplying
a two-digit number by a one-digit number. Let’s start by multiplying the
ones. There are five ones in the number
75, so we need to multiply five ones by six. Five times six is 30. Next, we need to multiply the tens
part of the number. The tens digit in the number 75 is
a seven, so we need to multiply seven 10s by six. We know that seven times six is
42. 42 10s are 420.
Finally, we just need to add
together our two partial products. What is 30 plus 420? Zero plus zero is zero. Three 10s plus two 10s gives us a
total of five 10s. And we only have a four in the
hundreds place, which gives us a total of four 100s. 30 plus 420 gives us a total of
450.
We calculated 75 multiplied by
six. The answer is 450. First, we multiplied the ones part
of the number or five times six. Then we multiplied our seven 10s by
six, which gave us 420. And finally, we added together our
two partial products to give us the answer. 75 multiplied by six is 450.
Find the missing number.
We have to multiply 23 by four. We can see that the first part of
the calculation has been done for us. And we need to find this missing
number. And we already know the answer; 23
multiplied by four gives us 92. When we’re multiplying a two-digit
number by a one-digit number, it helps to break apart our two-digit number. We can break the number 23 into its
tens and ones parts. So 23 has three ones and two 10s
worth 20. When we’re using this method,
multiplying using partial products, we start by multiplying the ones. And we know that 23 has three
ones. So first, we multiply three by
four. And that’s where we get the product
12.
Next, we have to multiply the tens
part of the number 23. We know that 23 has two 10s, which
are worth 20. So we have to calculate 20
multiplied by four, which is 80. Now, we can check that 12 plus 80
equals 92. Two plus zero gives us a total of
two ones. And one 10 plus eight 10s gives us
a total of nine 10s. So the missing number is 80. Three times four is 12. 20 times four is 80. 12 plus 80 equals 92. So the missing number is 80.
Liam spilled ink on his
multiplication homework. Help him remember what he did. Use his work to find 13 multiplied
by four. What calculation should he do to
find the missing number? And again, what calculation should
he do to find the missing number?
This is a three-part question. First, we have to help Liam finish
multiplying 13 by four. He’s already multiplied in the ones
place. Three ones multiplied by four is
12. Liam has also multiplied the tens
part of number 13. We know that 13 has one 10, and 10
multiplied by four is 40. Now all we need to do is add these
two partial products to find the total. Two plus zero gives us a total of
two ones. One 10 plus four 10s is five
10s. 13 multiplied by four is 52.
Next, we have to multiply 46 by
two. We can see that Liam has already
multiplied the ones. Six multiplied by two is 12. Now we need to help him multiply
the tens part of the number 46. 46 has four 10s. Four 10s multiplied by two gives us
a total of eight 10s. 40 multiplied by two is 80. And if we add our two partial
products together, 12 plus 80 gives us 92. The missing number in this
calculation is the number 80. Finally, we have to multiply 24 by
three. In this calculation, the ones
product is missing. The number 24 has four ones, and we
need to multiply them by three. Four times three is 12, and 12 plus
60 does total 72.
We helped Liam to complete his
multiplication homework. 13 multiplied by four is 52. 46 multiplied by two is 92. But Liam had spilled ink on the
tens part of his calculation. And we calculated that the product
of 40 and two is 80. So the missing part of his
calculation was the number 80. 24 multiplied by three is 72. Liam had spilled ink on the ones
part of his calculation. We multiplied four times three to
give us our missing product of 12. The missing numbers are 52, 80, and
12.
What have we learned in this
video? We have learned how to multiply
two-digit numbers by one-digit numbers by calculating partial products and using
expanded column multiplication.
