Video Transcript
Multiplying a Two-Digit Number by a
One-Digit Number: The Column Method with Regrouping
In this video, we will learn how to
multiply a two-digit number by a one-digit number using the standard written method
for calculations where there is regrouping. 23 is a two-digit number, and we
have to multiply it by five which is a one-digit number. In this video, we’re going to learn
how to multiply two-digit numbers by one-digit numbers using the standard written
method.
To help us understand how this
method works, we’ve modeled this multiplication. The number 23 has been modeled
using two 10s and three ones. There are five rows of 23 because
we’re multiplying 23 by five. When we use a standard written
method to add, subtract, or multiply, we always start in the ones column. We know the number 23 has three
ones, and we have to multiply them by five. Let’s count in threes five
times. Three, six, nine, 12, 15. Because we’ve got more than 10
ones, we’re going to need to regroup. We can take 10 of our ones and
exchange them for one 10. Now, we can record our five ones
under one 10 that we exchanged.
Step two is to multiply in the tens
column. We know the number 23 has two
10s. We have to multiply them by five
because we’re multiplying 23 by five. If you multiply two 10s by five, we
get two, four, six, eight, 10, and the one we exchanged makes 11 10s. Because we have more than 10 10s,
again, we have to regroup. We need to exchange our 10 10s for
100. So two 10s times five gives us 10
10s plus the one we exchanged makes 11. 11 10s is the same as one 10 and
one 100. 11 10s are 110. We put the one 100 in the hundreds
column and the one 10 in the tens column. 23 multiplied by five is 115.
We start by multiplying the ones
and record any regrouping. Then we multiply the tens and write
any regrouping in the hundreds column. Let’s practice what we’ve learned
now by answering some questions.
Find the result of the following:
29 multiplied by three equals what.
In this question, we have to
multiply a two-digit number, the number 29, by a single digit, three. And we can tell by the way the
question’s been set out that we have to use the standard written method. We know that two-digit numbers have
a tens digit and a ones digit. The number 29 has two 10s and nine
ones. When we multiply using the standard
written method, we always start by multiplying the ones first. So our first step is to multiply
nine by three. Nine times three is 27. We can write our seven ones in the
ones column and the two 10s in the tens column because 27 has two 10s and seven
ones. Because we’ve regrouped two 10s, we
need to remember to add those on when we’ve multiplied in the tens column.
So our next step is to multiply the
tens. Number 23 has two 10s, and we need
to multiply them by three. Two 10s multiplied by three gives
us a total of six 10s. And we need to add on the two 10s
that we regrouped earlier. Six 10s and two more 10s gives us a
total of eight 10s. 29 multiplied by three equals
87. When we multiply a two-digit number
by a one-digit number using the standard written method, first we multiply their
ones and regroup if we need to, and then we multiply the tens. We found the result of 29
multiplied by three using the standard written method. The result is 87.
Find the number that can replace
the question mark in the following: 56 multiplied by three.
In this question, we’re shown the
calculation 56 multiplied by three. But one of the digits is
missing. When we’re multiplying a two-digit
number by a one-digit number using the standard written method, we always start by
multiplying the ones first. The number 56 has six ones, and we
have to multiply them by three. We know that six times three equals
18. And we know that the number 18 has
one 10 and eight ones. So we can write the ones digit in
the ones column. This is the missing digit. We know that 18 has eight ones and
one 10, so we would need to regroup 10 of our ones and exchange them for one 10. We’ve written the 10 in the tens
column.
Although the rest of the
calculation has been done for us, we can work through it to make sure the answer’s
correct. Our next step is to multiply our
five 10s by three. Five 10s multiplied by three gives
us 15 10s. But we need to add the one that we
regrouped. 15 10s and one more gives us 16
10s. We can write the six in the tens
column and the one in the hundreds column. So 56 multiplied by three equals
168. The missing digit which replaces
the question mark is eight. All we had to do to find the
missing digit was multiply the ones. The missing digit is eight.
Look at this multiplication with an
error in the answer: 34 multiplied by four equals 126. Which digit in the answer is wrong
and needs to be replaced to make the answer correct? Write the correct answer.
In this question, we have to
calculate 34 multiplied by four to find the correct answer. We know that one of the digits in
the answer given is incorrect. So let’s calculate the answer. When we multiply a two-digit number
by a one-digit number using the standard written method, we always start by
multiplying the ones first. We know the number 34 has four
ones, and we need to multiply them by four. Four times four is 16. We can write the six in the ones
column. And we need to regroup 10 of our
ones and exchange them for one 10.
Next, we need to multiply the
tens. We got three 10s, and we need to
multiply them by four. We know that three times four is
12, so three 10s multiplied by four gives us 12 10s. And we need to add the one that we
regrouped earlier. 12 10s plus one more 10 gives us a
total of 13 10s. We can write three 10s in the tens
column and regroup 10 of our tens for 100. So 34 multiplied by four is
136.
So the digit in the calculation we
were given, which is incorrect, is the tens digit. It looks like whoever did the
calculation forgot to add the 10 that we’d regrouped. So the digit which is wrong is the
two. We need to replace that with a
three to make the answer correct. The correct answer should be 136
not 126. We found the error in the
calculation by working out 34 multiplied by four using the standard written
method. First, we multiplied the ones and
regrouped. Then we multiplied the tens. The digit which is wrong is the
two, which needs to be replaced with a three. And the correct answer is 136.
What have we learned in this
video? We have learned how to multiply a
two-digit number by a single digit using the standard written method. We learned that we multiply the
ones first and regroup if needed, and then we multiply the tens.
