Arrange the solutions of these expressions in ascending order. 26 multiplied by eight, 86 multiplied by six, 77 multiplied by three, and 74 multiplied by seven.
Here we have four multiplications. And, each of them involves multiplying a two-digit number by a single digit. We know we need to find the answer to each of these calculations because we’re told to arrange the solutions. And, we’re told to put them in ascending order. Remember that the ascending order means from smallest to largest. And so, once we’ve found out the value of each multiplication, we need to put them in order, starting with the smallest and going up to the largest. Because we’re multiplying by a single digit each time, we can use short multiplication to solve each problem.
The first thing we can do is to write each calculation out vertically. Now, let’s go through each one and find the answers. First, 26 times eight. And, we’ll start by multiplying the ones digit, which is six times eight. We know that five eights or eight times five equals 40. So, six times eight equals one more eight on top of 40. The answer is 48. So, we write an eight in the ones place and exchange 40 ones for four tens. Next, we’re gonna multiply our tens digit by eight. Two tens multiplied by eight equals 16 tens. We’ve already got four tens underneath, so that takes us to 20 tens. 26 times eight equals 208.
In our next calculation, we need to multiply 86 by six. Once again, we can start off by multiplying the ones. We know six fives are 30. So, six sixes must be 36. Now, what are eight tens multiplied by six? Well, if you remember from our first calculation, we multiplied six by eight. The answer was 48. So, we know that eight tens multiplied by six equals 48 tens. We’ve got three tens underneath, so the answer is going to be 51 tens. 86 multiplied by six equals 516.
If we look carefully at our next calculation, we can see there’s actually only one multiplication fact that we need to know. And, that’s the answer to seven times three. We know two sevens are 14. So, three sevens are seven more than 14. The answer is 21. Now, because our tens digit is the same as our ones digit, we’ve got to complete the same calculation again. Seven tens multiplied by three equals 21 tens plus the two tens underneath equals 23 tens or 230. 77 multiplied by three equals 231.
In our last calculation, we’re multiplying by seven. 74 times seven. First of all, what are four ones multiplied by seven? Well, if we look back to our previous calculation, we were working out the answer to seven threes or three sevens. We decided that answer was 21. Four sevens must be seven more than 21. The answer is 28. Can you see how we’re using facts that we already know to help us work out the answers to those that we don’t? And, there are seven tens in our number. What is seven tens multiplied by seven? We know five sevens are 35. Six sevens are 42. So, seven sevens must be seven more than 42, which is 49. We’ve got two tens underneath, so that takes us to 51. 74 multiplied by seven equals 518.
Now, we’ve solved each of the expressions. But, we’ve been told we need to arrange them in ascending order. Remember, that means from smallest to largest. To help us compare our numbers, we can write them vertically. 208, 516, 231, and 518. The column with the largest value is the hundreds column. So, if we’re looking for the smallest possible solution, we need to look for the calculation with the smallest number of hundreds.
We can see that there are actually two numbers with the smallest number of hundreds. 208 has two hundreds, and 231 also has two hundreds. To work out which of these two numbers is the smallest, there’s no point looking at the hundreds digit because they’re both two. We need to go to the tens digits. In 208, the tens digit is zero, and in 231 the tens digit is three. So, we can say that 208 is the smallest number, followed by 231. Let’s cross through both numbers to show that we’ve used them.
Now, let’s look at our two remaining numbers, and we need to compare the hundreds digits again. Both numbers have five hundreds. So, we can’t separate them and say which is the smallest. Once again, we’re going to have to go to the tens column and compare the tens. Well, we can see that both numbers have the same number of tens too. We’re going to have to go all the way to the ones column. 516 has six ones, and 518 has eight ones. Six is smaller than eight, so 516 must come before 518 in our order. 518 is the largest number.
First of all, we’ve found the answer to each calculation by using short multiplication. Then, we’ve put the numbers in order comparing them digit by digit. We put them in ascending order, which means we started with the smallest, we went up to the largest. The solutions of each multiplication in ascending order are 208, 231, 516, and 518.