Arrange the expressions on the cards in ascending order. Three times seven, eight times five, three times nine, nine times nine, and six times six.
We’ve been given five cards, and on each card there’s a multiplication. The problem asks us to arrange the expressions or the multiplications on the cards in ascending order. Remember, putting things in ascending order means starting with the smallest and going through to the largest. We need to find out the value of each multiplication to be able to help us put them in order.
But before we start, there is actually one card that we know where it belongs. Can you spot which one? Each card contains a single digit multiplied by another digit, and the largest possible digit is nine. One of our cards says nine multiplied by nine. In other words, the largest possible digit multiplied by the largest possible digit. Whatever the answer is, we know that it’s going to be the largest value. We know 10 nines are 90, so nine nines must be nine less than 90. Nine nines have a value of 81.
Let’s go through the multiplications on the other cards and we’ll use some different methods to find the answers. Firstly, three times seven. Let’s count in sevens three times to find the answer here. Seven, 14, 21. So, three multiplied by seven has a value of 21.
We could find the answer to eight times five by counting in fives eight times. But what about this method? We know that eight times 10 is 80. So, eight times five must be half of this amount. Half of 80 is 40. And so, eight fives have a value of 40.
Our next card says three times nine. We know that three multiplied by 10 is 30. So, three multiplied by nine is three less than this. 30 take away three equals 27. And so, three lots of nine equals 27. Nine, 18, 27.
We’ve already worked out what nine nines are. So, let’s count in sixes six times to find the value of six multiplied by six. Six, 12, 18, 24, 30, and 36. Six sixes are 36.
Now, we’ve worked out the value of all five expressions. Let’s put them in ascending order. The smallest value is 21, so let’s write this multiplication to start with. Three times seven is the multiplication that has the smallest value. The next smallest value is 27. And so, three times nine comes next. There are no more values in the 20s, but we next have 36. So, six times six comes next. We know 81 comes last. So, our missing number must be 40, which was the multiplication eight times five. In order, the values were 21, 27, 36, 40, and 81.
The expressions on the cards put in ascending order are three times seven, three times nine, six times six, eight times five, and nine times nine.