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How are multiplication and division related?
Goal:
Goal:
Think About It!
Goal: Identify how multiplication and division relate using equal groups.
If the figure skating couple is scored 90 points in total and each judge gave the same score, how many points did each judge give the couple? We can divide the total score by the number of judges to find each judge’s score.
Recall that multiplication facts are related to division facts. You can switch from a multiplication sentence to a division sentence by moving around the numbers!
For our problem, we can use one of our division strategies. Do you remember the strategies? Think of each strategy below. Then, click the name of the strategy to see how to find the quotient of our division sentence.
| Strategy | Using the Strategy to Solve 90 \({ \div }\) 10 |
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For arrays or pictures, you distribute the total number of points into 10 groups until you run out of points. You can use tally marks to represent the total points. You can draw 1 tally mark at a time in each of the 10 groups until all 90 have been drawn. 
90 \({ \div }\) 10 \({ \text{=} }\) 9 For 90 total points/tallies, you get 10 groups of 9 tallies in each group. 9 is the quotient! |
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For repeated subtraction, you subtract the divisor from the dividend over and over until you get to zero. The number of times you subtract the repeated subtrahend is the quotient. 90 – 10 – 10 – 10 – 10 – 10 – 10 – 10 – 10 – 10 = 0 90 \({ \div }\) 10 \({ \text{=} }\) 9 You have to subtract 10 nine times to get to zero. 9 is the quotient! |
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Use a multiplication table to switch from multiplication to division. Remember, multiplication and division are opposite operations. First, find the divisor in the left-hand column (10). Then, go across the row to the dividend (90). Then, look at the top of the column, and that will give you the quotient (9)! 
In the tenth row, 90 is in the 9 column. That means that 9 is the quotient! 90 \({ \div }\) 10 \({ \text{=} }\) 9 |
Zoe and Daniel want to figure out what the most total points will be per judge. Let’s look more into the division facts of 10 to help them do this.
Let’s take a closer look at the multiplication chart using the tenth row. You can use this row to find all of the division facts of 10!
In column 1, you see that 10 \({ \times }\) 1 \({ \text{=} }\) 10. This also means that 10 \({ \div }\) 10 \({ \text{=} }\) 1.
In column 2, you see that 10 \({ \times }\) 2 \({ \text{=} }\) 20, so 20 \({ \div }\) 10 \({ \text{=} }\) 2.
One team got 30 points. There are 10 judges. Use the chart to find the quotient of 30 \({ \div }\) 10. What did you find? Click Show Me to check your answer.
You see 30 in the third column. If you go to the top of the column, you will be at 3! So, 30 \({ \div }\) 10 \({ \text{=} }\) 3! Each judge gave 3 points!
You can continue this way to find all of the division facts of 10. Let’s see if we can find the rest of our quotients for our multiples of 10.
Locate each of the dividends below in the multiplication table in the 10th row. These numbers are the total points from the judges. Go to the top of that column to find your quotient! These numbers are the numbers of points given by each judge to get the total points.
So, if the total points for a team is 50 points, that means each of the 10 judges gave a score of 5 points. 50 \({ \div }\) 10 \({ \text{=} }\) 5
Write the division fact for all of the quotients in your notes. Click on the dividend to check your work.
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Dividend (total points) |
Column Found (points per judge) |
Division Fact |
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4 |
40 \({ \div }\) 10 \({ \text{=} }\) 4 |
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5 |
50 \({ \div }\) 10 \({ \text{=} }\) 5 |
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6 |
60 \({ \div }\) 10 \({ \text{=} }\) 6 |
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7 |
70 \({ \div }\) 10 \({ \text{=} }\) 7 |
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8 |
80 \({ \div }\) 10 \({ \text{=} }\) 8 |
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9 |
90 \({ \div }\) 10 \({ \text{=} }\) 9 |
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10 |
100 \({ \div }\) 10 \({ \text{=} }\) 10 |
Let’s look at one special case:
0 \({ \div }\) 10 \({ = }\) ?
Can you find this in the multiplication table? Take a look.
It is not there! But you could think of it this way: If you had 0 people and wanted to divide them into 10 groups, you would not be able to, since you have no people to divide!
Zero divided by anything is zero, because there is nothing to divide to start with!
0 \({ \div }\) 10 \({ = }\) 0
The multiplication table can help us learn and practice our division skills. Let’s keep going to learn our division facts of 10.