Lesson 1 of 10 · Grades 3 to 4
What multiplication means
Multiplication is a fast way to add equal groups. Instead of adding 8 four times, you multiply 4 by 8 and get the same total in one step. In this lesson you will see where the answer comes from and learn the names of the three numbers.
Equal groups
Picture an egg carton with 4 rows and 6 eggs in each row. Every row holds exactly the same number of eggs, so the carton is made of equal groups. One row is a group, and each group holds 6 eggs.
Those rows are the heart of multiplication. Whenever a story has groups of the same size, you can multiply to count everything at once instead of adding row after row. A box of 3 pencil cases with 8 pencils in each case, a tray of 5 rows of 7 muffins, and 6 bags of 9 apples all have the same shape: equal groups.
From adding to multiplying
Suppose you count the eggs the slow way. You add the rows: 6 + 6 + 6 + 6. The answer is 24. Now write the same thing as a multiplication: 4 × 6 = 24. The 4 counts the groups, and the 6 tells you how big each group is. The multiplication is a short name for the repeated addition.
Multiplying is not a different kind of arithmetic. It is adding equal amounts, written in a shorter way. That is why the answer always matches the repeated addition. If you ever forget what a multiplication means, you can add the groups again and check.
The names of the three numbers
Every multiplication has three jobs. The numbers you multiply together are the factors. In 4 × 6, both 4 and 6 are factors. The answer is the product. Here the product is 24.
The times sign tells you to combine the groups. Read 4 × 6 out loud as "four times six" or "four groups of six". Both readings describe the same picture: four groups, six in each group.
Watch out for this
The groups must be equal, or the multiplication does not describe the picture. Three bowls with 4 grapes, 7 grapes and 5 grapes are not three groups of 4. Adding them gives 16, but 3 × 4 gives 12. Count the groups first: if the group sizes are different, multiplication is the wrong tool.
Worked example
A baker fills 5 trays with buns. Each tray holds 8 buns. How many buns does the baker make?
Step 1: read the story for equal groups. There are 5 trays, and every tray holds the same number, 8. So there are 5 equal groups of 8.
Step 2: write the repeated addition. The baker makes 8 + 8 + 8 + 8 + 8 buns.
Step 3: turn the addition into a multiplication. Five equal groups of 8 is 5 × 8.
Step 4: work out the product. 5 × 8 = 40.
Answer: 40 buns.
Remember
- Multiplication counts equal groups quickly.
- The factors are the numbers you multiply.
- The product is the answer.
- Repeated addition and multiplication give the same total.
Try it
Answer the five questions below. Work them out first, then open each answer to check.
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There are 3 boxes. Each box holds 5 crayons. Write this as a multiplication and find the total.
Show answer
3 × 5 = 15 crayons. Three equal groups of five make fifteen.
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Write 6 + 6 + 6 + 6 as one multiplication, then solve it.
Show answer
4 × 6 = 24. There are 4 equal groups of 6, so the total is 24.
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A tray of muffins has 5 rows with 7 muffins in each row. How many muffins are on the tray?
Show answer
35 muffins. Five rows of seven make 35.
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In 8 × 4 = 32, which number is the product?
Show answer
32. The product is the answer to a multiplication.
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There are 6 fish bowls and 2 fish in each bowl. How many fish are there in all?
Show answer
12 fish. Six groups of two make 12.
Puzzle · Equal groups
Puzzle time
Each box in the picture holds the same number of dots. Which multiplication matches the picture exactly?
Show a hint
Count the boxes first. Then count the dots inside one box. The multiplication is boxes times dots in a box.
Show the answer
Answer: 4 × 7. There are 4 equal groups of 7, so the matching multiplication is 4 × 7 = 28. 7 × 7 gives 49, 3 × 7 gives 21, and 4 + 7 gives 11.