Story Problems
A school orders 24 boxes of markers. Each box contains 8 markers. They already had 60 markers in storage before the order. How many markers did the school receive in the order? What is the total number of markers they have now?
How many markers did the school receive in the order?
192 markers
What is the total number of markers they have now?
252 markers
2 x 132
264
2 x 23
46
22 x 43?
946
What is the name of the multiplication strategy when you double one number and halve the other, which keeps the product the same but may make the calculation easier.
Example:
25 × 16 →50 x 8 = 400
doubling and halving strategy
A publisher prints 42 boxes of books. Each box contains 14 books. How many books did they print in total? If each book sells for $12, how much money would they earn from selling all the books?
How many books did they print in total?
588 books
how much money would they earn from selling all the books?
$7,056
4 x 876
3,504
4 x 42
168
34 x 63
2,142
This is the traditional step-by-step method of multiplying numbers vertically. Each place value of one number is multiplied by each place value of the other, starting with the ones place. Some results are written in rows and then added together. This method relies on place value and regrouping.
Example:
236 × 47
→ Multiply 236 by 7 groups of 1, then by 4 groups of 10, and add both results.
Standard algorithm
Lena is making custom T-shirts for a concert. Each shirt costs $12 to make. She makes 18 shirts for the band and 25 shirts for fans. After selling all the shirts, she made a total of $900. How much did Lena spend making the shirts? How much profit did she earn?
How much did Lena spend making the shirts?
$ 516
How much profit did she earn?
$384
7 x 632
4,424
5 x 67
335
55 x 63
3,465
This visual method breaks numbers into place values and arranges them in a rectangle. Each section of the rectangle shows a partial product. Then all partial products are added together.
Example:
236 × 47→ Break into (200 + 30 + 6) and (40 + 7), multiply each pair, and sum all products.
area model
A bakery bakes 36 trays of cookies. Each tray holds 15 cookies. How many cookies did they bake? If They sell each cookie for $3. How much money would they make?
How many cookies did they bake?
540 cookies
How much money would they make?
$1,620
5,971
9 x 99
891
98 x 92
9,016
Each digit of one number is multiplied by each digit of the other based on place value, and then the partial products are added together.
Example:
236 × 47 = (200×40) + (30×40) + (6×40) + (200×7) + (30×7) + (6×7)
Partial product
A restaurant makes 28 pizzas for a party. Each pizza is sliced into 12 pieces. How many slices of pizza are there? If they sell each slice for $10, how much money would they make?
How many slices of pizza are there?
336 slices
how much money would they make?
$3,360
9 x 989
8,901
9 x 89
801
99 x 98
9,702
This is the most basic form of multiplication: adding a number to itself repeatedly.
Example:
5 × 4 = 5 + 5 + 5 + 5 = 20
repeated addition