Multiplying with Digits up to 10

Multiplying with digits up to 10 means finding the product of any two whole numbers from 0 through 10, such as \( 3 \times 4 \), \( 6 \times 9 \), or \( 10 \times 10 \). Every one of these facts describes the same idea: a number of equal groups being combined. If you already understand the multiplication sign, you know that \( 5 \times 3 \) means "5 groups of 3," and the goal here is to find that total quickly and reliably.

One of the clearest ways to see a multiplication fact is to draw it as an array, rows and columns of dots or squares. The array below shows 4 rows with 6 dots in each row, matching the fact \( 4 \times 6 = 24 \).

This is exactly the model used in groups and arrays up to 10: the number of rows is one factor, the number of columns is the other factor, and the total count of dots is the product. Once this picture feels natural, you can start moving away from drawing every dot and toward recalling the fact directly.

A multiplication chart up to 10 (sometimes called a multiplication table up to 10) organizes every fact from \( 1 \times 1 \) through \( 10 \times 10 \) into a grid. To find a product, look down the row for one factor and across the column for the other factor; the number where they meet is the answer. This is the same tool behind printed times tables up to 10, just arranged so any fact can be looked up in one glance.

Notice that the chart is a mirror image across its diagonal: the fact in row 7, column 8 is the same as the fact in row 8, column 7, both equal 56. That symmetry comes from the commutative property, \( a \times b = b \times a \), and it is one of the reasons a full set of multiplication facts up to 10 is easier to learn than it first looks.

Example 1: Find \( 6 \times 7 \).

Break 7 into \( 5 + 2 \). Then \( 6 \times 7 = 6 \times 5 + 6 \times 2 = 30 + 12 = 42 \).

Example 2: Find \( 8 \times 9 \).

Think of 9 as "one less than 10." Since \( 8 \times 10 = 80 \), subtract one group of 8: \( 80 - 8 = 72 \).

Example 3: Find \( 7 \times 8 \).

Split 8 into \( 4 + 4 \). Then \( 7 \times 8 = 7 \times 4 + 7 \times 4 = 28 + 28 = 56 \), matching the highlighted cell on the chart above.

A few strategies make times tables up to 10 much faster to recall:

Skip counting: for \( 4 \times 6 \), count by 4s six times: 4, 8, 12, 16, 20, 24.

Doubling: if you know \( 4 \times 6 = 24 \), then \( 8 \times 6 \) is just double that, \( 48 \).

Using 10 as an anchor: for facts with 9, multiply by 10 and subtract one group, since \( 9 \times n = 10 \times n - n \).

Swapping factors: use \( a \times b = b \times a \) to turn a harder fact into an easier one, such as switching \( 3 \times 9 \) into \( 9 \times 3 \).

Once multiplication facts up to 10 feel automatic, the next step is applying them to real situations, like counting seats in rows of chairs or fruit packed into boxes. For practice putting these facts to work in context, move on to multiplication word problems up to 10.

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