Multiplication Facts and Times Tables: Complete Guide

What are multiplication facts?

A multiplication fact is a mathematical statement showing the product of two numbers. These facts form the foundation of multiplication, allowing learners to solve problems efficiently without needing to count or use repeated addition every time.

Knowing basic facts, such as $4 \times 5 = 20$, is critical because these small products are used continuously in harder topics like long division, fractions, and algebra.

Memorizing facts is helpful, but understanding how the numbers connect is just as important.

How to read a times table

A times table is a grid that organizes multiplication facts. To find the product of two numbers, you find the intersection of the row for the first number and the column for the second number.

The table works in both directions. Finding the row for $6$ and the column for $7$ gives the same result as finding the row for $7$ and the column for $6$.

Example 1: Finding a product using a times table

Question: Use the times table to find the product of $8$ and $4$.

Method:

1. Locate the number $8$ in the left-hand column.
2. Locate the number $4$ in the top row.
3. Follow the row to the right and the column down until they meet.

Answer: The intersection contains the number $32$. The product is $32$.

Check: You can verify this by checking the $4$ row and $8$ column. That intersection also contains $32$.

Patterns in times tables

Times tables contain repeating visual and numerical patterns. Recognizing these patterns makes learning multiplication facts much faster and reduces the amount of straight memorization required.

• The $2$ times table: All products are even numbers ending in $0, 2, 4, 6$, or $8$. Multiplying by $2$ is the same as doubling the number.
• The $5$ times table: Every product ends in either a $0$ or a $5$. The sequence jumps by fives: $5, 10, 15, 20$, and so on.
• The $10$times table: Every product ends in a $0$. To multiply a whole number by $10$, you shift its digits one place to the left, which places a zero in the ones place.
• The $9$ times table: The tens digit increases by one, and the ones digit decreases by one. Additionally, the sum of the digits for any fact up to $9 \times 10$ always equals $9$.

Use known facts to find new facts

If you forget a multiplication fact, you can easily figure it out by using facts you already know. The two most common strategies involve rearranging the numbers or splitting them apart.

The commutative property of multiplication means that reversing the order of the numbers does not change the product. If you cannot remember $7 \times 5$, you can calculate $5 \times 7$ instead. This property nearly halves the number of facts you need to memorize.

You can also decompose, or break apart, a difficult fact into two simpler facts.

Example 2: Using decomposition to find a fact

Question: How can you use known facts to calculate $8 \times 6$?

Method:

1. Break the number $8$ into two smaller, easier numbers, such as $5$ and $3$.
2. Multiply both of those smaller numbers by $6$.
3. Calculate $5 \times 6 = 30$.
4. Calculate $3 \times 6 = 18$.
5. Add the two partial products together: $30 + 18$.

Answer: $8 \times 6 = 48$.

Check: Using a times table, the intersection of row $8$ and column $6$ is $48$.

Fact families

Multiplication and division are inverse operations. They undo each other. A fact family is a group of three numbers related by multiplication and division.

Understanding multiplication and division fact families allows you to solve division problems by thinking of the missing multiplication fact.

Example 3: Completing a fact family

Question: Write the missing equation for the fact family containing the numbers $3, 9$, and $27$. The given equations are $3 \times 9 = 27$, $9 \times 3 = 27$, and $27 \div 3 = 9$.

Method:

1. Identify the operations used in the family. A complete family has two multiplication facts and two division facts.
2. Notice that both multiplication facts are provided.
3. Notice that one division fact is provided: $27 \div 3 = 9$.
4. The missing fact must be the second division equation, swapping the divisor and the quotient.

Answer: The missing equation is $27 \div 9 = 3$.

Check: Since $9 \times 3 = 27$, dividing $27$ into $9$ equal groups results in exactly $3$ per group.

Practice strategies

Practicing little and often is the most effective way to learn times tables. Rote repetition alone can be frustrating, so mixing strategies helps build both memory and understanding.

• Use visual models: Draw arrays (grids of dots) or area models to see the total number of items visually.
• Skip counting: Practice counting aloud by the number you are learning, such as $3, 6, 9, 12, 15$.
• Focus on one table: Do not try to learn all tables at once. Master the $2, 5$, and $10$ times tables first before moving to more difficult numbers like $7$ and $8$.
• Use flashcards: Write the fact on one side and the product on the back to test your memory.

Frequently asked questions

Why are multiplication facts important?

They are the basic building blocks for higher-level mathematics. Knowing them well prevents errors and saves time when solving fractions, area calculations, and long division.

Which times table is the hardest to learn?

Many learners find the $7$ and $8$ times tables challenging because they have fewer obvious visual patterns. Using decomposition (breaking $7 \times 8$ into $5 \times 8$ and $2 \times 8$) helps simplify them.

Do I need to memorize times tables beyond $10$?

While many international charts go up to $10 \times 10$, learning up to $12 \times 12$ is common because $12$ is heavily used in measurements like months in a year or items in a dozen. Beyond $12$, standard written multiplication methods are more practical.