Multiplication tricks for 6, 7 and 8 (the hardest times tables)

Quick answer

After the 0, 1, 2, 3, 4, 5, 9 and 10 tables, only six facts are new: 6 × 6, 6 × 7, 6 × 8, 7 × 7, 7 × 8 and 8 × 8. For 6s, use ×5 plus one more group; for 7s, split 7 into 5 + 2; for 8s, double three times. Common Core expects them by the end of 3rd grade.

If your child sails through the 2s, 5s and 10s and then hits a wall at 6, 7 and 8, that's completely normal. These tables have fewer obvious patterns. The good news: by the time you get here, most of their facts are already known, and each one that's left has a trick that builds on easier facts.

The only six facts that are left

The 6, 7 and 8 rows of a 10 × 10 chart hold 30 facts, but most are turn-arounds of facts your child already knows: 7 × 3 is 3 × 7, 8 × 5 is 5 × 8, 6 × 9 is 9 × 6. Once the 0, 1, 2, 3, 4, 5, 9 and 10 tables are solid, just six facts are new:

That's nine flash cards in total, counting the turn-arounds. Our guide to the fastest way to learn times tables shows exactly how the other facts get crossed off.

Tricks for the 6 times table

×5 plus one more group

Six groups is five groups plus one more group. Your child knows the 5s, so they only need to add one more:

• 6 × 6 = 30 + 6 = 36
• 6 × 7 = 35 + 7 = 42
• 6 × 8 = 40 + 8 = 48

6 times an even number

When 6 multiplies an even number, the answer ends in that same number, and the tens digit is half of it: 6 × 2 = 12, 6 × 4 = 24, 6 × 6 = 36, 6 × 8 = 48. It's a fun pattern to spot.

Double the 3s

6 is double 3, so a ×6 fact is double the ×3 fact: 3 × 7 = 21, so 6 × 7 = 42.

Tricks for the 7 times table

Break 7 into 5 and 2

Seven groups is five groups plus two groups, and the 5s and 2s are easy:

• 7 × 6 = 30 + 12 = 42
• 7 × 7 = 35 + 14 = 49
• 7 × 8 = 40 + 16 = 56

This is the break-apart strategy (the distributive property). The Common Core uses this very fact as its 3rd-grade example: 8 × 7 = 8 × 5 + 8 × 2 = 40 + 16 = 56 (3.OA.B.5).

The “5, 6, 7, 8” hook

Write the numbers 5, 6, 7, 8 in a row. Read them as “56 = 7 × 8.” It's a fun way to remember a fact that often feels tricky.

Skip count the 7s

7, 14, 21, 28, 35, 42, 49, 56, 63, 70. Saying the sequence aloud a few times a week builds a backup route to every 7s fact.

Tricks for the 8 times table

Double, double, double

8 is 2 × 2 × 2, so doubling a number three times multiplies it by 8. If your child knows their doubles facts, this one is quick:

• 8 × 6: 6 → 12 → 24 → 48
• 8 × 7: 7 → 14 → 28 → 56
• 8 × 8: 8 → 16 → 32 → 64

The ones-digit pattern

Look at the ones digits in the 8s: 8, 6, 4, 2, 0, then 8, 6, 4, 2, 0 again. Knowing the pattern is a quick way to check an answer.

1. 8 × 1=8
2. 8 × 2=16
3. 8 × 3=24
4. 8 × 4=32
5. 8 × 5=40
6. 8 × 6=48
7. 8 × 7=56
8. 8 × 8=64
9. 8 × 9=72
10. 8 × 10=80

Ten groups minus two

8 × 7 = 10 × 7 − 2 × 7 = 70 − 14 = 56. Handy for kids who like the ×9 strategy (ten groups minus one).

Square facts: 6 × 6, 7 × 7 and 8 × 8

Three of the six facts are squares: a number times itself. Their arrays make perfect squares, which gives them a memorable shape.

Squares also make great stepping stones to their neighbors. Add one more group to reach the next fact:

• 6 × 6 = 36, so 6 × 7 = 36 + 6 = 42
• 7 × 7 = 49, so 7 × 8 = 49 + 7 = 56

On a printed multiplication chart, the square numbers run along the diagonal from top left to bottom right. Ask your child to find 36, 49 and 64.

How to practice the last few facts

• Make a “tricky nine” card set: the six facts plus their three turn-arounds. Practice them for a few minutes most days.
• One trick per fact. Let your child choose the trick that clicks for each fact and say it aloud: “7 × 7 is 35 plus 14, 49.”
• Mix in easy wins. Shuffle in facts your child already knows, so every session feels successful.
• Practice look-alikes side by side. 6 × 9 = 54 and 7 × 8 = 56 are easy to swap, so put both cards next to each other and talk about the difference.
• Climb a ladder. 6 × 8 = 48, 7 × 8 = 56, 8 × 8 = 64. Each step adds one more 8.

Practice problems

Ask your child to name the trick they used for each one.

6, 7 and 8 practice (with answers)

1. 6 × 7 = ?
2. 7 × 8 = ?
3. 8 × 6 = ?
4. 6 × 6 = ?
5. 7 × 7 = ?
6. 8 × 8 = ?
7. 7 × 6 = ?
8. 8 × 7 = ?
9. 6 × 4 = ?
10. 7 × 9 = ?
11. 8 × 3 = ?
12. 8 × 9 = ?

Show answers

Need more? Print our multiplication worksheets, or take one table at a time with the full 6, 7 and 8 times table pages, which include word problems and division facts.

Frequently asked questions

What is the trick for the 7 times table?

Split 7 into 5 and 2. Your child already knows the 5s and the 2s, so 7 × 6 = 5 × 6 + 2 × 6 = 30 + 12 = 42, and 7 × 8 = 40 + 16 = 56. For 7 × 8 there's also a memory hook: write 5, 6, 7, 8 in order, and 56 = 7 × 8.

What is the trick for the 8 times table?

Double, double, double. Because 8 = 2 × 2 × 2, doubling a number three times multiplies it by 8. For 8 × 7: double 7 is 14, double 14 is 28, double 28 is 56. You can also double the ×4 fact: 4 × 6 = 24, so 8 × 6 = 48.

What is the trick for the 6 times table?

Use the 5s and add one more group: 6 × 7 = 5 × 7 + 7 = 35 + 7 = 42. There's also a neat pattern for even numbers: 6 × 2 = 12, 6 × 4 = 24, 6 × 6 = 36 and 6 × 8 = 48. The answer ends in the number you multiplied by, and the tens digit is half of it.

What is the hardest times table to learn?

There's no official answer, but the 6s, 7s and 8s often feel hardest because they have fewer obvious patterns than the 2s, 5s, 9s or 10s. The good news is that most of their facts are turn-arounds of easier ones, so only six facts are left to learn by the time you get there.

How do I remember 7 × 8?

Try the counting hook: 5, 6, 7, 8 becomes 56 = 7 × 8. If your child prefers a reason, break it apart: 7 × 8 = 5 × 8 + 2 × 8 = 40 + 16 = 56. Or build on a square fact: 7 × 7 = 49, and one more 7 makes 56.

Should kids learn the 6, 7 and 8 times tables last?

Usually, yes. When the 0, 1, 2, 3, 4, 5, 9 and 10 tables come first, the turn-around rule covers most of the 6, 7 and 8 facts, and the strategies for the rest build on tables your child already knows, such as ×5 and doubling.

Sources

• Common Core State Standards: Grade 3, Operations & Algebraic Thinking — CCSSI

Written by The Mathing Team for parents and teachers. Grade expectations follow the Common Core State Standards for Mathematics; your state or school may sequence skills a little differently.