Multiplication Tables From 12 To 15
The tables from 12 to 15 are the products of each of these four numbers multiplied by $1, 2, 3$, and so on. They are the first tables past the 1-to-10 basics, and each one rebuilds cleanly from a smaller table rather than needing fresh recall.
Here is the master grid to the tenth multiple. Each individual table page linked at the end carries the same rows extended to $\times 20$.
× | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
12 | 12 | 24 | 36 | 48 | 60 | 72 | 84 | 96 | 108 | 120 |
13 | 13 | 26 | 39 | 52 | 65 | 78 | 91 | 104 | 117 | 130 |
14 | 14 | 28 | 42 | 56 | 70 | 84 | 98 | 112 | 126 | 140 |
15 | 15 | 30 | 45 | 60 | 75 | 90 | 105 | 120 | 135 | 150 |
How Do You Read These Tables?
Reading a row is the whole skill. Take the row for 14 and the column for 6: they cross at 84, so $14 \times 6 = 84$. The first number is the size of each group, the second is how many groups you have, and the cell is the total.
Each row also climbs by a fixed step equal to its own number: the 12 row rises by 12 every column (12, 24, 36), the 15 row by 15. Spot the step and you can extend any row past where the grid stops.
How To Learn The Tables From 12 To 15 (Patterns, Not Memorizing)
Bhanzu teaches the few patterns that generate a table rather than drilling its facts into recall. Every table from 12 to 15 is a ten plus a small remainder, so you can rebuild any row from the tens you already know instead of reciting it. That structural view is the number sense algebra later leans on.
What is the easiest way to learn tables from 12 to 15? Split each number into a ten and a units digit, then add two easy products: $12 \times n = (10 \times n) + (2 \times n)$. For $12 \times 7$: $70 + 14 = 84$.
The 12s split into a ten and a two: $12 \times n = 10n + 2n$. The 12s are also the 6s doubled, since $12 = 2 \times 6$, so from $6 \times 8 = 48$ you get $12 \times 8 = 96$.
The 13s split into a ten and a three: $13 \times n = 10n + 3n$. For $13 \times 6$: $60 + 18 = 78$.
The 14s are the 7s doubled, because $14 = 2 \times 7$. Since $7 \times 9 = 63$, $14 \times 9 = 126$; the same row also equals $10n + 4n$.
The 15s are ten-times plus half of that, because $15 = 10 + 5$ and 5 is half of 10: $15 \times n = 10n + 5n$. For $15 \times 6$: $60 + 30 = 90$. Every multiple of 15 is also half the matching multiple of 30.
What Do The Tables Look Like In Words?
Every row can be spoken as a sentence, which is how most learners first lock a table in. The 13 row reads "one times 13 is 13, two times 13 is 26, three times 13 is 39," on to "ten times 13 is 130."
The same spoken shape works for 12, 14, and 15 - only the number spoken changes. Read the row you find hardest aloud a few times, then test yourself against the grid.
Why Should You Learn The Tables From 12 To 15?
These are the tables that turn slow long-multiplication into quick mental work. A dozen is 12, so the 12s run through eggs, months, and hours; the 13, 14, and 15 tables round out the range that daily arithmetic reaches for most after the basics.
They also set up the pattern method itself. Once a student rebuilds $13 \times 8$ from $10 \times 8$ plus $3 \times 8$, the same split unlocks every table past 15 - the twenties, the thirties, and beyond all work the same way.
Where Do These Tables Appear?
These tables sit close to everyday counting. A dozen is 12, so eggs, buns, and months of the year all read off the 12 table; a fortnight is 14 days, so two-week cycles scale on the 14s; and 15 minutes is a quarter hour, so the 15s power clock math where $15 \times 4 = 60$ closes the hour. For pattern-based shortcuts across these, the Bhanzu guide to mental math tricks is a useful companion, and teachers treat fluent tables as the base of number sense rather than a memorisation chore.
Solved Examples
Example 1
What is $12 \times 8$?
Split 12 into $10 + 2$: $12 \times 8 = (10 \times 8) + (2 \times 8) = 80 + 16$.
$80 + 16 = 96$.
Final answer: $12 \times 8 = 96$.
Example 2 (Wrong path first)
A shelf holds 14 books. How many books on 9 such shelves?
Wrong attempt. The rusher reads $14 \times 9$ as $14 \times 10 = 140$ and stops there.
Why it breaks. Multiplying by 10 counts ten shelves, but there are only nine, so 140 is one shelf too many.
Correct. Take $14 \times 10 = 140$, then subtract one shelf of 14: $140 - 14 = 126$.
Final answer: 126 books.
Example 3
Find $15 \times 12$.
Split 12 into $10 + 2$: $15 \times 10 = 150$ and $15 \times 2 = 30$.
$150 + 30 = 180$.
Final answer: $15 \times 12 = 180$.
Example 4
Fill in the blank: $13 \times {?} = 91$.
Divide to find the missing factor: $91 \div 13 = 7$.
Final answer: $13 \times 7 = 91$.
Example 5
What is $14 \times 14$?
The 14s are the 7s doubled, so start from $7 \times 14 = 98$, then double: $98 \times 2 = 196$.
Final answer: $14 \times 14 = 196$.
Practice Questions
$12 \times 6 = {?}$
$13 \times 9 = {?}$
$14 \times 7 = {?}$
A box holds 15 pens. How many pens in 8 boxes?
$12 \times 12 = {?}$
Which is larger, $13 \times 8$ or $15 \times 7$?
Fill in the blank: $14 \times {?} = 112$.
$15 \times 20 = {?}$
Answers: 1. 72 2. 117 3. 98 4. 120 5. 144 6. $15 \times 7 = 105$ is larger than $13 \times 8 = 104$ 7. 8 8. 300.
Conclusion
Tables from 12 to 15 each split into a ten and a small remainder, so every row rebuilds from the tens you already know.
The 12s double the 6s, the 14s double the 7s, and the 15s are half the 30s.
Each individual table has its own detailed page linked below.
To take this further with a teacher, explore Bhanzu's mental maths for kids sessions or an elementary math tutor, and build calculation speed with speed math practice.
Read More
Multiplication Tables - the master hub with every times table in one place.
Tables from 1 to 20 - the full master-grid treatment for the 1-to-20 range.
12 times table and 13 times table - the lower half of this range in full.
14 times table and 15 times table - the upper half in full.
Math is Fun — Multiplication Tables - printable charts and an interactive grid.
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