\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)

Times Tables

Times Tables


Each box can hold 9 pencils, and there are 5 boxes ready to be filled.
Hugo wants to find out the total number of pencils needed to fill all the boxes.
Can you help Hugo?

Hugo starts by adding 9 five times, like this: $$9+9+9+9+9$$However, this takes time. Instead, he uses the times table for a quicker method.
As \(\begin{aligned}\textcolor{colordef}{5}\times \textcolor{colorprop}{0}&=\textcolor{olive}{0}\\\textcolor{colordef}{5}\times \textcolor{colorprop}{1}&=\textcolor{olive}{5}\\\textcolor{colordef}{5}\times \textcolor{colorprop}{2}&=\textcolor{olive}{10}\\\textcolor{colordef}{5}\times \textcolor{colorprop}{3}&=\textcolor{olive}{15}\\\textcolor{colordef}{5}\times \textcolor{colorprop}{4}&=\textcolor{olive}{20}\\\textcolor{colordef}{5}\times \textcolor{colorprop}{5}&=\textcolor{olive}{25}\\\textcolor{colordef}{5}\times \textcolor{colorprop}{6}&=\textcolor{olive}{30}\\\textcolor{colordef}{5}\times \textcolor{colorprop}{7}&=\textcolor{olive}{35}\\\textcolor{colordef}{5}\times \textcolor{colorprop}{8}&=\textcolor{olive}{40}\\\textcolor{colordef}{5}\times \textcolor{colorprop}{9}&=\textcolor{olive}{45}\\\textcolor{colordef}{5}\times \textcolor{colorprop}{10}&=\textcolor{olive}{50}\end{aligned}\), \(\textcolor{colordef}{5}\times \textcolor{colorprop}{9}=\textcolor{olive}{45}\).
So, Hugo will need 45 pencils to fill all the boxes. This example shows why learning the times table is helpful.


Definition Times Table
A Times Table is a list that shows the results of multiplying one number by the numbers from 0 to 10.
Example
Calculate \(4\times 9\) given the times table of \(4\) \(\begin{aligned}\textcolor{colordef}{4}\times \textcolor{colorprop}{0}&=\textcolor{olive}{0}\\\textcolor{colordef}{4}\times \textcolor{colorprop}{1}&=\textcolor{olive}{4}\\\textcolor{colordef}{4}\times \textcolor{colorprop}{2}&=\textcolor{olive}{8 }\\\textcolor{colordef}{4}\times \textcolor{colorprop}{3}&=\textcolor{olive}{12 }\\\textcolor{colordef}{4}\times \textcolor{colorprop}{4}&=\textcolor{olive}{16 }\\\textcolor{colordef}{4}\times \textcolor{colorprop}{5}&=\textcolor{olive}{20 }\\\textcolor{colordef}{4}\times \textcolor{colorprop}{6}&=\textcolor{olive}{24 }\\\textcolor{colordef}{4}\times \textcolor{colorprop}{7}&=\textcolor{olive}{28 }\\\textcolor{colordef}{4}\times \textcolor{colorprop}{8}&=\textcolor{olive}{32 }\\\textcolor{colordef}{4}\times \textcolor{colorprop}{9}&=\textcolor{olive}{36 }\\\textcolor{colordef}{4}\times \textcolor{colorprop}{10}&=\textcolor{olive}{40}\end{aligned}\)

In the times table of \(4\), we find \(4\times 9=36\).

Times Table of 2


How many eyes are there ?

You can count by 2s: 2, 4, 6, 8, and 10. So, there are \(5 \times 2 = 2 + 2 + 2 + 2 + 2 = 10\) eyes.
We can calculate more quickly with $$\begin{aligned}[t]5 \times 2 &= 2 \times 5\\&= 5 + 5 \\&= 10\\\end{aligned}$$


Proposition Times Table of 2
\(\begin{aligned} \textcolor{colordef}{2}\times \textcolor{colorprop}{0}&=\textcolor{olive}{0}\\\textcolor{colordef}{2}\times \textcolor{colorprop}{1}&=\textcolor{olive}{2}\\ \textcolor{colordef}{2}\times \textcolor{colorprop}{2}&=\textcolor{olive}{4 }\\ \textcolor{colordef}{2}\times \textcolor{colorprop}{3}&=\textcolor{olive}{6 }\\ \textcolor{colordef}{2}\times \textcolor{colorprop}{4}&=\textcolor{olive}{8 }\\ \textcolor{colordef}{2}\times \textcolor{colorprop}{5}&=\textcolor{olive}{10 }\\ \textcolor{colordef}{2}\times \textcolor{colorprop}{6}&=\textcolor{olive}{12 }\\ \textcolor{colordef}{2}\times \textcolor{colorprop}{7}&=\textcolor{olive}{14 }\\ \textcolor{colordef}{2}\times \textcolor{colorprop}{8}&=\textcolor{olive}{16 }\\ \textcolor{colordef}{2}\times \textcolor{colorprop}{9}&=\textcolor{olive}{18 }\\ \textcolor{colordef}{2}\times \textcolor{colorprop}{10}&=\textcolor{olive}{20}\end{aligned}\) \(\quad \quad\) \(\begin{aligned}\textcolor{colordef}{0}\times \textcolor{colorprop}{2}&=\textcolor{olive}{0}\\\textcolor{colordef}{1}\times \textcolor{colorprop}{2}&=\textcolor{olive}{2}\\\textcolor{colordef}{2}\times \textcolor{colorprop}{2}&=\textcolor{olive}{4 }\\\textcolor{colordef}{3}\times \textcolor{colorprop}{2}&=\textcolor{olive}{6 }\\\textcolor{colordef}{4}\times \textcolor{colorprop}{2}&=\textcolor{olive}{8 }\\\textcolor{colordef}{5}\times \textcolor{colorprop}{2}&=\textcolor{olive}{10 }\\\textcolor{colordef}{6}\times \textcolor{colorprop}{2}&=\textcolor{olive}{12 }\\\textcolor{colordef}{7}\times \textcolor{colorprop}{2}&=\textcolor{olive}{14 }\\\textcolor{colordef}{8}\times \textcolor{colorprop}{2}&=\textcolor{olive}{16 }\\\textcolor{colordef}{9}\times \textcolor{colorprop}{2}&=\textcolor{olive}{18 }\\\textcolor{colordef}{10}\times \textcolor{colorprop}{2}&=\textcolor{olive}{20}\end{aligned}\)

Times Table of 5


How many cubes are there if we count by 5s?

You can count by 5s: 5, 10, and 15 cubes.
There are \(3 \times 5 = 5 + 5 + 5 = 15\) cubes.


Proposition Times Table of 5
\(\begin{aligned}\textcolor{colordef}{5}\times \textcolor{colorprop}{0}&=\textcolor{olive}{0}\\\textcolor{colordef}{5}\times \textcolor{colorprop}{1}&=\textcolor{olive}{5}\\\textcolor{colordef}{5}\times \textcolor{colorprop}{2}&=\textcolor{olive}{10 }\\\textcolor{colordef}{5}\times \textcolor{colorprop}{3}&=\textcolor{olive}{15 }\\\textcolor{colordef}{5}\times \textcolor{colorprop}{4}&=\textcolor{olive}{20 }\\\textcolor{colordef}{5}\times \textcolor{colorprop}{5}&=\textcolor{olive}{25 }\\\textcolor{colordef}{5}\times \textcolor{colorprop}{6}&=\textcolor{olive}{30 }\\\textcolor{colordef}{5}\times \textcolor{colorprop}{7}&=\textcolor{olive}{35 }\\\textcolor{colordef}{5}\times \textcolor{colorprop}{8}&=\textcolor{olive}{40 }\\\textcolor{colordef}{5}\times \textcolor{colorprop}{9}&=\textcolor{olive}{45 }\\\textcolor{colordef}{5}\times \textcolor{colorprop}{10}&=\textcolor{olive}{50}\end{aligned}\) \(\quad \quad\) \(\begin{aligned}\textcolor{colordef}{0}\times \textcolor{colorprop}{5}&=\textcolor{olive}{0}\\\textcolor{colordef}{1}\times \textcolor{colorprop}{5}&=\textcolor{olive}{5}\\\textcolor{colordef}{2}\times \textcolor{colorprop}{5}&=\textcolor{olive}{10}\\\textcolor{colordef}{3}\times \textcolor{colorprop}{5}&=\textcolor{olive}{15}\\\textcolor{colordef}{4}\times \textcolor{colorprop}{5}&=\textcolor{olive}{20}\\\textcolor{colordef}{5}\times \textcolor{colorprop}{5}&=\textcolor{olive}{25}\\\textcolor{colordef}{6}\times \textcolor{colorprop}{5}&=\textcolor{olive}{30}\\\textcolor{colordef}{7}\times \textcolor{colorprop}{5}&=\textcolor{olive}{35}\\\textcolor{colordef}{8}\times \textcolor{colorprop}{5}&=\textcolor{olive}{40}\\\textcolor{colordef}{9}\times \textcolor{colorprop}{5}&=\textcolor{olive}{45}\\\textcolor{colordef}{10}\times \textcolor{colorprop}{5}&=\textcolor{olive}{50}\end{aligned}\)

Times Table of 10


How many cubes are there if we count by 10s?

You can count by 10s: 10, 20, and 30 cubes.
There are \(3 \times 10 = 10 + 10 + 10 = 30\) cubes.


Proposition Times Table of 10
\(\begin{aligned}\textcolor{colordef}{10} \times \textcolor{colorprop}{0} &= \textcolor{olive}{0} \\\textcolor{colordef}{10} \times \textcolor{colorprop}{1} &= \textcolor{olive}{10} \\\textcolor{colordef}{10} \times \textcolor{colorprop}{2} &= \textcolor{olive}{20} \\\textcolor{colordef}{10} \times \textcolor{colorprop}{3} &= \textcolor{olive}{30} \\\textcolor{colordef}{10} \times \textcolor{colorprop}{4} &= \textcolor{olive}{40} \\\textcolor{colordef}{10} \times \textcolor{colorprop}{5} &= \textcolor{olive}{50} \\\textcolor{colordef}{10} \times \textcolor{colorprop}{6} &= \textcolor{olive}{60} \\\textcolor{colordef}{10} \times \textcolor{colorprop}{7} &= \textcolor{olive}{70} \\\textcolor{colordef}{10} \times \textcolor{colorprop}{8} &= \textcolor{olive}{80} \\\textcolor{colordef}{10} \times \textcolor{colorprop}{9} &= \textcolor{olive}{90} \\\textcolor{colordef}{10} \times \textcolor{colorprop}{10} &= \textcolor{olive}{100}\end{aligned}\) \(\quad \quad\) \(\begin{aligned}\textcolor{colordef}{0} \times \textcolor{colorprop}{10} &= \textcolor{olive}{0} \\\textcolor{colordef}{1} \times \textcolor{colorprop}{10} &= \textcolor{olive}{10} \\\textcolor{colordef}{2} \times \textcolor{colorprop}{10} &= \textcolor{olive}{20} \\\textcolor{colordef}{3} \times \textcolor{colorprop}{10} &= \textcolor{olive}{30} \\\textcolor{colordef}{4} \times \textcolor{colorprop}{10} &= \textcolor{olive}{40} \\\textcolor{colordef}{5} \times \textcolor{colorprop}{10} &= \textcolor{olive}{50} \\\textcolor{colordef}{6} \times \textcolor{colorprop}{10} &= \textcolor{olive}{60} \\\textcolor{colordef}{7} \times \textcolor{colorprop}{10} &= \textcolor{olive}{70} \\\textcolor{colordef}{8} \times \textcolor{colorprop}{10} &= \textcolor{olive}{80} \\\textcolor{colordef}{9} \times \textcolor{colorprop}{10} &= \textcolor{olive}{90} \\\textcolor{colordef}{10} \times \textcolor{colorprop}{10} &= \textcolor{olive}{100}\end{aligned}\)

Times Table of 3


How many bananas are there?

You can count by 3s: 3, 6, 9, and 12 bananas.
There are \(4 \times 3 = 3 + 3 + 3 + 3 = 12\) bananas.


Proposition Multiplication table 3
\(\begin{aligned}\textcolor{colordef}{3}\times \textcolor{colorprop}{0}&=\textcolor{olive}{0}\\\textcolor{colordef}{3}\times \textcolor{colorprop}{1}&=\textcolor{olive}{3}\\\textcolor{colordef}{3}\times \textcolor{colorprop}{2}&=\textcolor{olive}{6 }\\\textcolor{colordef}{3}\times \textcolor{colorprop}{3}&=\textcolor{olive}{9 }\\\textcolor{colordef}{3}\times \textcolor{colorprop}{4}&=\textcolor{olive}{12 }\\\textcolor{colordef}{3}\times \textcolor{colorprop}{5}&=\textcolor{olive}{15 }\\\textcolor{colordef}{3}\times \textcolor{colorprop}{6}&=\textcolor{olive}{18 }\\\textcolor{colordef}{3}\times \textcolor{colorprop}{7}&=\textcolor{olive}{21 }\\\textcolor{colordef}{3}\times \textcolor{colorprop}{8}&=\textcolor{olive}{24 }\\\textcolor{colordef}{3}\times \textcolor{colorprop}{9}&=\textcolor{olive}{27 }\\\textcolor{colordef}{3}\times \textcolor{colorprop}{10}&=\textcolor{olive}{30}\end{aligned}\) \(\quad \quad\) \(\begin{aligned}\textcolor{colordef}{0}\times \textcolor{colorprop}{3}&=\textcolor{olive}{0}\\\textcolor{colordef}{1}\times \textcolor{colorprop}{3}&=\textcolor{olive}{3}\\\textcolor{colordef}{2}\times \textcolor{colorprop}{3}&=\textcolor{olive}{6}\\\textcolor{colordef}{3}\times \textcolor{colorprop}{3}&=\textcolor{olive}{9}\\\textcolor{colordef}{4}\times \textcolor{colorprop}{3}&=\textcolor{olive}{12}\\\textcolor{colordef}{5}\times \textcolor{colorprop}{3}&=\textcolor{olive}{15}\\\textcolor{colordef}{6}\times \textcolor{colorprop}{3}&=\textcolor{olive}{18}\\\textcolor{colordef}{7}\times \textcolor{colorprop}{3}&=\textcolor{olive}{21}\\\textcolor{colordef}{8}\times \textcolor{colorprop}{3}&=\textcolor{olive}{24}\\\textcolor{colordef}{9}\times \textcolor{colorprop}{3}&=\textcolor{olive}{27}\\\textcolor{colordef}{10}\times \textcolor{colorprop}{3}&=\textcolor{olive}{30}\end{aligned}\)

Times Table of 4


Each butterfly has 4 wings. How many wings are there?

You can count by 4s: 4, 8, 12, 16, and 20 wings.
There are \(5 \times 4 = 4 + 4 + 4 + 4 + 4 = 20\) wings.


Proposition Multiplication table 4
\(\begin{aligned}\textcolor{colordef}{4}\times \textcolor{colorprop}{0}&=\textcolor{olive}{0}\\\textcolor{colordef}{4}\times \textcolor{colorprop}{1}&=\textcolor{olive}{4}\\\textcolor{colordef}{4}\times \textcolor{colorprop}{2}&=\textcolor{olive}{8 }\\\textcolor{colordef}{4}\times \textcolor{colorprop}{3}&=\textcolor{olive}{12 }\\\textcolor{colordef}{4}\times \textcolor{colorprop}{4}&=\textcolor{olive}{16 }\\\textcolor{colordef}{4}\times \textcolor{colorprop}{5}&=\textcolor{olive}{20 }\\\textcolor{colordef}{4}\times \textcolor{colorprop}{6}&=\textcolor{olive}{24 }\\\textcolor{colordef}{4}\times \textcolor{colorprop}{7}&=\textcolor{olive}{28 }\\\textcolor{colordef}{4}\times \textcolor{colorprop}{8}&=\textcolor{olive}{32 }\\\textcolor{colordef}{4}\times \textcolor{colorprop}{9}&=\textcolor{olive}{36 }\\\textcolor{colordef}{4}\times \textcolor{colorprop}{10}&=\textcolor{olive}{40}\end{aligned}\) \(\quad \quad\) \(\begin{aligned}\textcolor{colordef}{0}\times \textcolor{colorprop}{4}&=\textcolor{olive}{0}\\\textcolor{colordef}{1}\times \textcolor{colorprop}{4}&=\textcolor{olive}{4}\\\textcolor{colordef}{2}\times \textcolor{colorprop}{4}&=\textcolor{olive}{8}\\\textcolor{colordef}{3}\times \textcolor{colorprop}{4}&=\textcolor{olive}{12}\\\textcolor{colordef}{4}\times \textcolor{colorprop}{4}&=\textcolor{olive}{16}\\\textcolor{colordef}{5}\times \textcolor{colorprop}{4}&=\textcolor{olive}{20}\\\textcolor{colordef}{6}\times \textcolor{colorprop}{4}&=\textcolor{olive}{24}\\\textcolor{colordef}{7}\times \textcolor{colorprop}{4}&=\textcolor{olive}{28}\\\textcolor{colordef}{8}\times \textcolor{colorprop}{4}&=\textcolor{olive}{32}\\\textcolor{colordef}{9}\times \textcolor{colorprop}{4}&=\textcolor{olive}{36}\\\textcolor{colordef}{10}\times \textcolor{colorprop}{4}&=\textcolor{olive}{40}\end{aligned}\)