International Baccalaureate · PYP 3

Times Tables to 10 × 10

⌚ ~162 min ▢ 18 blocks ✓ 117 exercises ➣ Prerequisites : Times Tables 2, 5 and 10, Times Tables 3 and 4

I Decompose with Addition

We need to find the total for 7 groups of 6 cubes, which is $7 \times 6$.
Multiplying by 7 directly can be difficult; multiplying by 5 is easier. We know that:

5 groups of 6 cubes have 30 cubes ($5 \times 6 = 30$).
2 groups of 6 cubes have 12 cubes ($2 \times 6 = 12$).

How can we use these two easy facts to solve the harder problem of $7 \times 6$?

Answer

Since 7 groups is 5 groups plus 2 more groups, we can add their totals together. $$\begin{aligned}[t] \text{Total for 7 groups} &= (\text{Total for 5 groups}) + (\text{Total for 2 groups})\\ 7 \times 6&= (5 \times 6) + (2 \times 6)\\ &=30+12\\ &=42\end{aligned} $$ So, there are 42 cubes in total.

Method — The “Break Apart” Strategy

This strategy uses the distributive property: a difficult multiplication can be “broken apart” into two easier ones, and the results added.
For example, to solve $7 \times 6$, we can break the 7 into a 5 and a 2: $$\begin{aligned}[t] \text{Total for 7 groups} &= (\text{Total for 5 groups}) + (\text{Total for 2 groups})\\ 7 \times 6&= (5 \times 6) + (2 \times 6)\\ &=30+12\\ &=42\end{aligned} $$

The second number can be broken apart too. To solve $7 \times 8$, we can break the 8 into a 5 and a 3: $$\begin{aligned}[t]7 \times 8&= (7 \times 5) + (7 \times 3)\\ &=35+21\\ &=56\end{aligned}$$

Skills to practice

Breaking Apart the First Number
Breaking Apart the Second Number

II The 6s Times Table

Discover

How many dots are there in total on these 4 dominoes?

Answer

We have 4 groups of 6. We can skip-count by 6s: 6, 12, 18, 24.

$$\begin{aligned}[t]4 \times 6 &= 6 + 6 + 6 + 6 && \text{(counting by 6s: }6, 12, 18, 24\text{)}\\ &= 24\end{aligned}$$ There are $24$ dots.

Proposition — Times Table of 6

The two columns give the same results: the order of the two numbers does not change the result. $\begin{aligned}\textcolor{colordef}{6}\times \textcolor{colorprop}{0}&=\textcolor{olive}{0}\\\textcolor{colordef}{6}\times \textcolor{colorprop}{1}&=\textcolor{olive}{6}\\\textcolor{colordef}{6}\times \textcolor{colorprop}{2}&=\textcolor{olive}{12 }\\\textcolor{colordef}{6}\times \textcolor{colorprop}{3}&=\textcolor{olive}{18 }\\\textcolor{colordef}{6}\times \textcolor{colorprop}{4}&=\textcolor{olive}{24 }\\\textcolor{colordef}{6}\times \textcolor{colorprop}{5}&=\textcolor{olive}{30 }\\\textcolor{colordef}{6}\times \textcolor{colorprop}{6}&=\textcolor{olive}{36 }\\\textcolor{colordef}{6}\times \textcolor{colorprop}{7}&=\textcolor{olive}{42 }\\\textcolor{colordef}{6}\times \textcolor{colorprop}{8}&=\textcolor{olive}{48 }\\\textcolor{colordef}{6}\times \textcolor{colorprop}{9}&=\textcolor{olive}{54 }\\\textcolor{colordef}{6}\times \textcolor{colorprop}{10}&=\textcolor{olive}{60}\end{aligned}$ $\quad \quad$ $\begin{aligned}\textcolor{colordef}{0}\times \textcolor{colorprop}{6}&=\textcolor{olive}{0}\\\textcolor{colordef}{1}\times \textcolor{colorprop}{6}&=\textcolor{olive}{6}\\\textcolor{colordef}{2}\times \textcolor{colorprop}{6}&=\textcolor{olive}{12}\\\textcolor{colordef}{3}\times \textcolor{colorprop}{6}&=\textcolor{olive}{18}\\\textcolor{colordef}{4}\times \textcolor{colorprop}{6}&=\textcolor{olive}{24}\\\textcolor{colordef}{5}\times \textcolor{colorprop}{6}&=\textcolor{olive}{30}\\\textcolor{colordef}{6}\times \textcolor{colorprop}{6}&=\textcolor{olive}{36}\\\textcolor{colordef}{7}\times \textcolor{colorprop}{6}&=\textcolor{olive}{42}\\\textcolor{colordef}{8}\times \textcolor{colorprop}{6}&=\textcolor{olive}{48}\\\textcolor{colordef}{9}\times \textcolor{colorprop}{6}&=\textcolor{olive}{54}\\\textcolor{colordef}{10}\times \textcolor{colorprop}{6}&=\textcolor{olive}{60}\end{aligned}$

Skills to practice

Counting by 6s
Multiplying by 6 using Decomposition
Multiplying by 6

III The 7s Times Table

Discover

There are 7 days in a week. How many days are there in 4 weeks?

Answer

We have 4 groups of 7. We can skip-count by 7s: 7, 14, 21, 28 days.

$$\begin{aligned}[t]4 \times 7 &= 7 + 7 + 7 + 7 && \text{(counting by 7s: }7, 14, 21, 28\text{)}\\ &= 28\end{aligned}$$ There are $28$ days.

Proposition — Times Table of 7

The two columns give the same results: the order of the two numbers does not change the result. $\begin{aligned}\textcolor{colordef}{7}\times \textcolor{colorprop}{0}&=\textcolor{olive}{0}\\\textcolor{colordef}{7}\times \textcolor{colorprop}{1}&=\textcolor{olive}{7}\\\textcolor{colordef}{7}\times \textcolor{colorprop}{2}&=\textcolor{olive}{14 }\\\textcolor{colordef}{7}\times \textcolor{colorprop}{3}&=\textcolor{olive}{21 }\\\textcolor{colordef}{7}\times \textcolor{colorprop}{4}&=\textcolor{olive}{28 }\\\textcolor{colordef}{7}\times \textcolor{colorprop}{5}&=\textcolor{olive}{35 }\\\textcolor{colordef}{7}\times \textcolor{colorprop}{6}&=\textcolor{olive}{42 }\\\textcolor{colordef}{7}\times \textcolor{colorprop}{7}&=\textcolor{olive}{49 }\\\textcolor{colordef}{7}\times \textcolor{colorprop}{8}&=\textcolor{olive}{56 }\\\textcolor{colordef}{7}\times \textcolor{colorprop}{9}&=\textcolor{olive}{63 }\\\textcolor{colordef}{7}\times \textcolor{colorprop}{10}&=\textcolor{olive}{70}\end{aligned}$ $\quad \quad$ $\begin{aligned}\textcolor{colordef}{0}\times \textcolor{colorprop}{7}&=\textcolor{olive}{0}\\\textcolor{colordef}{1}\times \textcolor{colorprop}{7}&=\textcolor{olive}{7}\\\textcolor{colordef}{2}\times \textcolor{colorprop}{7}&=\textcolor{olive}{14}\\\textcolor{colordef}{3}\times \textcolor{colorprop}{7}&=\textcolor{olive}{21}\\\textcolor{colordef}{4}\times \textcolor{colorprop}{7}&=\textcolor{olive}{28}\\\textcolor{colordef}{5}\times \textcolor{colorprop}{7}&=\textcolor{olive}{35}\\\textcolor{colordef}{6}\times \textcolor{colorprop}{7}&=\textcolor{olive}{42}\\\textcolor{colordef}{7}\times \textcolor{colorprop}{7}&=\textcolor{olive}{49}\\\textcolor{colordef}{8}\times \textcolor{colorprop}{7}&=\textcolor{olive}{56}\\\textcolor{colordef}{9}\times \textcolor{colorprop}{7}&=\textcolor{olive}{63}\\\textcolor{colordef}{10}\times \textcolor{colorprop}{7}&=\textcolor{olive}{70}\end{aligned}$

Skills to practice

Counting by 7s
Multiplying by 7 using Decomposition
Multiplying by 7

IV The 8s Times Table

Discover

A spider has 8 legs. How many legs do 4 spiders have altogether?

Answer

We have 4 groups of 8. We can skip-count by 8s: 8, 16, 24, 32 legs.

$$\begin{aligned}[t]4 \times 8 &= 8 + 8 + 8 + 8 && \text{(counting by 8s: }8, 16, 24, 32\text{)}\\ &= 32\end{aligned}$$ There are $32$ legs.

Proposition — Times Table of 8

The two columns give the same results: the order of the two numbers does not change the result. $\begin{aligned}\textcolor{colordef}{8}\times \textcolor{colorprop}{0}&=\textcolor{olive}{0}\\\textcolor{colordef}{8}\times \textcolor{colorprop}{1}&=\textcolor{olive}{8}\\\textcolor{colordef}{8}\times \textcolor{colorprop}{2}&=\textcolor{olive}{16 }\\\textcolor{colordef}{8}\times \textcolor{colorprop}{3}&=\textcolor{olive}{24 }\\\textcolor{colordef}{8}\times \textcolor{colorprop}{4}&=\textcolor{olive}{32 }\\\textcolor{colordef}{8}\times \textcolor{colorprop}{5}&=\textcolor{olive}{40 }\\\textcolor{colordef}{8}\times \textcolor{colorprop}{6}&=\textcolor{olive}{48 }\\\textcolor{colordef}{8}\times \textcolor{colorprop}{7}&=\textcolor{olive}{56 }\\\textcolor{colordef}{8}\times \textcolor{colorprop}{8}&=\textcolor{olive}{64 }\\\textcolor{colordef}{8}\times \textcolor{colorprop}{9}&=\textcolor{olive}{72 }\\\textcolor{colordef}{8}\times \textcolor{colorprop}{10}&=\textcolor{olive}{80}\end{aligned}$ $\quad \quad$ $\begin{aligned}\textcolor{colordef}{0}\times \textcolor{colorprop}{8}&=\textcolor{olive}{0}\\\textcolor{colordef}{1}\times \textcolor{colorprop}{8}&=\textcolor{olive}{8}\\\textcolor{colordef}{2}\times \textcolor{colorprop}{8}&=\textcolor{olive}{16}\\\textcolor{colordef}{3}\times \textcolor{colorprop}{8}&=\textcolor{olive}{24}\\\textcolor{colordef}{4}\times \textcolor{colorprop}{8}&=\textcolor{olive}{32}\\\textcolor{colordef}{5}\times \textcolor{colorprop}{8}&=\textcolor{olive}{40}\\\textcolor{colordef}{6}\times \textcolor{colorprop}{8}&=\textcolor{olive}{48}\\\textcolor{colordef}{7}\times \textcolor{colorprop}{8}&=\textcolor{olive}{56}\\\textcolor{colordef}{8}\times \textcolor{colorprop}{8}&=\textcolor{olive}{64}\\\textcolor{colordef}{9}\times \textcolor{colorprop}{8}&=\textcolor{olive}{72}\\\textcolor{colordef}{10}\times \textcolor{colorprop}{8}&=\textcolor{olive}{80}\end{aligned}$

Skills to practice

Counting by 8s
Multiplying by 8 using Decomposition
Multiplying by 8

V Decompose with Subtraction

Discover

Now consider $9 \times 8$. Multiplying by 9 directly can be difficult; multiplying by 10 is easier. We know that:

10 groups of 8 cubes have 80 cubes ($10 \times 8 = 80$).
1 group of 8 cubes has 8 cubes ($1 \times 8 = 8$).

How can knowing the answer for 10 groups help us find the answer for just 9 groups?

Answer

Since 9 groups is just 1 group less than 10 groups, we can start with the total for 10 groups and simply subtract the one extra group. $$\begin{aligned}[t]\text{Total for 9 groups} &= (\text{Total for 10 groups}) - (\text{Total for 1 group})\\ 9 \times 8 &= (10 \times 8) - (1 \times 8) \\ &= 80 - 8 \\ &= 72 \end{aligned}$$ So, there are 72 cubes in total.

Method — Using Subtraction to Break Apart

This is another way to use the distributive property. It is useful when multiplying by numbers that are close to a multiple of ten (like 8 or 9). To solve $9 \times 8$, you can think of 9 as $(10 - 1)$: $$\begin{aligned}[t] \text{Total for 9 groups} &= (\text{Total for 10 groups}) - (\text{Total for 1 group})\\ 9 \times 8 &= (10 \times 8) - (1 \times 8) \\ &= 80 - 8 \\ &= 72\end{aligned}$$

Skills to practice

Breaking Apart with a Subtraction

VI The 9s Times Table

Discover

There are 9 players on a baseball team. How many players are in 4 teams?

Answer

We have 4 groups of 9. We can skip-count by 9s: 9, 18, 27, 36 players.

$$\begin{aligned}[t]4 \times 9 &= 9 + 9 + 9 + 9 && \text{(counting by 9s: }9, 18, 27, 36\text{)}\\ &= 36\end{aligned}$$ There are $36$ players.

Proposition — Times Table of 9

The two columns give the same results: the order of the two numbers does not change the result. $\begin{aligned}\textcolor{colordef}{9}\times \textcolor{colorprop}{0}&=\textcolor{olive}{0}\\\textcolor{colordef}{9}\times \textcolor{colorprop}{1}&=\textcolor{olive}{9}\\\textcolor{colordef}{9}\times \textcolor{colorprop}{2}&=\textcolor{olive}{18 }\\\textcolor{colordef}{9}\times \textcolor{colorprop}{3}&=\textcolor{olive}{27 }\\\textcolor{colordef}{9}\times \textcolor{colorprop}{4}&=\textcolor{olive}{36 }\\\textcolor{colordef}{9}\times \textcolor{colorprop}{5}&=\textcolor{olive}{45 }\\\textcolor{colordef}{9}\times \textcolor{colorprop}{6}&=\textcolor{olive}{54 }\\\textcolor{colordef}{9}\times \textcolor{colorprop}{7}&=\textcolor{olive}{63 }\\\textcolor{colordef}{9}\times \textcolor{colorprop}{8}&=\textcolor{olive}{72 }\\\textcolor{colordef}{9}\times \textcolor{colorprop}{9}&=\textcolor{olive}{81 }\\\textcolor{colordef}{9}\times \textcolor{colorprop}{10}&=\textcolor{olive}{90}\end{aligned}$ $\quad \quad$ $\begin{aligned}\textcolor{colordef}{0}\times \textcolor{colorprop}{9}&=\textcolor{olive}{0}\\\textcolor{colordef}{1}\times \textcolor{colorprop}{9}&=\textcolor{olive}{9}\\\textcolor{colordef}{2}\times \textcolor{colorprop}{9}&=\textcolor{olive}{18}\\\textcolor{colordef}{3}\times \textcolor{colorprop}{9}&=\textcolor{olive}{27}\\\textcolor{colordef}{4}\times \textcolor{colorprop}{9}&=\textcolor{olive}{36}\\\textcolor{colordef}{5}\times \textcolor{colorprop}{9}&=\textcolor{olive}{45}\\\textcolor{colordef}{6}\times \textcolor{colorprop}{9}&=\textcolor{olive}{54}\\\textcolor{colordef}{7}\times \textcolor{colorprop}{9}&=\textcolor{olive}{63}\\\textcolor{colordef}{8}\times \textcolor{colorprop}{9}&=\textcolor{olive}{72}\\\textcolor{colordef}{9}\times \textcolor{colorprop}{9}&=\textcolor{olive}{81}\\\textcolor{colordef}{10}\times \textcolor{colorprop}{9}&=\textcolor{olive}{90}\end{aligned}$

Skills to practice

Counting by 9s
Multiplying by 9 using Decomposition
Multiplying by 9

VII The Full Multiplication Grid

Proposition — All Times Tables from 1 to 10

This grid shows all the times tables from 1 to 10 in one place. To find a product such as $7 \times 8$, find the row for 7 and the column for 8: the result is in the cell where they meet. The grid can also be read backwards: for $7 \times \square = 42$, go along the row for 7 to $42$, then up to the top of its column: $6$. So $7 \times 6 = 42$.

$\times$	$\textcolor{colorprop}{1}$	$\textcolor{colorprop}{2}$	$\textcolor{colorprop}{3}$	$\textcolor{colorprop}{4}$	$\textcolor{colorprop}{5}$	$\textcolor{colorprop}{6}$	$\textcolor{colorprop}{7}$	$\textcolor{colorprop}{8}$	$\textcolor{colorprop}{9}$	$\textcolor{colorprop}{10}$
$\textcolor{colordef}{1}$	$\textcolor{olive}{1}$	$\textcolor{olive}{2}$	$\textcolor{olive}{3}$	$\textcolor{olive}{4}$	$\textcolor{olive}{5}$	$\textcolor{olive}{6}$	$\textcolor{olive}{7}$	$\textcolor{olive}{8}$	$\textcolor{olive}{9}$	$\textcolor{olive}{10}$
$\textcolor{colordef}{2}$	$\textcolor{olive}{2}$	$\textcolor{olive}{4}$	$\textcolor{olive}{6}$	$\textcolor{olive}{8}$	$\textcolor{olive}{10}$	$\textcolor{olive}{12}$	$\textcolor{olive}{14}$	$\textcolor{olive}{16}$	$\textcolor{olive}{18}$	$\textcolor{olive}{20}$
$\textcolor{colordef}{3}$	$\textcolor{olive}{3}$	$\textcolor{olive}{6}$	$\textcolor{olive}{9}$	$\textcolor{olive}{12}$	$\textcolor{olive}{15}$	$\textcolor{olive}{18}$	$\textcolor{olive}{21}$	$\textcolor{olive}{24}$	$\textcolor{olive}{27}$	$\textcolor{olive}{30}$
$\textcolor{colordef}{4}$	$\textcolor{olive}{4}$	$\textcolor{olive}{8}$	$\textcolor{olive}{12}$	$\textcolor{olive}{16}$	$\textcolor{olive}{20}$	$\textcolor{olive}{24}$	$\textcolor{olive}{28}$	$\textcolor{olive}{32}$	$\textcolor{olive}{36}$	$\textcolor{olive}{40}$
$\textcolor{colordef}{5}$	$\textcolor{olive}{5}$	$\textcolor{olive}{10}$	$\textcolor{olive}{15}$	$\textcolor{olive}{20}$	$\textcolor{olive}{25}$	$\textcolor{olive}{30}$	$\textcolor{olive}{35}$	$\textcolor{olive}{40}$	$\textcolor{olive}{45}$	$\textcolor{olive}{50}$
$\textcolor{colordef}{6}$	$\textcolor{olive}{6}$	$\textcolor{olive}{12}$	$\textcolor{olive}{18}$	$\textcolor{olive}{24}$	$\textcolor{olive}{30}$	$\textcolor{olive}{36}$	$\textcolor{olive}{42}$	$\textcolor{olive}{48}$	$\textcolor{olive}{54}$	$\textcolor{olive}{60}$
$\textcolor{colordef}{7}$	$\textcolor{olive}{7}$	$\textcolor{olive}{14}$	$\textcolor{olive}{21}$	$\textcolor{olive}{28}$	$\textcolor{olive}{35}$	$\textcolor{olive}{42}$	$\textcolor{olive}{49}$	$\textcolor{olive}{56}$	$\textcolor{olive}{63}$	$\textcolor{olive}{70}$
$\textcolor{colordef}{8}$	$\textcolor{olive}{8}$	$\textcolor{olive}{16}$	$\textcolor{olive}{24}$	$\textcolor{olive}{32}$	$\textcolor{olive}{40}$	$\textcolor{olive}{48}$	$\textcolor{olive}{56}$	$\textcolor{olive}{64}$	$\textcolor{olive}{72}$	$\textcolor{olive}{80}$
$\textcolor{colordef}{9}$	$\textcolor{olive}{9}$	$\textcolor{olive}{18}$	$\textcolor{olive}{27}$	$\textcolor{olive}{36}$	$\textcolor{olive}{45}$	$\textcolor{olive}{54}$	$\textcolor{olive}{63}$	$\textcolor{olive}{72}$	$\textcolor{olive}{81}$	$\textcolor{olive}{90}$
$\textcolor{colordef}{10}$	$\textcolor{olive}{10}$	$\textcolor{olive}{20}$	$\textcolor{olive}{30}$	$\textcolor{olive}{40}$	$\textcolor{olive}{50}$	$\textcolor{olive}{60}$	$\textcolor{olive}{70}$	$\textcolor{olive}{80}$	$\textcolor{olive}{90}$	$\textcolor{olive}{100}$

Skills to practice

Multiplying by 1 to 10
Reading the Tables Both Ways

VIII Going further

Skills to practice

Completing Times Tables
Quiz

\(\times\)	\(\textcolor{colorprop}{1}\)	\(\textcolor{colorprop}{2}\)	\(\textcolor{colorprop}{3}\)	\(\textcolor{colorprop}{4}\)	\(\textcolor{colorprop}{5}\)	\(\textcolor{colorprop}{6}\)	\(\textcolor{colorprop}{7}\)	\(\textcolor{colorprop}{8}\)	\(\textcolor{colorprop}{9}\)	\(\textcolor{colorprop}{10}\)
\(\textcolor{colordef}{1}\)	\(\textcolor{olive}{1}\)	\(\textcolor{olive}{2}\)	\(\textcolor{olive}{3}\)	\(\textcolor{olive}{4}\)	\(\textcolor{olive}{5}\)	\(\textcolor{olive}{6}\)	\(\textcolor{olive}{7}\)	\(\textcolor{olive}{8}\)	\(\textcolor{olive}{9}\)	\(\textcolor{olive}{10}\)
\(\textcolor{colordef}{2}\)	\(\textcolor{olive}{2}\)	\(\textcolor{olive}{4}\)	\(\textcolor{olive}{6}\)	\(\textcolor{olive}{8}\)	\(\textcolor{olive}{10}\)	\(\textcolor{olive}{12}\)	\(\textcolor{olive}{14}\)	\(\textcolor{olive}{16}\)	\(\textcolor{olive}{18}\)	\(\textcolor{olive}{20}\)
\(\textcolor{colordef}{3}\)	\(\textcolor{olive}{3}\)	\(\textcolor{olive}{6}\)	\(\textcolor{olive}{9}\)	\(\textcolor{olive}{12}\)	\(\textcolor{olive}{15}\)	\(\textcolor{olive}{18}\)	\(\textcolor{olive}{21}\)	\(\textcolor{olive}{24}\)	\(\textcolor{olive}{27}\)	\(\textcolor{olive}{30}\)
\(\textcolor{colordef}{4}\)	\(\textcolor{olive}{4}\)	\(\textcolor{olive}{8}\)	\(\textcolor{olive}{12}\)	\(\textcolor{olive}{16}\)	\(\textcolor{olive}{20}\)	\(\textcolor{olive}{24}\)	\(\textcolor{olive}{28}\)	\(\textcolor{olive}{32}\)	\(\textcolor{olive}{36}\)	\(\textcolor{olive}{40}\)
\(\textcolor{colordef}{5}\)	\(\textcolor{olive}{5}\)	\(\textcolor{olive}{10}\)	\(\textcolor{olive}{15}\)	\(\textcolor{olive}{20}\)	\(\textcolor{olive}{25}\)	\(\textcolor{olive}{30}\)	\(\textcolor{olive}{35}\)	\(\textcolor{olive}{40}\)	\(\textcolor{olive}{45}\)	\(\textcolor{olive}{50}\)
\(\textcolor{colordef}{6}\)	\(\textcolor{olive}{6}\)	\(\textcolor{olive}{12}\)	\(\textcolor{olive}{18}\)	\(\textcolor{olive}{24}\)	\(\textcolor{olive}{30}\)	\(\textcolor{olive}{36}\)	\(\textcolor{olive}{42}\)	\(\textcolor{olive}{48}\)	\(\textcolor{olive}{54}\)	\(\textcolor{olive}{60}\)
\(\textcolor{colordef}{7}\)	\(\textcolor{olive}{7}\)	\(\textcolor{olive}{14}\)	\(\textcolor{olive}{21}\)	\(\textcolor{olive}{28}\)	\(\textcolor{olive}{35}\)	\(\textcolor{olive}{42}\)	\(\textcolor{olive}{49}\)	\(\textcolor{olive}{56}\)	\(\textcolor{olive}{63}\)	\(\textcolor{olive}{70}\)
\(\textcolor{colordef}{8}\)	\(\textcolor{olive}{8}\)	\(\textcolor{olive}{16}\)	\(\textcolor{olive}{24}\)	\(\textcolor{olive}{32}\)	\(\textcolor{olive}{40}\)	\(\textcolor{olive}{48}\)	\(\textcolor{olive}{56}\)	\(\textcolor{olive}{64}\)	\(\textcolor{olive}{72}\)	\(\textcolor{olive}{80}\)
\(\textcolor{colordef}{9}\)	\(\textcolor{olive}{9}\)	\(\textcolor{olive}{18}\)	\(\textcolor{olive}{27}\)	\(\textcolor{olive}{36}\)	\(\textcolor{olive}{45}\)	\(\textcolor{olive}{54}\)	\(\textcolor{olive}{63}\)	\(\textcolor{olive}{72}\)	\(\textcolor{olive}{81}\)	\(\textcolor{olive}{90}\)
\(\textcolor{colordef}{10}\)	\(\textcolor{olive}{10}\)	\(\textcolor{olive}{20}\)	\(\textcolor{olive}{30}\)	\(\textcolor{olive}{40}\)	\(\textcolor{olive}{50}\)	\(\textcolor{olive}{60}\)	\(\textcolor{olive}{70}\)	\(\textcolor{olive}{80}\)	\(\textcolor{olive}{90}\)	\(\textcolor{olive}{100}\)