乘法

Words to Math: Multiplication

In this section, we will learn to translate phrases into a mathematical expression by identifying key words that indicate multiplication.

When talking about multiplication, you will most likely see the terms "times", "multiplied by", "product of", and "by a factor of".

Let’s take a look at an example.

Sarah went to the grocery store to buy oranges. She realized that each bag of oranges contained $4$ oranges.

She bought $5$ bags of oranges. How many oranges did she buy in total?

We know that the term "of" often refers to multiplication, so the operator ‘$\times$’ is required.

The term "total" refers to equality, so the operator ‘$=$‘ can be used.

Since Sarah bought $5$ bags of oranges and each bag contains $4$ oranges, we can rewrite this into a mathematical expression.

Total Number of Oranges = $5$ Bags $\times$ $4$ Oranges $=$ $20$ Oranges

When talking about equality, you will most likely see the terms "equal to", "is", "the same as", and "amounts to".

Here are some phrases about multiplication translated into a mathematical expression.

1. $4$ times $5$ equals $20\quad\rightarrow\quad 4 \cdot 5=20$
2. The product of $11$ and $3$ amounts to $33\quad\rightarrow\quad 11 \cdot 3=33$
3. $7$ multiplied by a number $\quad\rightarrow\quad 7 \cdot x$
4. $8$ by $9$ plank of wood $\quad\rightarrow\quad 8 \cdot 9$

We are now going to take a look at some of the types of problems you might encounter about multiplication word problems.

We know that the term "times" refers to multiplication, so the operator ‘$\times$’ is required.

The term "is" refers to equality, so the operator ‘$=$‘ can be used.

Replacing times with ‘$\times$’ and is with ‘$=$‘, we can rewrite the phase given into a mathematical expression.

$8$ times $7$ is $56\quad\rightarrow\quad 8 \times 7 = 56$

Since $200$ people visit the museum every day and there are $7$ days in a week, we can rewrite this into a mathematical expression. $$200 \times 7 = 1{,}400$$ $1400$ people visit the museum in a week.

(Video) Solving Multiplication and Division Word Problems

by Ruth Erquiaga

Ruth Erquiaga has a very good explanation and strategy on how to identify and approach word problems. Specifically, the video focuses on multiplication and division.

$\large{\text{Summary}}$

The key word that designates multiplication or division is "each". "Each" means that the groups being combined or split up need to be equal in size, which is true of multiplication and division, but not necessarily true of addition and subtraction.

Other words like "total", "area", "in all", and "altogether" can designate multiplication or division as long as the context of the problem allows you to work with equal sized groups.

The video covers a general strategy for translating word problems.

1. Read the problem entirely
2. Find if the total is given. A given total means that the problem will be division or subtraction. No given total means the problem will be addition or multiplication.
3. Find if the groups are equal. Equal groups will mean multiplication or division. Unequal groups will mean addition or subtraction.

From steps 2 and 3, you can conclude which operation you need to do!

Word Problems with Multiplication

The key to solving word problems is to translate them into mathematical expressions. This is made easier if you can pick out key phrases that tell you what type of operation the problem is asking for. We'll call these signal words.