Division
In English grammar, the verbs in a sentence are responsible for making questions.
In a mathematical equation, the language of the equal sign (=) is the verb.
The To Be Verb
Look at this division equation:
12 ÷ 3 = 4 “twelve divided by three is four”
The number four is on the right side of the equal sign.
There are two numbers (12 divided by 3) on the left side.
The division operation is a singular phrase. In math, 12 ÷ 3 is a single idea. English grammar describes 12 ÷ 3 as the subject of the sentence. In math, this subject is always singular.
Since the subject is singular, the verb must be in singular form, too. For the equal sign, the third-person singular “to be” form “is” agrees with the singular idea of the division operation. This is the grammar of basic operations in math. This is why we use “is” for the equal sign no matter how many numbers or operations are on either side.
The information that a math operation is singular helps us make questions about a math equations.
Let’s look at the Yes/No questions for division equations.
12 ÷ 3 = 4 “twelve divided by three is four”
“Twelve divided by three” is the subject. “Is” is the verb. They change places.
“Is twelve divided by three four?”
The answer can only be yes or no. This is called a Yes/No question.
Your Turn — Practice yes/no questions with “is” for the equal sign
For the equal sign, we have the following “is” phrases to say the equal sign:
- is equal to
- is equivalent to
- is the same as
- is the same amount as
- is the same value as
The “is” phrases get separated when making yes/no questions.
For example,
12 ÷ 3 = 4 the questions are:
“Is 12 divided by 3 equal to 4?”
“Is 12 divided by 3 equivalent to 4?”
“Is 12 divided by 3 the same as 4?”
“Is 12 divided by 3 the same amount as 4?”
“Is 12 divided by 3 the same value as 4?”
Your Turn — Practice yes/no questions with “is” phrases
Remember when the long division sign (⟌ ) is used, the numbers change places. The language is different.
For example,
4
3⟌12 the questions are:
“Is 3 divided into 12 equal to 4?”
“Is 3 divided into 12 equivalent to 4?”
“Is 3 divided into 12 the same as 4?”
“Is 3 divided into 12 the same amount as 4?”
“Is 3 divided into 12 the same value as 4?”
Your Turn — Practice yes/no questions with “divided into”
The Other (non-To Be) Verbs
The other words used for the equal sign (=) are “equals” and “makes”.
First, we will practice with “equals”.
For example,
24 ÷ 6 = 4 “twenty-four divided by six equals four”
We will use the 3rd-person singular verb grammar rule to make a yes/no question. We begin the sentence with “does” and drop the final -s on the word “equals”.
For example,
24 ÷ 6 = 4 The question is, “does 24 divided by 6 equal 4?”
18 ÷ 9 = 2 The question is, “does 18 divided by 9 equal 3?”
Your Turn — Practice yes/no questions for “equals”
“makes”
The word makes for the equal sign also uses the final -s for the 3rd person singular verb form. The way to make a yes/no question for “makes” is the same as above for “equals”.
For example,
24 ÷ 3 = 8 The question is, “does 24 divided by 3 make 8″?
21 ÷ 7 = 3 The question is, “does 21 divided by 7 make 3?
Your Turn — Practice yes/no questions for “makes”
The last phrase we use for division also uses the “does” word for yes/no questions.
- goes into
This phrase uses the word “times” for the answer.
Remember the example:
2
5⟌10
“5 goes into 10 2 times”
The question form starts with the word “does” and the phrase “goes into” changes to “go into”.
For example:
Does 5 go into 10 2 times?
Does 3 go into 12 4 times?
Does 5 go into 15 3 times?
Your Turn
It also possible to make a different kind of yes/no question with the “goes into” phrase.
For example:
6
2⟌12
“2 goes into 12 6 times”
This question form uses the first word of “can”. The phrase “goes into” changes to “go into”.
For example:
Can 2 go into 12 6 times?
Can 3 go into 12 4 times?
Can 4 go into 20 5 times?
Your Turn
Summary
- The equal sign is the verb in mathematical equations
- If the equal sign is said with “is”, the question formation follows the “to be” grammar pattern.
- If the equal sign is said with a non-to be verb, the question formation follows the grammar pattern that uses “does”.
- The phrase “goes into” uses “times” in its answer. The grammar is different.
- Yes/No sentences are used to ask if an answer is correct
