Division
When the answer is unknown, an open-ended question is the way to ask for the answer.
Just like the previous chapters on addition, subtraction, and multiplication, this chapter is separated into “to-be” and “non-to be” verbs in division problems.
The “To Be” Open-Ended Questions–To Be Verb “is”
For the equal sign, we can simply say “is”.
Look at the simple equation:
15 ÷ 3 = 5 “fiifteen divided by three is five”
The 3rd-person singular grammar rule is used to form questions.
For example,
15 ÷ 3 = 5 “Is fifteen divided by three five?”
The above question is used to double check the answer.
Sometimes, people need to ask for the answer.
The division operation of “fifteen divided by three” is singular. It changes places with the verb “is” used for the equal sign. The subject and verb change places, and we use the question word “what” to ask for the answer.
For example, questions that use “what”
18 ÷ 3 = _____
The question is, “what is eighteen divided by three?”
48 ÷ 16 = _____
The question is, “what is 16 divided into 48?”
And the same grammar works for the question term “how much”.
For example:
36 ÷ 6 = _____
The question is, “how much is 36 divided by 6?”
45 ÷ 15 = _____
The question is, “how much is 15 divided into 45?”
Your Turn — Practice making open-ended questions with “what”, “how much”, and “is”
Your Turn — Practice making open-ended questions with “how much” and “is”
The “To Be” Open-Ended Questions–To Be Phrases
The equal sign can also be said with a variety of “is” phrases.
- is equal to
- is equivalent to
Let’s look at a couple of examples about forming questions with “is” phrases.
For example:
22 ÷ 11 = ______
“What is 22 divided by 11 equal to?”
or
“What is 22 divided by 11 equivalent to?”
Examples with “how much”:
96 ÷ 12 = ______
“How much is 96 divided by 12 equal to?”
or
How much is 96 divided by 12 equivalent to?”
We can use the question words “what” or “how much” at the beginning of the question. The word “is” moves in front of the addition operation. The other words in the phrase stay to the right of the addition operation. The “is” phrases are split into two by numbers.
Your Turn — Practice open-ended questions with “what”, “how much” and the “is equal to” phrase.
Practice identifying open-ended questions with “what”, “how much” and the “is equivalent to” phrase.
The other “is” phrases use the word “same”. Remember, the following:
- is the same as
- is the same amount as
- is the same value as
Let’s look at a couple of examples of questions with the phrase “is the same as”.
52 ÷ 26 = ______
“What is 52 minus 26 the same as?”
“How much is 52 minus 26 the same as?”
or
26⟌52
“What is 26 divided into 52 the same as?”
“How much is 26 divided into 52 the same as?”
We can use the question words “what” or “how much” at the beginning of the question. The word “is” moves in front of the addition operation. The other words in the phrase stay to the right of the addition operation. The words in “is” phrases are separated by numbers.
Your Turn — Practice open-ended questions for “what”, “how much” with “is the same as” phrase
Next, practice open-ended questions with “what”, “how much” and the “is the same amount as” phrase.
Practice one more time with open-ended questions with “what”, “how much” and the “is the same value as” phrase.
The “To Be” Open-Ended Questions–Other Verbs (not To Be)
There are other words to say the equal sign. They do not use the “to be” verb. Do you remember the other ways we can say the equal sign?
- equals
- makes
Notice the final -s at the end of both of the words “equal” and “make” used for the equal sign. The final -s identifies the verb as a 3rd-person singular verb as we saw with the word “is”. Let’s learn about the “equals” verb first.
“equals”
Let’s look at the equation.
8 ÷ 4 = ______
We must use the 3rd-person singular verb grammar rule to make an open-ended question with non-to be verbs. We begin the sentence with a question word, e.g. “what”, then use “does”, write the division operation, and then drop the final -s from the word “equals”.
For example:
8 ÷ 4 = ______ The question is, “What does eight divided by four equal“?
8 ⟌16 The question is, “What does 8 divided into 16 equal?
The same process is true for the question phrase “how much”.
Use the question phrase “how much” then “does” at the beginning of the question. Drop the final -s from make.
For example:
8 ÷ 4 = ______ The question is, “How much does eight divided by four equal“?
8 ⟌16 The question is, “How much does 8 divided into 16 equal?
Your Turn — Practice making open-ended questions with “what”, “how much”, and “equals”
The other “non to-be” verb works in the same way as equals. We have seen this with addition, subtraction, and multiplication, too.
The word is:
“makes”
It follows the same 3rd-person singular grammar pattern to form a question. Use a question word, e.g. “what” and “does” before the math operation. Drop the final -s from makes.
For example:
20 ÷ 5 = ______ The question is, “What does 20 divided by 5 make“?
5⟌20 The question is, “What does 5 divided into 20 make?
The same process is true for the question phrase “how much”.
Use the question phrase “how much” then “does” at the beginning of the question. Drop the final -s from make.
For example:
35 ÷ 7 = ______ The question is, “How much does 35 divided by 7 make“?
7⟌35 The question is, “How much does 7 divided into 35 make?
Your Turn — Practice open-ended questions with “what” “how much” and “makes”
Summary
The multiplication operation on one side of the equal sign (=) is singular.
The answer on the other side of the equal sign (=) is also singular.
The grammar for question formation uses 3rd-person singular rules for making questions that ask for the answer.
