Several people have asked me about this topic over the years... here's the basic question:
It seems that in Math Mammoth Multiplication 1 book, the multiplicand is second number and not the first. I had been taught that the equations are multiplicand x multiplier = product. I know that either order will produce the same product but is there a reason that you have the the equations multiplier x multiplicand? Just want to make sure that I am consistent when teaching my son.
In case you don't know, "multiplicand" is the number or quantity we are multiplying, and "multiplier" is the number we multiply by.
Yes, I do have a reason for it. It has to do with what happens down the road a bit.
In 4th grade, students encounter the thought of a fractional part of a quantity, such as finding 3/4 of $36. While we first use a twostep operation to find the answer, eventually (in 5th grade) students will learn how this corresponds to the fraction multiplication ¾ × 36.
Notice how the word "OF" from "3/4 of $36" translates into MULTIPLICATION, and the multiplicand is written SECOND.
Also in 5th grade, students will learn about multiplication as a scaling operation. For example, if something is 50 cm long and it is scaled by the factor 1.2, the new length will be 1.2 × 50 cm = 60 cm. (In Math Mammoth, scaling in multiplication is first studied in the lesson Multiplying Decimals by Decimals in grade 5B.)
This then ties in with PERCENTAGES. Scaling some quantity by 1.2 is the same as 120% of the quantity. As you know, 120% is the same as the decimal 1.2. We can then equate the word "of" in statements of "percentage of something" with multiplication operation:
68% of $450 ↓ ↓ ↓ 0.68 × $450
This is extremely handy, not only with percents, but in algebra. Using this principle it is so easy to build algebraic equations such as:
0.9p = 5.6
where p is an unknown price so that when it's discounted by 10%, the new price is $5.60.
Back to 3rd grade multiplication.... I want children to see multiplication in that order (multiplier × multiplicand) so that when they get to percentages, and encounter 68% of $450, they will be able to quickly "translate" that to 0.68 × $450 (where we also have the multiplicand as the 2nd number).
But, children don't need to learn the terms "multiplier" and "multiplicand". I am afraid they may just confuse the issue. It's sufficient to simply use the term "FACTOR" for both numbers.
See also
By Maria Miller
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