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# Multiplying mixed numbers

Multiplying mixed numbers is similar to multiplying whole numbers, except that you have to account for the fractional parts as well. By converting mixed numbers into improper fractions, you can multiply the two numbers together in a straightforward way. Once you have the product as an improper fraction, you can convert it back into a mixed number. Created by Sal Khan and Monterey Institute for Technology and Education.

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• When we have one mixed number and one whole number, why do we only multiply the numerator; for example; 9 x 1 1/12 = 9x13 /12, why can't we do 9 x 13/ 9x12?
• 1st question:
'When we have one mixed number and one whole number, why do we only multiply the numerators?'

•When calculating a Whole Number × a Fraction it can appear like only the numerators are multiplied, (but the denominators are too).

The unseen denominator math is:
(1 × other denominator), because all whole numbers have a denominator of one
,
so the calculation always equals the other denominator
.

So even without knowing why, by default we still get the correct denominator.

2nd question:
'9 x 1 1/12 = 9x13/12
Why can't we do 9x13/9x12?'

We don't multiply the Whole Number to both the numerator and denominator, because it mimics a Multiplicative Identity Fraction 9/9 = 1, (so ×1, no longer ×9).
So it doesn't answer to 9 × 1 1/12, it results in a wrong value.

First we transform the Mixed Number value into an Improper Fraction, (denominator × whole number + numerator, keep denominator), ex…

Nine times one and one twelfths.
=
9 × 1 1/12
=
9 × (12 × 1 +1)/12 ←transforming
=
9 × 13/12
= …
To multiply fractions:
(numerator × numerator), and
(denominator × denominator
).

A Whole Number's denominator always equals one, so that makes the multiplication always:
(1 × other denominator).

Therefore the whole number 9 has a denominator of one!

So the calculation is always the same, it's considered 'understood', so the following denominator math often isn't shown, except when learning it:

9 × 13/12
=
9/1 × 13/12 ←showing denominators
=
(9 × 13)/(1 × 12) ←often not shown
=
(9 × 13)/12

So mathematically the denominators are multiplied too, it's presumed 'known' to have occurred, we just don't bother writing it out because it always results in the denominator not equal to 1, the 'other' denominator.

Question 2
'9 x 1 1/12 = 9x13/12
Why can't we do 9x13/9x12?'

We can't do: 9×13/9×12,
9 ×numerator/9 ×denominator,
because it would be a miscalculation, and equivalent to: 9/9 × 13/12
.

9/9 is a Multiplicative Identity Fraction: the same numerator and denominator is equal to 1.

so it won't solve: 9 × 13/12

(9 × 13)/(9 × 12)
=
117/108
=
Simplify with GCF: 9
=
13/12 ←wrong value
It's multiplying by a fraction that equals one, so after we simplify, we're back to 13/12 again.

Complete calculations for:
nine times thirteen twelfths
=
9 × 13/12

=
(9 × 13)/(1 × 12) ←often unseen
=
(9 × 13)/12
=
117/12

simplify with GCF 3
=
39/4 ←correct value 🥳
=
9 3/4 ←mixed number form
=
9.75 ←decimal form

(≧▽≦) Hope this helps someone!
• What if you can't divide any of the Numerator's or Denominator's by anything?
• Good question Jennifer,

if you cant divide either the numerator or the denominator it will stay the same number,
10/10 = 10(/)2/10(/) = 5/5- you cannot
simplify 5/5 so it will stay 5/5.

((/) is division)
• idk if someone asked but When you multiply a whole number by a fraction, you only multiply and whole number by the numerator. It's because a whole number is a whole, (or wholes), which makes it unnecessary to multiply it with the denominator. Like for example, 9 = 9/1, correct? So when we do 9/1 * 1 1/2, the denominator is not effected.
• Correct! you have the right idea!

It is because a Whole Number's denominator is one, so when it's multiplied the result will always be the other fraction's denominator.

Which is why we can immediately multiply the whole number to the numerator of a fraction, and still have the correct denominator value.

•Example Walkthrough and
Different Method Solution
(1 vote)
• Can you use the same method to multiply 5×6 1/3?
• what is the opposite of 0.93
• To get an opposite of a number, just change the sign. If it is a negative, make it positive. If it is positive, make it a negative
• can anyone explain to me beacuse i am confused
(1 vote)
• Sure! Multiplying a mixed number is easy once you have figured it out. All you have to do is make the mixed number an improper fraction, and then multiply them. Here's an example.

Let's say you were asked to multiply 1 1/3 by 1 1/2. First, you would want to make these mixed numbers improper fractions.

1 1/3 = 4/3
1 1/2 = 3/2
Now they are much easier to multiply. You can now rewrite the question to this:
4/3 * 3/2 (* is a multiplying symbol.)

First, multiply the numerators:
4 * 3 = 12

Then the denominators:
3 * 2 = 6

Now you have 12/6 as your final answer, or 2. Hope this helped you. :)
• I have a question how do you do 6/11 to 1 1/6
I’m having trouble getting the answer plz can you teach us 😊 this week and you helped for most probs.
• What is an Improper Fraction?
• Hello, Leilani!

To answer your question, Improper Fractions are fractions when the numerator (ex. 1/6), is larger than the denominator. Here is what an improper fraction would look like:

9/2

10/5

Hope this helps someone :>
(1 vote)
• Is there there another way to multiply fractions?