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2.3d: Multiply with whole numbers and fractions
Whole numbers can be made into fractions by putting them over 1.
If we have a number such as 15,
we can always place it over 1
because remember, this bar means division
and 15 ÷ 1 is 15,
so we have not changed the number by placing it over 1.
Also by placing it over 1, it will make multiplying with fractions much easier.
Let us see this in example 1.
Example 1 has 3/8 x 20.
Remembering that the rules from multiplying with fractions
was to multiply the numerators and multiply the denominators
after we have reduced.
We first must have both of them looking like fractions.
To do this, we place the 20 over 1,
now we have 3/8 x 20 over 1.
We are now able to multiply these fractions.
First we will start by reducing,
remember it is always easier to see if there are any numbers
that you can divide out
before multiplying the two fractions together.
I can see that a 4 will go into both the 8 and the 20,
8 ÷ 4 is 2
and 20 ÷ 4 is 5.
I now have reduced each of these fractions
and can multiply 3 x 5 is 15
and 2 x 1 is 2.
Since there are no more numbers in common in the numerator and the denominator,
I have found my answer, it is 15/2.
Let us see example 2.
Once again in example 2, we have a whole number.
We can place this whole number over 1
because it does not change the number.
Now let us re-write this.
35 over 1 x 6 over 7.
Remember, reducing before moving on helps us
to have it reduced when we get to the answer.
7 goes into 35 five times and 7 goes into 7 once.
We can now multiply the two numerators together
and 5 x 6 is 30
and 1 x 1 is 1.
Remember, 30 over 1 is the same thing as 30,
so the simplified answer of 30 over 1 is simply 30.
In conclusion, remember that when we have whole numbers to place them over 1
and then continue multiplying the fractions together as you would normally.