In this publication, we will consider how an ordinary (simple) fraction can be multiplied by a decimal. We will also analyze examples to consolidate the theoretical material.
Product of common and decimal fractions
To multiply an ordinary fraction by a decimal (and vice versa, because the result does not change from a permutation of the factors), it is necessary to represent one of the fractions as another.
Notes:
1. Infinite decimals are required first, i.e. leave a finite number of digits after the decimal point.
2. Mixed ordinary fractions must first be converted to.
Examples
Example 1
and 2,19.
Solution 1
Let’s translate:
=
=
= 0,15
Now let’s execute:
0,15 ⋅ 2,19 = 0,3285.
Solution 2
Let’s transform:
=
=
It remains only to find:
⋅
=
=
Example 2
.
Solution
Convert the given mixed fraction to an improper one:
=
=
Next, we have a choice: either we translate the decimal fraction into an ordinary one, or vice versa. Let’s choose the first option.
=
=
Now we divide one simple fraction by another:
:
=
⋅
=
=
= 2
= 2
≈ 2,5528