Multiplication of integers by a fraction and a mixed number
In this article, we will learn how to multiply an integer with a fraction and a mixed number without any problem!
When it comes to multiplication exercises, there is no need to find a common denominator and all we have to do is convert the integers and mixed numbers into equivalent fractions.
Steps to Solve the Multiplication of Integers with a Fraction and a Mixed Number
How to convert an equivalent fraction into a mixed number?
We will learn with the example
Convert the equivalent fraction 62241 into a mixed number.
Solution:
To convert an equivalent fraction into a mixed number, we will divide the numerator by the denominator and refer only to the whole number we receive (ignore the remainder).
241:62=3…….
This will be the whole number.
Then, we subtract from the given numerator the result of multiplying the whole number by the denominator to see how much is left to "complete" it.
That is:
241−(3×62)=55
The result we receive will be written in the numerator.
The denominator will remain the same.
We obtain: 36255
You can always test yourself and see if you return to the same equivalent fraction.
Examples and exercises with solutions for multiplying integers by a fraction and a mixed number
Exercise #1
51×87×232=
Video Solution
Step-by-Step Solution
First, let's convert the mixed fraction to an improper fraction as follows:
51×87×33×2+2=
Let's solve the equation in the numerator:
51×87×36+2=
51×87×38=
Since the only operation in the equation is multiplication, we'll combine everything into one equation:
5×8×31×7×8=
Let's simplify the 8 in the numerator and denominator of the fraction:
5×31×7=
Let's solve the equations in the numerator and denominator and we get:
157
Answer
157
Exercise #2
43×32×241x=
Video Solution
Step-by-Step Solution
Let's begin by combining the simple fractions into a single multiplication exercise:
4×33×2×241x=
Let's now proceed to solve the exercise in the numerator and denominator:
126×241x=
Finally we'll simplify the simple fraction in order to obtain the following:
21×241x=181x
Answer
181x
Exercise #3
87×287×41=
Video Solution
Step-by-Step Solution
First, let's convert the mixed fraction to a simple fraction as follows:
87×88×2+7×41=
Let's solve the exercise in the numerator:
87×816+7×41=
87×823×41=
Since the only operation in the exercise is multiplication, we'll combine everything into one exercise:
8×8×47×23×1=
Let's solve the exercises in the numerator and denominator:
64×47×23=256161
Answer
256161
Exercise #4
32×732×321=
Video Solution
Step-by-Step Solution
First, we'll convert the mixed fractions to simple fractions as follows:
32×37×3+2×23×2+1=
Let's solve the exercises in the fraction multiplier:
32×321+2×26+1=
32×323×27=
Since the only operation in the exercise is multiplication, we'll combine everything into one exercise and get:
3×3×22×23×7=9×246×7=18322
Answer
1798
Exercise #5
365×565×31x=
Video Solution
Step-by-Step Solution
First, let's convert all mixed fractions to simple fractions:
63×6+5×65×6+5×31x=
Let's solve the exercises with the eight fractions:
618+5×630+5×31x=
623×635×31x=
Since the exercise only involves multiplication, we'll combine all the numerators and denominators: