Evaluate one-sixth multiplied by
three and three-sevenths.
There are a couple of ways of
approaching this problem. One way would be to convert three
and three-sevenths into an improper fraction first. To convert a mixed number to an
improper fraction, we begin by multiplying the whole number by the denominator. Three multiplied by seven is
21. We do this because there are
seven-sevenths in one whole one. This means there are 21 sevenths in
three whole ones. We then add the numerator to this
answer. 21 plus three is equal to 24. As the denominator stays the same,
three and three-sevenths is equal to twenty-four sevenths.
We need to multiply one-sixth by
twenty-four sevenths. We recall that to multiply two
fractions 𝑎 over 𝑏 and 𝑐 over 𝑑, we simply multiply the numerators and
separately multiply the denominators. 𝑎 over 𝑏 multiplied by 𝑐 over 𝑑
is equal to 𝑎𝑐 over 𝑏𝑑. In this question, we could multiply
one by 24 and then six by seven. In order to make our life easier,
it is always worth checking if we can cross simplify or cross cancel first. As both six and 24 are divisible by
six, we can simplify our calculation. We are now left with one multiplied
by four on the top and one multiplied by seven on the bottom. One-sixth multiplied by three and
three-sevenths is equal to four-sevenths.
An alternative method to solve this
question would be to split our mixed number into two parts. We could split it into three and
then three-sevenths. We would then multiply these
individually by one-sixth. We know that any integer or whole
number can be written as this number over one. Therefore, three is the same as
three over one. In both of these calculations, we
can divide three and six by three. This means that one-sixth
multiplied by three is equal to one-half. One-sixth multiplied by
three-sevenths is equal to one fourteenth.
We now need to find the sum of
these two fractions. In order to add two fractions, we
need to ensure we have a common denominator. As two multiplied by seven is equal
to 14, we can multiply the numerator and denominator of the first fraction by
seven. This gives us seven over 14 plus
one over 14. Adding the numerators gives us
eight over 14 which, once again, simplifies to four-sevenths. This confirms that one-sixth
multiplied by three and three-sevenths is equal to four-sevenths.