1.3 K) Multiplying Fractions – Part 2
Complete the calculation below.
Both of the components of the question above are mixed numbers. This means that we need to convert the components from mixed numbers to improper fractions before we are able to multiply across.
To convert a mixed number into a fraction, we need to get the whole number into the fraction. We get the whole number into the fraction by multiplying the whole number by the denominator of the fraction that it is going in to. We then add this number to the original numerator to obtain the numerator for the improper fraction. The denominator of the fraction stays the same.
Let’s convert the first mixed number into an improper fraction. There are 2 wholes and the denominator of the fraction is 2. Therefore, to get the 2 wholes into the fraction, we multiply 2 by 2, which gives us 4. We then need to add this to the numerator in the fraction part of the mixed number (1), which is 5 (4 + 1). The first mixed number as an improper fraction is 5/2.
We now do the same with the second mixed number. There is 1 whole and the denominator of the fraction is 3. Therefore, to get the 1 whole into the fraction, we multiply 1 by 3, which gives us 3. We then add this to the numerator of the fraction, which is 2. Therefore, the second mixed number as an improper fraction is 5/3.
The calculation with improper fractions instead of mixed numbers is:
We are now able to multiply straight across; we multiply the two numerators and the two denominators.
The next step is to get the fraction into its simplest form and convert it into a mixed number; the order does not matter. I am going to convert this improper fraction into a mixed number first and then check whether it can be simplified. We get the fraction into a mixed number by seeing how many times the denominator fully goes into the numerator; we divide 25 by 6, which gives us 4 remainder 1. Therefore, we have 4 wholes and 1 sixth.
The next step is to check that the fraction is in its simplest form. To check that the fraction is in its simplest form, we see if there are any common factors between the numerator and the denominator, and if we find any, we divide the numerator and denominator by the factors that we found. There are no common factors between 1 and 6, which means that the fraction is already in its simplest form.
Therefore, the answer for this question is 4 1/6.
Complete the calculation below.
Like the example before, both of the components in the question are mixed numbers. This means that we need to convert them into improper fraction before we are able to multiply them.
For the first mixed number, there are 3 wholes and the denominator is 5. Therefore, we are multiplying 3 by 5, which gives us 15. We then add the numerator in the fraction part of the mixed number (2) to this number. This means that the numerator for the improper fraction is 17 (15 + 2) and the improper fraction is 17/5.
Let’s do the same for the second fraction. There are 4 wholes and the numerator is 3, so we multiply 4 by 3, which give us 12. We then add the original numerator on (1). This means that the second mixed number as an improper fraction is 13/3.
The calculation with improper fractions rather than mixed numbers is:
We are now able to multiply across; multiply the numerators and multiply the denominators.
The final step is to convert the answer into a mixed number and simplify. It does not matter which one of these you do first. I am going to find the fraction as a mixed number first. To do this, I am looking for how many times the denominator fully goes into the numerator (221 ÷ 15), which gives us 14 with a remainder of 11 (the remainder is the numerator for the fraction part of the mixed number). The improper fraction as a mixed number 14 11/15.
We now need to see if the fraction part of the mixed number can be simplified, which it can’t because there are no common factors between 11 and 15. Therefore, the answer to this question is 14 11/15.