Video Transcript
Evaluate 0.4 times five-quarters,
giving your answer as a decimal.
In this question, we are asked to
find the product of two rational numbers and give our answer as a decimal. There are many ways that we can
answer this question. For instance, we could convert both
numbers into decimals and then evaluate the multiplication. And while this would work, it is
usually easiest to multiply rational numbers given as fractions. So, we will convert 0.4 into a
fraction. We know that one-fifth is 0.2. So we can double this to see that
two-fifths is 0.4. This allows us to rewrite the
product as two-fifths multiplied by five-quarters.
We can now recall that we can
multiply fractions together by multiplying their numerators and denominators
separately. In general, we have that 𝑎 over 𝑏
times 𝑐 over 𝑑 is equal to 𝑎 times 𝑐 over 𝑏 times 𝑑. Applying this result to our product
yields two times five divided by five times four.
We could now evaluate the
expressions in the numerator and denominator. However, we can note that there is
a shared factor of five in the numerator and denominator that we can cancel. Similarly, we can note that there
is a shared factor of two in the numerator and denominator. Canceling the shared factors leaves
us with one over two.
Finally, we need to give our answer
as a decimal. We can do this by recalling that
one-half is equal to 0.5.
