8.06 Story problems with multiplying fractions and whole numbers
Are you ready?
Do you remember how to multiply a fraction by a whole number?
What is the value of $4\times\frac{3}{4}$4×34?
Learn
When a problem is given as a story or description, we first want to determine what value we are trying to solve for - this will often be in the last sentence. After that, we look back through the rest of the story to find:
- any numbers/values that we know
- a keyword that will tell us what operation to use
When our answer to a story problem is an improper fraction, it often helps to think about which whole numbers the fraction is closest to in order to better understand the answer.
For example, if $7$7 people at a party each eat $\frac{3}{8}$38 of a pizza, we can multiply to find that they eat $\frac{21}{8}$218 of a pizza in total. But how many pizzas should be ordered in total? If we rewrite $\frac{21}{8}$218 as the mixed number $2\frac{5}{8}$258, we can see that they eat more than $2$2 and less than $3$3 pizzas - so we would want to have ordered $3$3 pizzas for the party!
Apply
Question 1
Derek is finishing a painting and needs a certain shade of purple. He can get this shade by mixing $2$2 ounces of red paint with $\frac{8}{3}$83 as much blue paint.
How much blue paint does Derek mix?
Between which two whole numbers does this lie?
$3$3 ounces and $4$4 ounces
A$4$4 ounces and $5$5 ounces
B$5$5 ounces and $6$6 ounces
C$6$6 ounces and $7$7 ounces
D
Thinking about which whole numbers an improper fraction is closest to can help us better understand an answer.
This can be done in a few ways, such as by converting to a mixed number.