5.11 Story problems with multiplying a fraction by a whole number
Are you ready?
Do you remember how to multiply a fraction by a whole number?
What is the value of $8\times\frac{2}{3}$8×23?
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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!
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Question 1
Edward's local supermarket sells bags of flour with a mass of $\frac{2}{5}$25 kg. Edward buys $6$6 bags of flour.
What is the total mass of Edward's purchase?
Between which two whole numbers does the total mass lie?
$1$1 kg and $2$2 kg
A$2$2 kg and $3$3 kg
B$3$3 kg and $4$4 kg
C$4$4 kg and $5$5 kg
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.