Answer:
- The actual product is less than the estimate
- The numbers differ by less than one
Step-by-step explanation:
Given
Product of 3 and two-fifths & [tex]-3\frac{7}{8}[/tex]
Required
Compare actual result with approximated result
Calculating the actual result;
3 and two-fifths means [tex]3\frac{2}{5}[/tex]
So, the Product of 3 and two-fifths & [tex]-3\frac{7}{8}[/tex] becomes
[tex]Product = 3\frac{2}{5} * -3\frac{7}{8}[/tex]
Convert fractions to improper
[tex]Product = \frac{17}{5} * -\frac{31}{8}[/tex]
Combine fractions to form one
[tex]Product = \frac{-17 * 31}{5 * 8}[/tex]
Multiply numerators and denominator
[tex]Product = \frac{-527}{40}[/tex]
Convert fraction to decimal
[tex]Product = -13.175[/tex]
The nearest half of -13.175 is -13
Hence;
[tex]Estimate = -13[/tex]
By comparison:-
- The actual product (-13.175) is less than the estimate (-13)
- The difference between both results is less than 1;
The difference is calculated as follows
Difference = |Actual Product - Estimate|
Difference = |-13.175 - (-13)|
Difference = |-13.175 +13|
Difference = |-0.175|
Difference = 0.175
