Question

Javier rounded to the nearest half to estimate the product of 3 and two-fifths and Negative 3 and StartFraction 7 over 8 EndFraction. How do the estimate and the actual product compare? The actual product is less than the estimate. The numbers differ by less than one. The actual product is greater than the estimate. The numbers differ by less than one. The actual product is less than the estimate. The numbers differ by more than one. The actual product is greater than the estimate. The numbers differ by more than one.

Answer 1

B

Explanation:

The actual product is greater than the estimate. The numbers differ by less than one. took the test 2021

Answer 2

- The actual product is less than the estimate

- The numbers differ by less than one

Explanation:

Given

Product of 3 and two-fifths &
`-3(7)/(8)`

Required

Compare actual result with approximated result

Calculating the actual result;

3 and two-fifths means
`3(2)/(5)`

So, the Product of 3 and two-fifths &
`-3(7)/(8)` becomes

`Product = 3(2)/(5) * -3(7)/(8)`

Convert fractions to improper

`Product = (17)/(5) * -(31)/(8)`

Combine fractions to form one

`Product = (-17 * 31)/(5 * 8)`

Multiply numerators and denominator

`Product = (-527)/(40)`

Convert fraction to decimal

`Product = -13.175`

The nearest half of -13.175 is -13

Hence;

`Estimate = -13`

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