Question

Which is the best estimate of (3/5)(17 5/6) - 18?

a) 6
b) 4
c) 8
d) 10

Answer 1

To find the best estimate of (3/5)(17 5/6) - 18, we can convert the mixed number to an improper fraction, perform the multiplication, and then subtract 18. The best estimate is approximately -1.3, which is closest to 4.

Step-by-step explanation:

To find the best estimate of (3/5)(17 5/6) - 18, we can first convert the mixed number 17 5/6 to an improper fraction.

17 5/6 as an improper fraction is ((17 * 6) + 5)/6 = 107/6.

Now we can calculate (3/5)(107/6) = (3 * 107)/(5 * 6) = 321/30 = 10 21/30.

To subtract 18, we can convert 18 to the fraction 18/1.

Now we can subtract: (10 21/30) - (18/1) = (10 * 30 + 21)/(30) - (18) = 321/30 - 18 = -33/30 = -1 3/10.

Therefore, the best estimate of (3/5)(17 5/6) - 18 is approximately -1.3, which is closest to option b) 4.

Answer 2

The best estimate of (3/5)(17 5/6) - 18 is:

c) 8

Step-by-step explanation:

The best estimate of
`\( (3/5)(17 \ 5/6) - 18 \)` can be determined by breaking down the expression step by step. First, calculate
`\( (3/5)(17 \ 5/6) \)` by multiplying the whole number (17) by the fraction (5/6) and then multiplying the result by 3. Next, subtract 18 from this product.

The calculation yields
`\( (3/5)(17 \ 5/6) \approx 10.2 \).` Now, subtracting 18 from this result gives
`\( 10.2 - 18 = -7.8 \).` Among the given options, the closest value is 8, which is the answer (c).

In summary, the expression
`\( (3/5)(17 \ 5/6) - 18 \)` evaluates to approximately -7.8, and the closest option is 8. This indicates that option c) is the best estimate of the given expression. The negative sign in the result signifies that the expression's value is less than 18, and option c) accurately represents this outcome.