Question

1. explain how a student could arrive at the following answers (which are incorrect).

a) $12.04 + 6.315 = 7.519$
b) $81.087 - 4.0053 = 4.1034$

1. arrange the numbers from smallest to largest.

a) $-1.99, -1.999, -2, -1.9999, -2.00009, -1.9909, -1.9889$
b) $-4.1, -4.109, -4.108, -4.018, -4.0119, -4.0302, -4.000001$

1. deborah is saving to buy a stereo for $637.95. she has saved $347.21 from baby sitting and will work for the next six weekends earning $162.80. how much more does she have to earn to buy the stereo?

1. the odometer on rubina’s car reads 36 026.3 km. rubina plans a camping trip that requires 6725.2 km to drive there and back from. if the car must be serviced at 50 000 km, how many kilometers can rubina drive after coming back from her camping trip before servicing her car?

1. ellie has $230.00 to spend on school clothes. if she spends $63.18 for shoes, $72.35 on a jacket and $47.25 on pants, how much does she have left over?

1. kate wants to buy three items that cost $6.99, $9.99, and $3.99. if she has $20, will she have enough money to pay for all three items? explain.

Explanation:

Problem 8

Part a)

Step1: Identify student's error

The student aligned numbers by rightmost digit instead of decimal points, treating them as whole numbers: $1204 + 6315 = 7519$, then incorrectly placed a decimal to get $7.519$.

Part b)

Step1: Identify student's error

The student aligned numbers by rightmost digit instead of decimal points, treating them as whole numbers: $81087 - 40053 = 41034$, then incorrectly placed a decimal to get $4.1034$.

Part a)

Step1: Recall negative number ordering

For negative numbers, the larger the magnitude, the smaller the number.

Step2: Sort the values

Order from smallest (largest magnitude) to largest (smallest magnitude): $-2.00009, -2, -1.9999, -1.999, -1.9909, -1.99, -1.9889$

Part b)

Step1: Recall negative number ordering

For negative numbers, the larger the magnitude, the smaller the number.

Step2: Sort the values

Order from smallest (largest magnitude) to largest (smallest magnitude): $-4.109, -4.108, -4.1, -4.0302, -4.018, -4.0119, -4.000001$

Step1: Calculate total saved/earned

Total = Saved amount + (Weekly earnings × 6)
$\$347.21 + (6 \times \$162.80) = \$347.21 + \$976.80 = \$1324.01$

Step2: Calculate needed amount

Needed = Cost of stereo - Total saved/earned
$\$637.95 - \$1324.01$ (Note: The student made an error here—they only added one weekend's earnings instead of 6. The correct total earnings are 6×162.80, not just 162.80.)
Wait, correction: The stereo costs $\$637.95$. The total available is $\$347.21 + (6 \times \$162.80) = \$347.21 + \$976.80 = \$1324.01$. Since this is more than $\$637.95$, the student's mistake was only adding one weekend's earnings instead of 6.
But if we assume the question is correct, the student's error was miscalculating total earnings. The correct calculation:

Step1: Total earned from work

$6 \times 162.80 = 976.80$

Step2: Total money available

$347.21 + 976.80 = 1324.01$

Step3: Surplus (no more money needed)

$1324.01 - 637.95 = 686.06$
But the student only added one weekend's earnings. The student's work was wrong, but the correct answer is that she already has enough money, with a surplus of $\$686.06$.

Answer:

a) The student misaligned the numbers by their rightmost digits (not decimal points), added $1204 + 6315 = 7519$, and incorrectly placed a decimal to get $7.519$.
b) The student misaligned the numbers by their rightmost digits (not decimal points), subtracted $81087 - 40053 = 41034$, and incorrectly placed a decimal to get $4.1034$.

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Problem 9