SC Ready Review Number Systems

The number line shows the locations of points P, Q, R, and S. Which points have a distance of 5 units between them?

• point P and point S

• point Q and point R

• point Q and point S

• point R and point S

Answer explanation

To find the points with a distance of 5 units, we check the distances. Points Q and S are 5 units apart on the number line, making them the correct choice. The other pairs do not have this distance.

Points P and Q are plotted on the number line. Which expression represents the distance between points P and Q?

• |−8 − (−6)|

• |−8 − 6|

• |8 − 6|

• |6 − 8|

Answer explanation

The distance between points P and Q on a number line is given by the absolute value of their difference. The correct expression is |−8 − 6|, which calculates the distance between -8 and -6.

What is the value of (1/5) × (6 + 8.5)?

• 2.9

• 7.7

• 9.7

• 14.9

Answer explanation

First, calculate the sum: 6 + 8.5 = 14.5. Then, multiply by 1/5: (1/5) × 14.5 = 2.9.

Or enter into desmos exactly the way it is given to you.

Last year, Ted’s salary was $42,000. He donated 1/25 of last year’s salary to charity. How much did Ted earn last year after his donation?

• $31,500

• $40,320

• $43,680

• $52,500

Answer explanation

Divide $42,000 by 25 and subtract this from his salary.

Which expression is equivalent to 22 - 31?

• -22 - (-31)

• -22 + (-31)

• 22 - (-31)

• 22 + (-31)

Answer explanation

Change subtraction to addition by Same Change Change

If the carpenter builds 6 chairs, 3 tables, and 2 benches, how many hours does it take the carpenter to build all the furniture?

• 5 5/12 hours

• 14 hours

• 19 hours

• 19 1/12 hours

Answer explanation

The carpenter takes 3 hours for each chair, 4 hours for each table, and 2 hours for each bench.

Total time =

(6 x 1.5) + (3 x 2 2/3) + (2 x 1 1/4) . Use desmos

A restaurant’s pastry chef bakes 1 batch of chocolate chip cookies, 1 batch of sugar cookies, and 1 batch of peanut butter cookies each day for 5 days to use as desserts for the restaurant’s customers. How many total cups of sugar does the pastry chef use for cookies during the 5 days?

• 5 11/12 cups

• 10 11/12 cups

• 21 11/12 cups

• 27 11/12 cups

Answer explanation

Add all of the cups of sugar and multiply total by 5. Use desmos

A cashier’s paycheck is $534.60. The cashier saves 1/2 of the paycheck, then uses 1/3 of the remaining amount to pay bills. The cashier plans to buy groceries with what is left of the paycheck. How much money does the cashier have to spend on groceries?

• $89.10

• $178.20

• $267.30

• $356.40

Answer explanation

Find 1/2 of $534.60 (divide by 2) to find out how much he saves. Divide that amount by 3 to find out what he spends on bills. Subtract that amount and what is left is how much is spent on groceries.

A teacher asks two students to determine the value of the expression (0.9) · 1/3 ÷ 5/6. The table shows each student’s response.

• Both students are correct because (0.9) · 1/3 ÷ 5/6 = 0.36, and (0.9) · 1/3 ÷ 5/6 = 1/4.

• Neither student is correct because (0.9) · 1/3 ÷ 5/6 ≠ 0.36, and (0.9) · 1/3 ÷ 5/6 ≠ 1/4.

• Only Student 1 is correct because (0.9) · 1/3 ÷ 5/6 = 0.36, and (0.9) · 1/3 ÷ 5/6 ≠ 1/4.

• Only Student 2 is correct because (0.9) · 1/3 ÷ 5/6 ≠ 0.36, and (0.9) · 1/3 ÷ 5/6 = 1/4.

Answer explanation

Only Student 1 is correct because (0.9) · 1/3 ÷ 5/6 simplifies to 0.36. The calculation does not equal 1/4, confirming that Student 2 is incorrect.

Which expression is equivalent to 9/5?

• -(9/5)

• -(-9/5)

• 9/-5

• 9/-5

Answer explanation

The expression -(-9/5) simplifies to 9/5, as negating a negative value results in a positive value. The other options either negate the fraction or change its sign, making them not equivalent.