Number (9)

Question 1

What is the result of adding -7 and 12?

Answer 1

-7 + 12 = 5. Think of moving 12 steps right from -7 on a number line.

Question 2

Subtract 15 - (-8). Explain your reasoning.

Answer 2

15 - (-8) = 15 + 8 = 23.

Question 3

Multiply -3 * 6. How do you know the sign of the answer?

Answer 3

Negative times positive is negative; -3 * 6 = -18.

Question 4

Divide -24 ÷ (-6). What is the rule for dividing signs?

Answer 4

Negative ÷ negative = positive; -24 ÷ -6 = 4.

Question 5

Convert 3/4 to a decimal and explain the method.

Answer 5

3 ÷ 4 = 0.75.

Question 6

Convert 0.625 to a fraction in simplest form and explain.

Answer 6

0.625 = 625/1000 = 5/8 after simplification.

Question 7

Estimate 48 × 19 using mental math. Explain your steps.

Answer 7

Round 19 to 20, 48 × 20 = 960, then subtract 48, 960 - 48 = 912.

Question 8

Explain why 0.3 + 0.7 = 1.0 using place value understanding.

Answer 8

0.3 + 0.7 = 10 tenths = 1 whole; sum of parts equals one whole.

Question 9

Explain the difference between a rational and irrational number.

Answer 9

Rational numbers can be expressed as a fraction a/b; irrational numbers cannot (e.g., √2).

Question 10

When estimating √50, what perfect squares would you use and why?

Answer 10

Use √49 = 7 and √64 = 8; √50 is slightly greater than 7.