Number Sense and Algebraic Thinking Flashcards

Which of the following best represents the value of 2³ × 2⁴?

Answer: 2⁷

When multiplying exponential expressions with the same base, you add the exponents: 2³ × 2⁴ = 2^(3+4) = 2⁷.

If a store sells apples for $1.25 each and oranges for $0.75 each, how much does it cost to buy 4 apples and 6 oranges?

Answer: $9.50

4 × $1.25 = $5.00 and 6 × $0.75 = $4.50, so the total is $5.00 + $4.50 = $9.50.

Which number is a prime number?

Answer: 53

53 is prime because it has no divisors other than 1 and itself; 51 = 3×17, 55 = 5×11, and 57 = 3×19.

Solve for x: 3x - 7 = 14

Answer: x = 7

Adding 7 to both sides gives 3x = 21, then dividing by 3 gives x = 7.

What is the least common multiple (LCM) of 8 and 12?

Answer: 24

The LCM of 8 and 12 is 24 because 24 is the smallest number that both 8 and 12 divide into evenly.

A number is increased by 40% and then decreased by 20%. What is the net percentage change?

Answer: 12% increase

Starting with 100, a 40% increase gives 140, and a 20% decrease gives 140 × 0.80 = 112, which is a 12% net increase.

Which of the following is an example of an irrational number?

Answer: √2

√2 ≈ 1.41421… is irrational because it cannot be expressed as a ratio of two integers, while √9 = 3, √25 = 5, and 0.75 = 3/4 are all rational.