Translation with Variables

Question 1

Translate: “There are 40% as many tulips as roses in the garden.”

Answer 1

T = 0.4×R
(The number of tulips is 40% of the number of roses.)

Question 2

Translate: “She earns 50% as much money as her brother.”

Answer 2

S = 0,5xB
(Her salary is 50% of her brother’s salary.)

Question 3

Translate: “Every row in a wall has the same number of bricks.”

Answer 3

W = RxB

Question 4

Translate: “There are 5 times as many peanuts as cashews in the bowl.”

Answer 4

P = 5xC
(The number of peanuts is 5 times the number of cashews)

Question 5

Translate: “There are 3 apples for every 2 oranges in the basket.”

Answer 5

3/2 = A/O -> 3O = 2A
(The ratio of apples to oranges is 3:2)

Question 6

What is the base in an exponential expression?

Answer 6

It’s the number that is multiplied by itself. In a^n, ‘a’ is the base.

Question 7

What rule applies when multiplying exponents with the same base?

Answer 7

a^m * a^n = a^(m+n)

Question 8

What rule applies when dividing exponents with the same base?

Answer 8

a^m / a^n = a^(m-n)

Question 9

What does a negative exponent mean?

Answer 9

It indicates a reciprocal: a^(-n) = 1/a^n

Question 10

How do you handle a fraction raised to a power?

Answer 10

(a/b)^n = a^n / b^n

Question 11

How can exponents help in factoring?

Answer 11

Use the common base to factor out: e.g., 2^3 + 2^4 = 2^3(1 + 2^1)

Question 12

If a^x = a^y, what must be true?

Answer 12

x = y, assuming a ≠ 0 and a ≠ 1

Question 13

What strategy helps solve exponential equations?

Answer 13

Express both sides with the same base.

Question 14

How does the ‘same base or same exponent’ rule help?

Answer 14

It allows setting exponents or bases equal to simplify or solve.