A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.

By buying two shirts, Alex will save $20 x \( \frac{35}{100} \) = \( \frac{$20 x 35}{100} \) = \( \frac{$700}{100} \) = $7.00 on the second shirt.

So, his total cost will be
$20.00 + ($20.00 - $7.00)
$20.00 + $13.00
$33.00

The distributive property for multiplication helps in solving expressions like a(b + c). It specifies that the result of multiplying one number by the sum or difference of two numbers can be obtained by multiplying each number individually and then totaling the results: a(b + c) = ab + ac. For example, 4(10-5) = (4 x 10) - (4 x 5) = 40 - 20 = 20.

A number in scientific notation has the format 0.000 x 10^exponent. To convert to scientific notation, move the decimal point to the right or the left until the number is a decimal between 1 and 10. The exponent of the 10 is the number of places you moved the decimal point and is positive if you moved the decimal point to the left and negative if you moved it to the right:

0.0009545 in scientific notation is 9.545 x 10^-4

To divide fractions, invert the second fraction and then multiply:

\( \frac{3}{6} \) ÷ \( \frac{2}{9} \) = \( \frac{3}{6} \) x \( \frac{9}{2} \)

To multiply fractions, multiply the numerators together and then multiply the denominators together:

\( \frac{3}{6} \) x \( \frac{9}{2} \) = \( \frac{3 x 9}{6 x 2} \) = \( \frac{27}{12} \) = 2\(\frac{1}{4}\)