04 Math Foundations Free Online FlashCards

What is the order of operations?

Evaluate parentheses and exponents first, then multiplication and division from left to right, followed by addition and subtraction from left to right. For example, $18 - 2 \times 5 = 8$.

How should decimal points be aligned when adding or subtracting?

Line up decimal points before adding or subtracting so that digits with the same place value are aligned.

What do a fraction’s numerator and denominator represent?

A fraction represents parts out of equal parts: the numerator counts the parts, and the denominator gives the total number of equal parts. The denominator cannot be zero.

How do you add fractions with different denominators?

Rewrite the fractions with a common denominator, combine their numerators, and simplify the result. For example, $\frac{1}{4} + \frac{1}{6} = \frac{5}{12}$.

How do you divide one fraction by another?

Multiply by the reciprocal of the second fraction, then simplify. For example, $\frac{2}{3} \div \frac{4}{5} = \frac{5}{6}$.

How do you convert a percent to a decimal?

Divide a percent by $100$ to write it as a decimal, or multiply a decimal by $100$ to write it as a percent. For example, $32\% = 0.32$.

How do you find a part when you know the rate and whole?

Use $\text{part} = \text{rate} \times \text{whole}$. For example, $15\%$ of $80$ is $0.15 \times 80 = 12$.

How do you calculate percent change?

Divide the change by the original amount, then multiply by $100\%$. Use the original amount as the denominator.

Why does the order of quantities matter in a ratio?

A ratio compares quantities by division, and the order matters. A ratio of nurses to patients is not the same as a ratio of patients to nurses.

How can you solve a proportion by cross-multiplying?

A proportion states that two ratios are equal, such as $\frac{a}{b} = \frac{c}{d}$. Solve it by cross-multiplying: $a \times d = b \times c$.

How do you use a conversion factor to change units?

Multiply by an equivalent ratio of units, arranged so the starting units cancel. For example, $2.5\,\mathrm{L} \times \frac{1000\,\mathrm{mL}}{1\,\mathrm{L}} = 2500\,\mathrm{mL}$.

How does $750\,\mathrm{mg}$ convert to grams?

Since $1000\,\mathrm{mg} = 1\,\mathrm{g}$, $750\,\mathrm{mg} = 0.750\,\mathrm{g}$. Converting to a larger unit decreases the numerical value.