Fraction and Integer Arithmetic Review

Flashcards covering rules for fractions, integers, BEDMAS, stacked equations, and number line graphing from lecture notes.

In fraction terminology, what do the top and bottom numbers represent?

The top number is the numerator and the bottom number is the denominator.

What is Strategy #1 for finding a common denominator when adding or subtracting fractions?

Check if the larger denominator divided by the smaller denominator yields a non-decimal value. If it does, the larger number is your common denominator, and you do not change its denominator.

What is Strategy #2 for finding a common denominator if Strategy #1 yields a decimal value?

Multiply the denominators by each other, ensuring you multiply both the numerator and the denominator of each fraction by the same value.

What are the core rules for multiplying fractions?

Do NOT get a common denominator. Cross-reduce when possible, then multiply top by top ($\text{top} \times \text{top}$) and bottom by bottom ($\text{bottom} \times \text{bottom}$).

What is the Keep-Change-Flip rule used for dividing fractions?

Keep the first fraction the same, Change division ($\times$) to multiplication ($\times$), and Flip the second fraction upside down. Then apply the multiplication rules.

What are the sign rules for adding and subtracting integers with same signs versus different signs?

For same signs, keep the sign and add the digits. For different signs, take the sign of the larger digit and subtract the smaller digit from the larger digit.

What are the sign rules for multiplying and dividing integers?

Same signs ($++$ or $--$) equal a positive ($+$) result. Different signs ($+-$  or $-+$) equal a negative ($$-$)  result.

How should side-by-side signs be handled in an expression?

Apply the sign rules of multiplication to reduce the side-by-side signs down to a single sign before calculating (for example, $7 - (-6) = 7 + 6 = 13$).

How do you calculate whole numbers with fractions?

Change the whole number to a fraction simply by putting it over $1$ (for example, $4 = \frac{4}{1}$).

What must be done before calculating with mixed fractions?

Change them to improper fractions first (for example, $3\frac{4}{5} = \frac{3 \times 5 + 4}{5} = \frac{19}{5}$).

How do you evaluate fractions with exponents?

Apply the exponent to both the numerator and the denominator separately (for example, $(\frac{3}{4})^2 = \frac{3^2}{4^2} = \frac{9}{16}$).

What are the steps and priority order in BEDMAS?

Brackets (work to do within), Exponents, Divide and Multiply (whichever comes first from left to right), Add and Subtract (whichever comes first from left to right).

How do you solve a Stacked Question using BEDMAS?

Solve the top expression using BEDMAS, solve the bottom expression using BEDMAS, and then divide (if decimals) or reduce (if whole numbers). For example, $\frac{40 - 32 \times 2}{4.6 \times 1.9} = \frac{40 - 64}{8.74} = \frac{-24}{8.74} = -2.75$.

What are the rules for graphing decimals and fractions on a number line?

For decimals, always use $10$ ticks. For fractions, the denominator is the number of ticks and the numerator is where to put the dot (get a common denominator if fractions in the same section have different denominators). Always count away from zero, and ensure end values of the number line are whole numbers.