Numerical Ability (Complete Mastery) Practice Flashcards

Complete mastery flashcards for Numerical Ability including PEMDAS, Integers, Fractions, Decimals, Percentages, and word problem strategies.

What are the specific components of the MDAS / PEMDAS Rule in the correct order of operations?

1. Parenthesis (Brackets and Braces, inner to outer); 2. Exponents (Powers and Roots); 3. Multiplication OR Division (Left to Right); 4. Addition OR Subtraction (Left to Right).

According to the MDAS / PEMDAS rule, how should the expression $10 \times 2 \times 5$ be calculated to avoid the 'MD' trap?

Calculate from Left to Right: $10 \times 2 = 5$, then $5 \times 5 = 25$. (Assuming the operation intended was $10 \times 2 \times 5$ per the transcript logic of division preceding multiplication leftwards).

What is the rule for adding integers with different signs, such as $-10 + 3$?

Subtract the smaller number from the bigger number and copy the sign of the bigger number (e.g., $-10 + 3 = -7$).

In integer multiplication and division, what is the result if there is an odd number of negatives?

The result is NEGATIVE.

Explain the 'Friend-Enemy Logic' for multiplying and dividing integers.

'Friend of my Friend = Friend' ($+$); 'Enemy of my Enemy = Friend' ($+$); 'Friend of my Enemy = Enemy' ($-$).

What are the three steps for manual addition or subtraction of fractions with different denominators?

1. Find the LCD (Least Common Denominator); 2. Convert both fractions to equivalent fractions using the LCD; 3. Add/Subtract the numerators only.

How do you perform the 'Butterfly Method' hack for adding two fractions?

Multiply the diagonals (wings) and add them to create the new Top; multiply the bottoms together to create the new Bottom.

What is the 'Cancel First!' hack in fraction multiplication?

Before multiplying, check if a top number and a bottom number share a factor and divide them out to simplify first.

What does the acronym K.C.F. stand for in fraction division?

K (KEEP the first fraction), C (CHANGE division to multiplication), F (FLIP the second fraction into its reciprocal).

What is the 'D to P' (Decimal to Percent) mnemonic for moving decimal points?

Step forward (RIGHT) 2 places, because in alphabetical order 'D' comes before 'P'.

How do you convert a percent to a decimal?

Move the decimal point 2 places to the LEFT and remove the $\%$ symbol.

In the formula for finding Percentage ($P = B \times R$), what operation does the word 'of' signify?

Multiply.

What is the 'IS over OF' hack for finding the Rate ($R = P/B$)?

Place the number associated with 'is' over the number associated with 'of' (e.g., '5 is what percent of 20' is $\frac{5}{20}$).

What is the formula for finding the Base ($B$)?

$Base = \frac{Percentage}{Rate}$ (or $B = P/R$).

What is the formula for Percent Increase/Decrease?

$\frac{\text{New} - \text{Old}}{\text{Old}} \times 100\%$ (or 'Change over Original').

In Age Problems, what is the 'Key Logic' regarding the age difference between two people?

The age difference between two people is CONSTANT forever; it never changes despite time passing.