Mathematics - Arithmetic and Word Problem Practice Questions

Apply root and power rules to solve for k, showing how cube roots, square roots, and power rules lead to k equals 12.

Solve a pair of congruences: a ≡ 2 (mod 5) and a ≡ 5 (mod 6) with a < 40. The solution shows a = 17, so the remainder when a is divided by 7 is 3.

Apply the difference of squares: a^2 - b^2 = (a-b)(a+b). Use 49 and 35 to show (49−35)(49+35) = 14×84, which simplifies to 84.

Master exponent rules in arithmetic, including power of power and multiplying or dividing exponents with the same base, and solving for exponents when bases match through sample questions.

Show that for 24 consecutive odd integers, the median is the average of the 12th and 13th terms, which equals the given mean of 48.

Identify prime factors of 462 and apply divisibility rules to determine valid divisors like 22, using the factors 2, 3, 7, and 11.

Solve an arithmetic question using powers of ten, convert between powers and decimal placement, and apply multiplication and division by ten to determine the correct power-of-ten answer.

Solve an arithmetic question by selecting values P and Q within given ranges, choosing P near -1.5 and Q near 1.2, leading to option C.

Solve a linear inequality from the caption: 12 minus 3x less than -18. Move terms and divide by -3, noting the sign flips, yielding x > 10.

Apply exponent rules for like bases to multiply and divide powers, simplify expressions, and solve for exponents, as demonstrated in arithmetic question 18.

Use arithmetic mean to relate X, Y, and 20 with an average of 11, then compute the mean of 2X+3, 2Y-4, and 8 to verify X+Y=13.

Cross-multiply the equation (x-3)/(x+2) = (x+3)/(x-7) and simplify to find x = 1, keeping the domain restriction x ≠ -2 and x ≠ 7.

The lecture demonstrates simplifying a rational expression by factoring the numerator and denominator, verifying with cross-multiplication, and canceling terms to obtain (x+6)/(x+2).

This arithmetic question computes the percent decrease from the original population of 2105 to 1705, using a 400 decrease and a divide-by-2105-and-100 approach to estimate the percent.

Determine a point’s coordinates in the XY plane by applying Pythagoras theorem: x^2 + y^2 = 40, using the origin and example (6,2).

Solve for x and y from the relation three x equals two y equals five, substitute values, square y, and simplify to verify the result.

Explore converting percent to fractions and solving division of fractions by multiplying with reciprocals, illustrated by computing one over four hundred from zero point twenty five percent.

Compute the percent of not white marbles by using (X minus Y) over X times 100, with X as total marbles and Y as white marbles.

Compute the probability that four numbers drawn without replacement from one, two, three, four appear in order, resulting in 1/24.

Apply the ratio 2:3 to y and x under y equals x/5, then substitute and rearrange to find y or x, yielding 10/3.

Compare the spreads of data around the mean to determine standard deviation; larger differences between numbers indicate greater spread and higher standard deviation.

Explore solving proportional relationships by equating 75 percent of X to 125 percent of Y, then simplifying to determine that Y equals 60 percent of X.

Assign 2, 3, and 5 to A, B, and C distinct, and maximize the expression by placing the largest number in the numerator and the smallest in the denominator.

Analyze when statements about X and Y on the number line hold, including X+Y < Y, X*Y < 0, and key modulus properties.

Explore how a positive integer with remainder three when divided by six constrains K to six x plus three and determine which expressions are even or odd using parity rules.

Solve a linear word problem with x and y where 2x+3y equals 1.75 percent of 8x; derive y=4x and determine x or y.

Compute an arithmetic expression using negative exponents and fractions. Students learn to convert to common denominators, flip fractions, and expand terms to simplify.

Demonstrates converting 0.000125 into scientific notation and a fraction, showing 125 times 10^-6 equals 1/8000 and clarifying the decimal-to-fraction relationship.

Compute the missing score x in a frequency table for ten students by equating total scores to the mean times count, revealing x equals sixty-five.

Apply the square-difference identity, A^2 − B^2 = (A+B)(A−B), to evaluate a numeric example; the steps simplify to seven, confirming option B as the answer.

Explore a recurrence sequence defined by T_n with given T1 and T2. Compute T3 and T4 and apply multiplication sign rules to verify results.

Compute the 12 fee for the defined operation using the difference of squares and algebra to arrive at the result six.

Analyze a positive two-digit number with digits a and b and its reversed form, and show that K is a multiple of eleven.

Solve a difference of squares problem by factoring X^2 minus Y^2 as (X-Y)(X+Y)=12, then use the equations X-Y=4 and X+Y=3 to find X=7/2.

Explore a modular arithmetic problem: if X is a positive integer and X+2 is divisible by 10, determine the remainder of X^2+4X+9 when divided by 10.

Explore how adding a fifth number changes the arithmetic mean of four numbers, and derive the equation to solve for the fifth number using the sum of all numbers.

The lecture demonstrates solving a division with remainder by isolating the remainder E and deriving an expression like E equals Q minus W.

Solve an arithmetic word problem about ages by using seven years ago relationships, deriving Bob's present age in terms of K given Kate is now 11.

Use elimination on two simultaneous linear equations in X and Y to cancel Y, derive X, and select the resulting value (option C).

Relate 1 decimeter to both microns and angstroms to derive 1 micron equals 10,000 angstroms.

This lecture presents solving a linear equation to express y in terms of x from 3x + 2y = 0, yielding y = -3x/2.

Explore simplifying a complex arithmetic expression by canceling factors through multiplications and divisions, ending with three halves and identifying the correct answer choice B.

practice solving arithmetic and word problems by factoring and cross multiplication to derive and solve quadratics such as x^2+4x-5=0.

Identify the greatest common factor across numeric coefficients and variable powers, using the smallest exponent for x, y, and w as the gcd factor.

Develop problem-solving skills in distance equals velocity times time by solving a word problem about a spaceship's travel using algebra and powers of ten.

Practice solving for X by making X the subject, flipping sides, using division and multiplication, and rationalizing the denominator to simplify radicals in an equation.

calculate the decimal equivalent of (2/5)^5 by converting 2/5 to 0.4 and applying the exponent; move the decimal point five places to obtain 0.01024.

Rationalize the denominator by multiplying by the conjugate, apply the difference of squares, and simplify to obtain 3 plus 2 root two.

Factor out the common factor under the radical, apply the product property to get sqrt(49) × sqrt(81) = 7 × 9 = 63, and identify the answer as option C.

Calculate the sales tax percentage from the original price P and total price T using tax = T − P and tax percent = ((T − P)/P) times 100.

Explore reciprocals and reciprocal operations in arithmetic, using expressions like 2 over Kay and 1 over Kay to simplify and solve a problem, ending with option b.

Combine the given averages: A+B=2J and C+D+E=3K. Add J to form A+B+C+D+E+J=3J+3K, then divide by six to obtain the overall average (J+K)/2.

Learn how factorials work and how to factor out 89 factorial from (91! - 90! + 89!) / 89!, then simplify to a compact form such as 9(1990^2 + 1).

Explore how percent relationships between X and Y are analyzed, using long division to derive a recurring decimal, culminating in the mixed number 44 4/9.

Apply cross-multiplication to a rectangle's reduced dimensions, finding x meters that yield an eight-to-three ratio, illustrating algebraic reasoning in arithmetic word problems.

Solve a system of exponent equations by rewriting numbers with common bases, equating exponents, and solving X+Y=3 and X-3Y=-2 to find Y = 5/4.

Explore binomial expansions, such as (a−b)^2 and (a+b)^2, and use unit digit checks to quickly compare answer choices, as demonstrated with 73^2 and 74^2.

Rewrite expressions as powers using prime factorization, equate exponents when bases match, and solve for K, showing that K equals 12.

Explore arithmetic question 81 by tracing how eight times eight relates to eighty-one, leading to the conclusion that the answer is a.

Express A as 1869k + 102 and use 1869 equals 89 times 21 to find A mod 89, giving a remainder of 13.

Determine the roots of the quadratic equation X^2 - 10X - 24 = 0 by factoring into (X-12)(X+2), yielding X = 12 or X = -2.

Solve a square-root equation by expanding and squaring, factor the resulting quadratic, find possible x values, and verify the domain to confirm x = 6.

apply the mean formula to three numbers W, X, Y and the adjusted values W+2, X-3, Y+8. derive the sum W+X+Y from the given average and compute their new average.

Using prime factorization, determine the greatest common divisor as 18 and the least common multiple as 102, then compute x plus y as 120.

Solve for y from zero point twenty five plus x equals y and y over x equals zero point two using cross multiplication, yielding y equals minus one over sixty.

This lecture practices arithmetic and binomial expansion, using the relation 1/x plus x^2 equals 16 to apply (a+b)^2 and solve for the expression.

Solve an arithmetic question involving powers and exponents, such as fourth power six and fourth power five, using factoring and exponent rules. Cancel terms to yield the final answer four.

Calculate the average of two numbers by adding X and Y and halving the sum; the lecture derives X+Y=20 and the average equals 10.

Explore how the mean of five consecutive negative integers relates to the range, showing that the difference between the greatest and least terms is four.

Apply combinations to choose two girls from four and two boys from five for a party, distinguishing from permutations, with a final count of 60.

Tackle absolute value equations with x and y from the arithmetic and word problem practice, solving |x+5|=3 and |(2y-1)/3|=5, and explore possible x+y sums.