Multiples and Divisibility Rules

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Questions and Answers

What is the slope of the line represented by the equation -4x + 8y = 32?

Slope -2 (correct)

Slope 2

Slope -1

Slope 4

Find the slope of the line through the points (-7, -9) and (9, -9).

0 (correct)

-4

Which equation describes a horizontal line?

y = x + 4

y = 4 (correct)

x = 4

y = x + 8

Which of the following equations has a slope of -4 and contains the point (2, 3)?

y = -4x + 11 Signup and view all the answers

Determine whether the graphs of the equations 3x - 4y = 4 and 8x + 6y = 4 are parallel, perpendicular, or neither.

Perpendicular Signup and view all the answers

What is the slope of the line represented by the equation if rewritten as y = mx + b?

-5 Signup and view all the answers

Write the equation of a line that contains the points (2, 0) and (-7, 5).

y = -x + 6 Signup and view all the answers

Express x^(-6) using positive exponents.

1/x^6 Signup and view all the answers

What are six multiples of 22?

22, 44, 66, 88, 110, 132 Signup and view all the answers

Which of the following numbers is 738 divisible by?

2, 3, 6 Signup and view all the answers

Determine the factors of 42.

1, 2, 3, 6, 7, 14, 21, 42 Signup and view all the answers

What is the prime factorization of 36?

2 · 2 · 3 · 3 Signup and view all the answers

Which of the following represents the prime factorization of 30?

2 · 3 · 5 Signup and view all the answers

What is the result of simplifying the expression 56x/8x?

7y Signup and view all the answers

What is the least common multiple (LCM) of 7 and 9?

63 Signup and view all the answers

Which of the following numbers is 735 divisible by?

3, 5 Signup and view all the answers

What is the result of rounding 4.17553 to the nearest tenths?

4.2 Signup and view all the answers

What is the median of the numbers 52, 72, 279, 250, 405, 471?

264.5 Signup and view all the answers

Estimate the sum of 0.06, 57.37, by rounding to the nearest one.

58 Signup and view all the answers

Calculate the average of the numbers: 67, 77, 53, 73, 50, 77, 51.

64 Signup and view all the answers

What percentage of students in the college do not attend soccer or basketball matches?

44% Signup and view all the answers

How many fewer CDs are projected to be sold in 2009 than in 2011?

400,000 CDs Signup and view all the answers

What is the perimeter of a polygon with sides measuring 32 m, 15 m, 15 m, and 26 m?

88 m Signup and view all the answers

Round 7.11563 to the nearest hundredths.

71.16 Signup and view all the answers

What is the result of multiplying $8x^2y^2$ and $4x^3y$?

$24x^3y^2$ Signup and view all the answers

Which inequality is correct when comparing $-3/5$ and $-2/7$?

<blockquote> </blockquote> Signup and view all the answers

What is the simplified result of adding $\frac{3x}{8}$ and $\frac{5x}{7}$?

$\frac{57x}{56}$ Signup and view all the answers

When subtracting $\frac{1x}{5}$ from $\frac{7x}{10}$, what is the simplified form?

$\frac{3x}{10}$ Signup and view all the answers

What is the mixed number equivalent of $\frac{34}{3}$?

12 Signup and view all the answers

When adding $71x$ and $65x$, what is the mixed numeral result?

$14x$ Signup and view all the answers

What is the result when multiplying $2\frac{1}{5}$ by $31/4$?

$6$ Signup and view all the answers

What is the result of dividing $2$ by $17$?

$\frac{2}{17}$ Signup and view all the answers

What is the result of simplifying the expression $(-5x^4y)^2$?

25 x^8 y^2 Signup and view all the answers

What is the degree of the polynomial $15x^8yz - 4x^6y^2 + x^5yz^3$?

8 Signup and view all the answers

Evaluate the polynomial $-2x^2 - y^2 + xy$ for $x = -2$ and $y = 4$. What is the result?

-16 Signup and view all the answers

What is the scientific notation of the number 0.000637?

6.37 × 10^-4 Signup and view all the answers

If you collect like terms from $-4x^7 + 7x^9 - 3x^8 - 2x^7 + 8x^8 + 9x^9$, what is the simplified form?

16x^9 + 5x^8 - 6x^7 Signup and view all the answers

What is the result when adding the polynomials $(3 + 9x^5 + 9x^2) + (2x^5 - 4x^2 + 8)$?

11 + 5x^5 + 11x^2 Signup and view all the answers

Convert the number 25657 into scientific notation. What is the correct representation?

2.5657 × 10^4 Signup and view all the answers

What is the simplified result of the polynomial expression $b^{-2} b^{10}$?

b^{12} Signup and view all the answers

Study Notes

Multiples

A multiple of a number is the product of that number and an integer.
The multiples of 22 are 22, 44, 66, 88, 110, 132, and so on.

Divisibility Rules

A number is divisible by 2 if it is even.
A number is divisible by 3 if the sum of its digits is divisible by 3.
A number is divisible by 5 if its units digit is a 0 or a 5.
A number is divisible by 6 if it is divisible by both 2 and 3.
A number is divisible by 9 if the sum of its digits is divisible by 9.
A number is divisible by 10 if its units digit is a 0.

Factors

Factors of a number are the numbers that divide evenly into that number.
The factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42.
The factors of 28 are 1, 2, 4, 7, 14, and 28.

Prime Factorization

Prime factorization is the process of expressing a number as a product of prime numbers.
The prime factorization of 36 is 2 x 2 x 3 x 3.
The prime factorization of 30 is 2 x 3 x 5.

Multiplication and Division of Fractions

To multiply fractions, multiply the numerators and the denominators.
To divide fractions, multiply the first fraction by the reciprocal of the second fraction.

Simplifying Fractions

To simplify a fraction, divide both the numerator and the denominator by their greatest common factor.

Least Common Multiple (LCM)

The least common multiple of two or more numbers is the smallest number that is a multiple of all of the numbers.
The LCM of 7 and 9 is 63.
When finding the LCM of expressions with variables, the LCM must include the highest power of each variable.

Inequalities

To write a true sentence using < or >, compare the absolute values of the numbers.
The number with the smaller absolute value is less than the number with the larger absolute value.

Adding and Subtracting Fractions

To add or subtract fractions, they must have the same denominator. Find a common denominator and simplify the expression.

Mixed Numbers

A mixed number is a number expressed as a whole number and a fraction.
To convert a mixed number to an improper fraction, multiply the whole number by the denominator of the fraction and add the numerator. Keep the same denominator.

Adding and Multiplying Mixed Numbers

To add mixed numbers, add the whole numbers and then add the fractions.
To multiply mixed numbers, convert them to improper fractions and then multiply.

Rounding Decimals

To round a decimal to the nearest tenth, look at the digit in the hundredths place. If it is 5 or greater, round the tenths digit up. If it is less than 5, keep the tenths digit the same.
To round a decimal to the nearest hundredth, look at the digit in the thousandths place. If it is 5 or greater, round the hundredths digit up. If it is less than 5, keep the hundredths digit the same.
To round a decimal to the nearest thousandth, look at the digit in the ten-thousandths place. If it is 5 or greater, round the thousandths digit up. If it is less than 5, keep the thousandths digit the same.

Estimating

To estimate, round each number to the nearest one, tenth, or hundredth and then perform the calculation.

Average

The average of a set of numbers is the sum of the numbers divided by the number of numbers in the set.

Median

The median of a set of numbers is the middle number when the numbers are arranged in order from least to greatest.
If there are an even number of numbers, the median is the average of the two middle numbers.

Mode

The mode of a set of numbers is the number that appears most often in the set.

Circle Graphs

A circle graph shows the percentage of a whole that is represented by each part of the whole.
To find the percentage of the circle graph that does not represent a certain category, subtract the percentage of the given categories from 100%.

Pictographs

A pictograph uses symbols to represent data.
Each symbol represents a certain quantity.
To find the number of symbols to represent a certain quantity, divide the quantity by the value that each symbol represents.

Perimeter

The perimeter of a polygon is the total distance around the polygon.
To find the perimeter of a polygon, add up the lengths of all of its sides.

Area

The area of a polygon is the amount of surface that it covers.
Formulas for calculating the area of different polygons are needed.

Linear Equations

A linear equation is an equation that can be written in the form y = mx + b, where m is the slope of the line and b is the y-intercept.
The slope of a line is the ratio of the rise to the run.
The y-intercept of a line is the point where the line crosses the y-axis.

Graphing Linear Equations

To graph a linear equation, plot the y-intercept and then use the slope to find other points on the line.
The slope tells you how many units to move up or down and how many units to move right or left.

Parallel and Perpendicular Lines

Parallel lines have the same slope.
Perpendicular lines have slopes that are negative reciprocals of each other.

Exponents

A positive exponent indicates the number of times a base is multiplied by itself.
A negative exponent indicates the number of times a base is divided by itself.

Scientific Notation

Scientific notation is a way of writing very large or very small numbers in a compact form.
A number in scientific notation is expressed as a number between 1 and 10 multiplied by a power of 10.

Polynomials

A polynomial is an expression that consists of one or more terms.
Each term in a polynomial is a product of a coefficient and one or more variables raised to non-negative integer powers.
The degree of a polynomial is the highest power of the variable in the polynomial.

Adding and Subtracting Polynomials

To add polynomials, combine like terms.
To subtract polynomials, change the sign of each term in the second polynomial and then combine like terms.

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Description

This quiz covers key concepts like multiples, divisibility rules, factors, and prime factorization. Test your understanding of how to identify multiples of numbers and the rules that determine divisibility. Additionally, explore the process of prime factorization and its significance in mathematics.

Multiples and Divisibility Rules - Math 10th Class

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