Basic Math & Pre-Algebra Workbook For Dummies with Online Practice book cover

Basic Math & Pre-Algebra Workbook For Dummies with Online Practice

Author:
Mark Zegarelli
Published: April 17, 2017

Overview

Master the fundamentals first for a smoother ride through math

Basic Math & Pre-Algebra Workbook For Dummies is your ticket to finally getting a handle on math! Designed to help you strengthen your weak spots and pinpoint problem areas, this book provides hundreds of practice problems to help you get over the hump. Each section includes a brief review of key concepts and full explanations for every practice problem, so you'll always know exactly where you went wrong. The companion website gives you access to quizzes for each chapter, so you can test your understanding and identify your sticking points before moving on to the next topic. You'll brush up on the rules of basic operations, and then learn what to do when the numbers just won't behave—negative numbers, inequalities, algebraic expressions, scientific notation, and other tricky situations will become second nature as you refresh what you know and learn what you missed.

Each math class you take builds on the ones that came before; if you got lost somewhere around fractions, you'll have a difficult time keeping up in Algebra, Geometry, Trigonometry, and Calculus—so don't fall behind! This book provides plenty of practice and patient guidance to help you slay the math monster once and for all.

  • Make sense of fractions, decimals, and percentages
  • Learn how to handle inequalities, exponents, square roots, and absolute values
  • Simplify expressions and solve simple algebraic equations
  • Find your way around a triangle, circle, trapezoid, and more

Once you get comfortable with the rules and operations, math takes on a whole new dimension. Curiosity replaces anxiety, and problems start feeling like puzzles rather than hurdles. All it takes is practice. Basic Math & Pre-Algebra Workbook For Dummies is your ultimate math coach, with hundreds of guided practice practice problems to help you break through the math barrier.

Master the fundamentals first for a smoother ride through math

Basic Math & Pre-Algebra Workbook For Dummies is your ticket to finally getting a handle on math! Designed to help you strengthen your weak spots and pinpoint problem areas, this book provides hundreds of practice problems to help you get over the hump. Each section includes a brief review of key concepts and full explanations for every practice problem, so you'll always know exactly where you went wrong. The companion website gives you access to quizzes for each chapter, so you can test your understanding and identify your sticking points before moving on to the next topic. You'll brush up on the rules of basic operations, and then learn what to do when the numbers just won't behave—negative numbers, inequalities, algebraic expressions, scientific notation, and other tricky situations will become second nature as you refresh what you know and learn what you missed.

Each math class you

take builds on the ones that came before; if you got lost somewhere around fractions, you'll have a difficult time keeping up in Algebra, Geometry, Trigonometry, and Calculus—so don't fall behind! This book provides plenty of practice and patient guidance to help you slay the math monster once and for all.
  • Make sense of fractions, decimals, and percentages
  • Learn how to handle inequalities, exponents, square roots, and absolute values
  • Simplify expressions and solve simple algebraic equations
  • Find your way around a triangle, circle, trapezoid, and more

Once you get comfortable with the rules and operations, math takes on a whole new dimension. Curiosity replaces anxiety, and problems start feeling like puzzles rather than hurdles. All it takes is practice. Basic Math & Pre-Algebra Workbook For Dummies is your ultimate math coach, with hundreds of guided practice practice problems to help you break through the math barrier.

Basic Math & Pre-Algebra For Dummies Cheat Sheet

A little understanding can go a long way toward helping master math. Some math concepts may seem complicated at first, but after you work with them for a little bit, you may wonder what all the fuss is about. You'll find easy-to-understand explanations and clear examples in these articles that cover basic math concepts — like order of operations; the commutative, associative, and distributive properties; radicals, exponents, and absolute values — that you may remember (or not) from your early math and pre-algebra classes. You'll also find handy and easy-to-understand conversion guides for converting between metric and English units and between fractions, percents, and decimals.

Articles From The Book

11 results

Basic Math Articles

How to Divide Decimals

Dividing decimals is similar to dividing whole numbers, except you have to handle the decimal point before you start dividing. Here’s how to divide decimals step by step:

  1. Move the decimal point in the divisor and dividend.

    Turn the divisor (the number you’re dividing by) into a whole number by moving the decimal point all the way to the right. At the same time, move the decimal point in the dividend (the number you’re dividing) the same number of places to the right.

  2. Place a decimal point in the quotient (the answer) directly above where the decimal point now appears in the dividend.

  3. Divide as usual, being careful to line up the quotient properly so that the decimal point falls into place.

    Line up each digit in the quotient just over the last digit in the dividend used in that cycle.

As with whole-number division, sometimes decimal division doesn’t work out evenly at the end. With decimals, however, you never write a remainder. Instead, attach enough trailing zeros to round the quotient to a certain number of decimal places. The digit to the right of the digit you’re rounding to tells you whether to round up or down, so you always have to figure out the division to one extra place.

See the following chart:

Sample questions

  1. Divide the following: 9.152 / 0.8 = ?

    11.44. To start out, write the problem as usual:

    Turn 0.8 into the whole number 8 by moving the decimal point one place to the right. At the same time, move the decimal point in 9.1526 one place to the right. Put your decimal point in the quotient directly above where it falls in 91.25:

    Now you’re ready to divide. Just be careful to line up the quotient properly so that the decimal point falls into place.

  2. Divide the following: 21.9 / 0.015 = ?

    1,460. Set up the problem as usual:

    Notice that two trailing zeros are attached to the dividend because you need to move the decimal points in each number three places to the right. Again, place the decimal point in the quotient directly above where it now appears in the dividend, 21900:

    Now you’re ready to divide. Line up the quotient carefully so the decimal point falls into place:

    Even though the division comes out even after you write the digit 6 in the quotient, you still need to add a placeholding zero so that the decimal point appears in the correct place.

Practice questions

  1. Divide these two decimals: 9.345 / 0.05 = ?

  2. Solve the following division: 3.15 / 0.021 = ?

  3. Perform the following decimal division, rounding to one decimal place: 6.7 / 10.1.

  4. Find the solution, rounding to the nearest hundredth: 9.13 / 4.25.

Following are answers to the practice questions:
  1. 9.345 / 0.05 = 186.9. To start out, write the problem as usual:

    Turn the divisor (0.05) into a whole number by moving the decimal point two places to the right. At the same time, move the decimal point in the dividend (9.345) two places to the right. Place the decimal point in the quotient directly above where it now appears in the dividend:

    Now you’re ready to divide. Be careful to line up the quotient properly so that the decimal point falls into place.

  2. 3.15 / 0.021 = 150. Write the problem as usual:

    You need to move the decimal point in the divisor (0.021) three places to the right, so attach an additional trailing zero to the dividend (3.15) to extend it to three decimal places:

    Now you can move both decimal points three places to the right. Place the decimal point in the quotient above the decimal point in the dividend:

    Divide, being careful to line up the quotient properly:

    Remember to insert a placeholding zero in the quotient so that the decimal point ends up in the correct place.

  3. 6.7 / 10.1 = 0.7. To start out, write the problem as usual:

    Turn the divisor (10.1) into a whole number by moving the decimal point one place to the right. At the same time, move the decimal point in the dividend (6.7) one place to the right:

    The problem asks you to round the quotient to one decimal place, so fill out the dividend with trailing zeros to two decimal places:

    Now you’re ready to divide:

    Round the quotient to one decimal place:

  4. 9.13 / 4.25 = 2.15. First, write the problem as usual:

    Turn the divisor (4.25) into a whole number by moving the decimal point two places to the right. At the same time, move the decimal point in the dividend (9.13) two places to the right:

    The problem asks you to round the quotient to the nearest hundredth, so fill out the dividend with trailing zeros to three decimal places:

    Now divide, carefully lining up the quotient:

    Round the quotient to the nearest hundredth:

Basic Math Articles

How to Divide Big Numbers with Long Division

To divide larger numbers, use long division. Unlike the other Big Four operations, long division moves from left to right. For each digit in the dividend (the number you’re dividing), you complete a cycle of division, multiplication, and subtraction. In some problems, the number at the very bottom of the problem isn’t a 0. In these cases, the answer has a remainder, which is a leftover piece that needs to be accounted for. In those cases, you write r followed by whatever number is left over.

Sample questions

  1. Divide 956 / 4.

    239. Start off by writing the problem like this:

    To begin, ask how many times 4 goes into 9 — that is, what’s 9 / 4? The answer is 2 (with a little left over), so write 2 directly above the 9. Now multiply 2 x 4 to get 8, place the product directly below the 9, and draw a line beneath it:

    Subtract 9 – 8 to get 1. (Note: After you subtract, the result should be less than the divisor (in this problem, the divisor is 4). Then bring down the next number (5) to make the new number 15.

    These steps are one complete cycle. To complete the problem, you just need to repeat them. Now ask how many times 4 goes into 15 — that is, what’s 15 / 4? The answer is 3 (with a little left over). So write the 3 above the 5, and then multiply 3 x 4 to get 12. Write the product under 15.

    Subtract 15 – 12 to get 3. Then bring down the next number (6) to make the new number 36.

    Another cycle is complete, so begin the next cycle by asking how many times 4 goes into 36 — that is, what’s 36 / 4? The answer this time is 9. Write down 9 above the 6, multiply 9 x 4, and place this below the 36.

    Now subtract 36 – 36 = 0. Because you have no more numbers to bring down, you’re finished, and the answer (that is, the quotient) is the very top number of the problem:

  2. Divide 3,042 / 5.

    608 r 2. Start off by writing the problem like this:

    To begin, ask how many times 5 goes into 3. The answer is 0 — because 5 doesn’t go into 3 — so write a 0 above the 3. Now you need to ask the same question using the first two digits of the divisor: How many times does 5 go into 30 — that is, what’s 30 / 5? The answer is 6, so place the 6 over the 0. Here’s how to complete the first cycle:

    Next, ask how many times 5 goes into 4. The answer is 0 — because 5 doesn’t go into 4 — so write a 0 above the 4. Now bring down the next number (2), to make the number 42:

    Ask how many times 5 goes into 42 — that is, what’s 42 / 5? The answer is 8 (with a little bit left over), so complete the cycle as follows:

    Because you have no more numbers to bring down, you’re finished. The answer (quotient) is at the top of the problem (you can drop the leading 0), and the remainder is at the bottom of the problem. So 3,042 / 5 = 608 with a remainder of 2. To save space, write this answer as 608 r 2.

Practice questions

  1. Divide 741 / 3.

  2. Evaluate 3,245 / 5.

  3. Figure out 91,390 / 8.

  4. Find 792,541 / 9.

The following are the answers to the practice questions:
  1. 247

  2. 649

  3. 11,423 r 6

  4. 88,060 r 1

Basic Math Articles

Pre-Algebra Practice Questions: Comparing Fractions Using Cross-Multiplication

Cross-multiplication is a handy tool for finding the common denominator for two fractions, which is important for many operations involving fractions. In the following practice questions, you are asked to cross-multiply to compare fractions to find out which is greater or less.

Practice questions

1. Find the lesser fraction:

2. Among these three fractions, which is greatest:

Answers and explanations

1. Of the two fractions,

Cross-multiply to compare the two fractions:

Because 35 is less than 36,

2. Of the three fractions,

Use cross-multiplication to compare the first two fractions.

Because 21 is greater than 20, this means that 1/10 is greater than 2/21, so you can rule out 2/21. Next, compare 1/10 and 3/29 by cross-multiplying.

Because 30 is greater than 29, 3/29 is greater than 1/10. Therefore, 3/29 is the greatest of the three fractions.