Number Sense and Problem Solving

Lesson 1 · Compare and order numbers

Place value

The value of a digit depends on its place. Each place is worth ten times the place on its right, so a digit is worth more the further left it sits.

The number is 1,436,879: “one million, four hundred thirty-six thousand, eight hundred seventy-nine.” The 1 has the greatest value (one million). The 9 has the least (nine ones). Commas split the digits into groups of three from the right, which makes long numbers easier to read.

Comparing and ordering

Line the numbers up by place value, then compare from the left:

• A number with more digits is greater (for whole numbers).
• If they have the same number of digits, compare the first digits. If those match, move one place right and compare again.

💡 The symbol always opens toward the bigger number.

Rounding

1. Find the place you are rounding to, and look at the digit just to its right.
2. If that digit is 5 or more, add 1 to the rounding place. If it is less than 5, leave the rounding place as it is.
3. Change every digit to the right of the rounding place to 0.

Next: Lesson 2, whole number operations →

Lesson 2 · Whole number operations

Addition

The answer to an addition is the sum (or total). Stack the numbers with the ones lined up, then work from right to left.

   1
   40
  129
+  24
-----
  193

💡 Check an answer by rounding: 40 + 130 + 20 = 190, which is close to 193.

Subtraction

The answer is the difference. Put the greater number on top. If a top digit is smaller than the one below it, borrow 1 from the next column to the left.

  4 17
  5  7
- 3  8
------
  1  9

    9
  1 10 15
  2  0  5
-    6  7
---------
  1  3  8

Multiplication

Multiplying is a quick way to add the same amount many times: 24 + 24 + 24 = 24 × 3. The answer is the product.

     24
   × 63
   ----
     72   ← 24 × 3
+  1440   ← 24 × 60
   ----
   1512

Division

Dividing splits an amount into equal groups. The amount being divided is the dividend, the number you divide by is the divisor, and the answer is the quotient. Anything left over is the remainder.

   251 r2
  ------
4 ) 1006
   - 8
     20
   - 20
      06
    -  4
       2

💡 Knowing your times tables by heart saves real time on the test, even with a calculator.

Next: Lesson 3, calculator skills →

Lesson 3 · GED® test calculator skills

On the computer, the calculator opens when you click the calculator icon at the top of the screen, and you can drag it so it doesn't cover the question. If you would rather use a handheld one, you need to bring your own TI-30XS MultiView™. Buying one to practise with as you work through the book is a good idea.

The four operations

Every calculation follows the same pattern:

• Always clear first, so nothing from the last question is left in the calculator.
• Made a typing mistake? Press delete to go back, then type it again.
• Subtract with the − key on the right, with the other operations. The (−) key at the bottom makes a number negative; it does not subtract.
• Multiplication shows on the screen as *, even though the key is marked ×.
• For subtraction and division, the order matters: enter the number you start with first.

The 2nd key

Some keys have a second job, printed in green above them. To use it, press the green 2nd key in the top-left corner first, let go, and then press the key. Don't press them at the same time. You will see “2nd” at the top of the display while it is switched on.

Square root (√) is the 2nd function of x². Percent (%) is the 2nd function of the left bracket (, and the 2nd function of the right bracket ) turns an answer into a percent. Chapter 3 covers percents in depth.

Next: Lesson 4, word problems →

Lesson 4 · Word problems

The five-step method

1. What is the question asking me to find? Say it in your own words.
2. What information do I need? Pick out only the numbers that matter.
3. Which operation? Add, subtract, multiply or divide (or more than one).
4. What is my solution? Do the calculation with the numbers from step 2.
5. Does my answer make sense? Re-read the question. Did you answer what it asked?

💡 GED questions often include numbers you don't need, and the wrong answer choices are usually built from them.

Multi-step problems

Many test questions need two or more calculations. Keep asking two things: what is the question asking me to find? and have I answered it yet?

Next: Lesson 5, distance and cost →

Lesson 5 · Distance and cost

A formula describes how quantities are related. The letters in it are variables. Put in the values you know, and the formula gives you the one you don't.

Distance = rate × time

d = r × t

d is the distance, r the rate (speed, such as miles per hour), and t the time.

Cost = number of units × rate

c = n × r

c is the total cost, n the number of units, and r the rate, meaning the price per unit. “Per” means “for each one”.

Rearranging a formula

If you know any two of the three values, you can find the third by dividing:

💡 Check by putting every value back into the original formula: 4 × $11 = $44. ✔

The GED® formula sheet

You don't have to memorise these. The test gives you a formula sheet, and d = rt and “total cost = (number of units) × (price per unit)” are both on it. The rest are taught in later chapters.

Next: summary and quiz →

Chapter summary

• A digit's value depends on its place. Compare numbers place by place from the left, and round by looking at the digit just to the right of the rounding place.
• Line up the columns to add and subtract, and regroup when a column needs it. Multiplying is repeated adding; dividing splits into equal groups, sometimes with a remainder.
• On the TI-30XS, always clear first, subtract with − (not (−)), and press 2nd before a green function such as √ or %.
• Solve word problems in five steps: find the question, pick the information you need, choose the operations, solve, and check you answered the question. Watch for extra information and half-finished answers.
• d = rt and c = nr. Know two values and you can find the third; check by putting the values back in.

Mini-quiz

Source: GED® Test Prep Mathematics, Chapter 1 (Number Sense and Problem Solving). Explanations, the Try it questions' answers, the tools and the quiz are Guru Jazzy's own. GED® is a registered trademark of the American Council on Education; this page is not made or endorsed by GED Testing Service.