Decimals and Fractions

Lesson 1 · Decimal basics

Decimal place value

You already use decimals with money: in $10.25, the 25 is 25 cents, or 25 hundredths of a dollar. The places to the right of the point get ten times smaller each step.

To read 2.375, say the whole number, say “and” for the point, read the digits after the point as a whole number, then name the place of the last digit: “two and three hundred seventy-five thousandths.”

💡 The test may write a zero in front of the point. It changes nothing: 0.75 = .75.

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 it alone.
3. Drop every digit to the right of the rounding place. (With whole numbers you change them to zeros; after the decimal point you simply leave them off.)

Comparing and ordering

Line up the decimal points, then add zeros on the right so every number has the same number of decimal places. Now you can compare them as if they were whole numbers.

45.80   ← Matt
45.66   ← Alonzo

0.850
1.800
0.800
0.819

💡 A longer decimal is not always bigger. 0.8 beats 0.799 because 8 tenths is more than 7 tenths.

Next: Lesson 2, decimal operations →

Lesson 2 · Decimal operations

Adding and subtracting

Write the numbers in a column with the points in a line. Fill the gaps with placeholder zeros if it helps, then work from right to left as with whole numbers.

   3.400
  12.060
+  0.875
--------
  16.335

  14.512
-  8.700
--------
   5.812

  9.000
- 3.604
-------
  5.396

💡 Check by rounding to whole numbers: 9 − 4 = 5, close to 5.396. ✔

Multiplying

You don't need to line up the points. Multiply as if there were no decimal points, then count the decimal places in both numbers. The answer has that many decimal places.

    2.6    ← 1 place
 × 0.45    ← 2 places
 ------
    130
 + 1040
 ------
   1170  →  1.170

Dividing

Decide where the point goes before you divide.

• If the divisor (the number you divide by) is a whole number, put the point in the answer directly above the point in the dividend.
• If the divisor is a decimal, move its point to the right until it is a whole number. Move the dividend's point the same number of places, adding zeros if you need to.

    2.4
   -----
6 ) 14.4
  - 12
     2 4
   - 2 4
       0

💡 On a multiple-choice question you often don't need to finish dividing. After one or two steps, only one choice may still fit.

Next: Lesson 3, fraction basics →

Lesson 3 · Fraction basics

What a fraction means

A fraction shows part of a whole with two numbers. The denominator (bottom) is the number of equal parts in the whole. The numerator (top) is the number of parts you are counting.

This bar has 4 equal parts and 3 are shaded, so 34 of it is shaded.

💡 If a question is hard to picture, sketch it: a bar or a circle cut into equal parts.

Improper fractions and mixed numbers

Equal fractions: raising and reducing

The numerator and denominator are the fraction's terms. Multiply or divide both terms by the same number and you get an equal fraction. A fraction is in lowest terms when no number except 1 divides both terms.

💡 To raise to a given denominator, ask “what times the old denominator gives the new one?” For 34 = ?16: 4 × 4 = 16, so multiply the top by 4 too.

Next: Lesson 4, fraction operations →

Lesson 4 · Fraction operations

Adding and subtracting

Like fractions share a denominator. Add or subtract the numerators and keep the denominator.

💡 If your answer isn't one of the choices, check that you reduced it. Test answers are always in lowest terms.

Multiplying

You don't need a common denominator. Multiply the numerators, multiply the denominators, then reduce. Change any mixed number to an improper fraction first.

Dividing

Invert the divisor (the fraction you are dividing by): swap its top and bottom. Then change ÷ to × and multiply. Write whole and mixed numbers as improper fractions first.

💡 Multiplying by a fraction less than 1 gives a smaller answer (you are finding “part of”). Dividing by one gives a bigger answer. Use this to check.

Next: Lessons 5 and 6, equivalents and the number line →

Lesson 5 · Fraction and decimal equivalencies

Equivalents worth memorising

13 and 23 never come out exactly: 1 ÷ 3 = 0.3333… with the 3s going on forever. A bar over a digit means it repeats, so 0.3̅ = 0.333…

Lesson 6 · Decimals and fractions on the number line

Zoom in on the stretch between 0 and 1½ and you can mark it in quarters. Each mark can be named as a decimal (above) or a fraction (below). The dot is at 0.75, or 34: more than 0.5 and less than 1.

Reading a point

1. Find two labelled marks and the gap between them.
2. Count the equal steps in that gap. Each step is the gap divided by the number of steps.
3. Count steps from a labelled mark to the point.

💡 Some test questions ask you to click a spot on the line to place a dot. Work out the value first, then count the steps.

Next: Lesson 7, calculator skills →

Lesson 7 · Decimal and fraction calculator skills

Decimals

The decimal point key is in the white number pad, under the 2. Everything else works as in Chapter 1.

Fractions

The keys you need:

💡 If the answer comes out as an improper fraction such as 94, press 2nd x10ⁿ and then enter to see it as 214.

Next: summary and quiz →

Chapter summary

• Decimal places are tenths, hundredths, thousandths and so on. Round by looking at the digit to the right; compare by lining up the points and adding zeros.
• To add or subtract decimals, line up the points. To multiply, count the decimal places in both numbers. To divide by a decimal, move both points the same number of places first.
• The denominator counts the equal parts in the whole; the numerator counts the parts you have. Change between improper fractions and mixed numbers, and raise or reduce by multiplying or dividing both terms.
• Add and subtract fractions over a common denominator, regrouping mixed numbers when you need to. Multiply straight across; to divide, invert the divisor and multiply. Reduce every answer.
• A fraction is a division: 38 = 3 ÷ 8 = 0.375. A decimal becomes a fraction over its last place value. Some fractions, like 13, repeat forever.
• On a number line, find the size of each step, then count. On the TI-30XS, use n/d, 2nd n/d for mixed numbers, and the toggle key to switch between fraction and decimal.

Mini-quiz

Source: GED® Test Prep Mathematics, Chapter 2 (Decimals and Fractions). Explanations, the Try it questions' answers, the converter 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.