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Adding and Subtracting Decimals Study Guide (page 2)

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Updated on Oct 4, 2011

Borrowing

Next, look at a subtraction example that requires "borrowing." Notice that borrowing works exactly the same as it does when you're subtracting whole numbers.

Example: 2 – 0.456

  1. Put a decimal point at the right of the whole number (2) and line up the numbers so their decimal points are aligned: 2.
  2. Tack zeros onto the end of the shorter decimal to fill in the "holes":

    0.456

    2.000

    0.456

  3. Move the decimal point directly down into the answer and subtract after borrowing:

  4. Check the subtraction by addition:

    Our answer is correct because we got back the first number in the subtraction problem.

Combining Addition and Subtraction

The best way to solve problems that combine addition and subtraction is to "uncombine" them; separate the numbers to be added from the numbers to be subtracted by forming two columns. Add each of the columns and you're left with two figures; subtract one from the other and you have your answer.

Example: 0.7 + 4.33 – 2.46 + 0.0861 – 1.2

1. Line up the numbers to be added so their decimal points are aligned:
2. Tack zeros onto the ends of the shorter decimals to fill in the "holes":
3. Move the decimal point directly down into the answer and add:
4. Line up the numbers to be subtracted so their decimal points are aligned:
5. Tack zeros onto the end of the shorter decimal to fill in the "holes":
6. Move the decimal point directly down into the answer area and add:
7. Subtract the step 6 answer from the step 3 answer, lining up the decimal points, filling in the "holes" with zeroes, and moving the decimal point directly down into the answer area:

Working with Decimals and Fractions Together

When a problem contains both decimals and fractions, it's usually easiest to change the numbers to the same type, either decimals or fractions, depending on which you're more comfortable working with. Consult Lesson 6 if you need to review changing a decimal into a fraction and vice versa.

Example: Fraction-to-decimal conversion:

1. Convert to its decimal equivalent:
2. Add the decimals after lining up the decimal points and filling the "holes" with zeros:

Decimal-to-fraction conversion:

1. Convert 0.37 to its fraction equivalent:
2. Add the fractions after finding the least common denominator:

Both answers, 0.745 and , are correct. You can easily check this by converting the fraction to the decimal or the decimal to the fraction.

Tip

Look for a sales receipt from a recent shopping trip, preferably one with several items on it. Randomly select three items and rewrite them on a separate sheet of paper. Add a zero to each number, but add it to a different place in each one. For instance, you could add a zero to the right side of one number, the center of another, and the tenths column of another. Now add the column of newly created numbers. Then check your answer. Did you remember to align the decimal points before adding? Practice this kind of exercise with everything you buy, or think of buying, during the day.

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