Chapter Outline

Fraction

A fraction describes a part of a whole.

The numerator (the top number) tells how many parts are in the fraction. The denominator (the bottom number) tells the number of parts in a whole.

Understanding Fractions

There are several forms of fractions:

• In a proper fraction the numerator is less than the denominator.
• In an improper fraction the numerator is equal to or larger than the denominator.
• A mixed number is a whole number and an improper fraction.

Reducing means writing a fraction with smaller numbers. Remember that a reduced fraction is equal to the original fraction. To reduce a fraction, follow these steps:

• Divide both the numerator and the denominator by a number that divides into them evenly.
• Check to see whether another number divides evenly into the new numerator and the new denominator.

Working with Fractions

The opposite of reducing fractions is raising fractions to higher terms. To raise a fraction to higher terms, follow these steps:

• Divide the original denominator into the new numerator to find the multiplier.
• Multiply the original numerator by the multiplier.

To change an improper fraction to a whole or mixed number, follow these steps:

• Divide the denominator into the numerator.
• Write the remainder as a fraction. Put the remainder over the original denominator.
• Reduce the remaining fraction if possible.

To change a mixed number to an improper fraction, follow these steps:

• Multiply the denominator by the whole number.
• Add the numerator.
• Write the total over the denominator.

The size of the numerator compared to the size of the denominator tells something about the size of a fraction:

• A fraction is equal to ½ when the numerator is half of the denominator.
• A fraction is less than ½ when the numerator is less than half of the denominator.
• A fraction is greater than ½ when the numerator is greater than half of the denominator.

To estimate fraction problems, round mixed numbers to the nearest whole number:

• For a mixed number with a fraction of ½ or more, round to the next whole number.
• For a mixed number with a fraction of less than ½, drop the fraction and use the whole number.

To add or subtract fractions, you need to find the lowest common denominator, the smallest number that can be divided evenly by all the denominators in a problem. To find the lowest common denominator for two or more fractions, follow these steps:

• Try the largest denominator to see whether the other denominators divide into it evenly.
• If that doesn’t work, go through the multiplication table of the largest denominator until you find a number that the other denominators divide into evenly.

Adding Fractions

To add mixed numbers, follow these steps:

• Add the whole numbers and fractions separately.
• Combine the sums to simplify the answer.

Subtracting Fractions

To subtract fractions, you must sometimes borrow or rename fractions.

Multiplying Fractions

To multiply fractions, whole numbers, and mixed numbers, first write each number in fraction form. A shortcut for multiplying fractions is called canceling. To cancel, find a number that divides evenly into the numerator of one fraction and the denominator of the other. To multiply fractions, follow these steps:

• Multiply the numerators together.
• Multiply the denominators together.
• Reduce the answer if possible.

Dividing Fractions

In division problems, you must invert the divisor. To divide with fractions, whole numbers, or mixed numbers, follow these steps:

• Write each number in fraction form.
• Invert the divisor and change the ÷ sign to a × sign.
• Follow the rules for multiplying fractions.

Fractions and Decimals

To change a decimal to a fraction, follow these steps:

• Write the digits in the decimal as the numerator.
• Write the denominator that corresponds to the number of places.
• Reduce the fraction.

To change a fraction to a decimal, follow these steps:

• Divide the denominator into the numerator.
• Write a decimal point and zeros to the right of the decimal point in the dividend.

Scientific Notation with Small Numbers

To write a small number in scientific notation, follow these steps:

• Move the decimal point in the number to get a number between 1 and 10.
• Write x 10^-x.
• The power x is the number of places that the decimal point has to move.

Fraction Word Problems

To mark a fraction answer on a number grid, follow these steps:

• Write the answer in the blank boxes across the top of the grid. Use a separate box for each digit and for the slash.
• Below each digit and slash, fill in the corresponding circle. The circles for the slash are in the first row below the blank boxes.