A03 - eLearning - Math: Fractions and Decimals 111

To convert an improper fraction to a mixed number, simply divide the numerator by the denominator. A fraction can be envisioned as a division problem where the numerator is divided by the denominator.

To convert the improper fraction 18/4, simply divide 18 by 4. 4 divides into 18 a total of 4 times, with a remainder of 2. 4 becomes the whole number portion of the mixed number, while 2 becomes the new numerator of the fraction. Since the denominator of the original fraction was 4, 18/4 converts to the mixed number 4 2/4. As with any operation involving fractions, reduce the fraction so that 4 2/4 becomes 4 1/2.

For example, solve the division problem 45 ÷ 0.5.

To make the divisor, 0.5, a whole number, move the decimal one place to the right. Also move the decimal in the dividend, 45, one place. Since 45 is a whole number, to move the decimal, first add a decimal and a zero to the end of the number. Then move the decimal over one place to make the dividend 450. Next, divide 450 by 5 to find 90. The decimal point for the answer is already correct, because it carried over from where it appears in the dividend.

An item that normally costs $56.00 is reduced by 25%. How much will the item cost after the reduction?

$42.00

0.0649 rounded to the nearest hundredth equals:

0.06

0.68 - 0.287 =

0.393

A bar with a diameter of 0.75 inches needs to be reduced by 40%. What will the new diameter of the bar be?

0.45 inches

A 12 inch bar needs to have 10% trimmed off of one end. How much will be cut off of the bar?

1.20 inches

8.64 ÷ .8 =

10.8

Convert the improper fraction 21/8 to a mixed number.

2 5/8

6/14 - 1/7 =

2/7

7/10 ÷ 2/3 =

21/20

8 ¾ x 2 5/8=

22 31/32

3/4 x 4/7 =

3/7

1/4 + 3/8 =

5/8

1.59 x 4.15 =

6.5985

3 4/9 ÷ 7 ½ =

62/135

1.456 + 6.02 =

7.476

4 1/2 + 3 7/8 =

8 3/8

Convert the mixed number 5 3/16 to an improper fraction.

83/16

The greatest common factor for the fraction 9/45 is

9. Nine is the largest number that can be divided into both 9 and 45. The GCF can't be larger than either number in the fraction. To reduce 9/45, divide 9 into the numerator, 9, and the denominator, 45. 9 divided by itself is 1 and 45 divided by 9 is 5. Thus, the fraction reduces to 1/5.

Dividing fractions is very similar to multiplying fractions, with one exception. When dividing two fractions, invert the second fraction in the division problem. Inverting a fraction switches the locations of the numerator and the denominator.

After inverting the second fraction, multiply the two fractions to find the answer. Dividing fractions often results in an improper fraction, or a fraction in which the numerator is larger than the denominator.

For example, to divide 5 2/5 by 4 10/11, first convert the mixed numbers to the improper fractions 27/5 and 54/11. Next, invert the numerator and denominator of the second number so it appears as 11/54. Then, reduce the fractions. Since 27 is a factor of 54, they reduce to 1 and 2.

After reducing, multiply the numerators and denominators to find the improper fraction 11/10. Finally, convert the result back into a mixed number. 10 divides into 11 once with a remainder of 1, so the final answer is 1 1/10.

An improper fraction is a fraction in which the numerator is larger than the denominator. For example, 11/8 is an improper fraction. The larger numerator indicates that the fraction is an amount greater than one whole.

An improper fraction can be changed to a mixed number, which is a whole number combined with a fraction. The improper fraction 11/8 converts to the mixed number 1 3/8.

For example, a tool is regularly priced at $22.00, but the manufacturer has reduced its price by 35%. To find the new cost of the tool, first determine 35% of $22.00.

Begin by converting 35% to a decimal by moving the decimal two places to the left. 35% converts to 0.35. Next, multiply the decimal by the original whole quantity. 0.35 multiplied by 22 equals 7.7. This means that 35% of 22 is 7.7. Since the new price of the item is 35% less than the original price, subtract the percentage value from the original price. 22 minus 7.7 equals 14.3. Add a dollar sign and a zero in the hundredths place to show that the new price is $14.30.

When subtracting mixed numbers, it may be necessary to borrow from the whole.

Borrowing is essentially subtracting an amount from the whole number and adding that amount to the fraction.

Like multiplication problems, dividing mixed numbers requires changing any mixed numbers to improper fractions. After converting the mixed numbers, follow the same steps used to divide proper fractions.

First invert the numerator and denominator of the second fraction, then multiply. Finish by converting the improper fraction back into a mixed number.

For example, multiply 3.62 by 2.50. Both numbers have two decimal places, and thus there are four total decimal places in the problem.

First, multiply 362 by 250 to find 90500. Since the original numbers have four total decimal places, count four places from the right of the answer, and place the decimal point in front of the fourth digit. The answer is 9.0500, with four numbers following the decimal point.

First, drop the percent sign, then move the decimal to the left two places.

For example, 14% converts to 0.14. This conversion process may also require adding zeros to the number, especially when converting percentages containing decimals. For example, 0.0223% converts to 0.000223.

To convert a mixed number to an improper fraction, multiply the whole number by the denominator, and add this number to the numerator. The sum becomes the new numerator. Place the new numerator over the same denominator from the original mixed number.

For example, 4 1/2 can be converted back to an improper fraction using this method. 4 times 2 is 8, and 8 plus 1 equals 9. 9 becomes the new numerator, so the fraction is now 9/2, which is a reduced form of 18/4.

The rules for adding and subtracting regular fractions apply to adding and subtracting mixed numbers and improper fractions. If the mixed numbers or improper fractions share a common denominator, solve the problem without any conversions. Simply add the whole numbers together as well as the numerators of the fractions.

For example, 5 1/5 + 10 3/5 adds together for a result of 15 4/5.

If the mixed numbers do not have a common denominator, find a common denominator between the two fractions.

For example, to add 3 1/3 and 11 4/9, first find the lowest common denominator, which is 3. Convert the fractions to 3 3/9 and 11 4/9, then add the whole numbers and numerators to find the answer of 14 7/9.

When adding fractions with different denominators, convert all fractions so that they have the same denominator.

Fractions with different denominators cannot be mixed. For example, 4/5 cannot be added to 1/10 until both fractions are changed to have identical denominators.

If the fractions have different denominators, use the lowest common denominator between the two fractions.

If the fractions have different denominators, use the lowest common denominator between the two fractions. To subtract 2/3 from 4/5, find the lowest common denominator between 3 and 5, which is 15.

For example, in the problem 3 1/3 x 5 7/8, the whole number 3 converts to 9/3. Combined with the fraction 1/3, the total improper fraction becomes 10/3. Similarly, the mixed number 5 7/8 converts to the improper fraction 47/8.

Once the mixed numbers are converted to improper fractions, reduce like numerators and denominators. Because 2 is a common factor of 8 and 10, divide both numbers by 2 to reduce the fractions to 5/3 and 47/4. Next, multiply the numerators and then the denominators to find the improper fraction 235/12. Finally, divide the numerator by the denominator to convert the result back into a mixed number. 12 divides into 235 a total of 19 times with a remainder of 7, so the final result is 19 7/12.

The most important step in multiplying and dividing mixed numbers is converting the mixed numbers to improper fractions.

Once the numbers are improper fractions, they can be multiplied in the same manner as regular fractions.

To add fractions with different denominators, first find the lowest common denominator for the two fractions.

The lowest common denominator for 4/5 and 1/10 is 10, because 10 is the smallest number that can be divided evenly by both 5 and 10. Since the denominator of 1/10 is already 10, only 4/5 must be converted. To convert 4/5, multiply the denominator by 2. The denominator is now 10, to match 1/10. To keep the first fraction proportional, multiply the numerator by 2 as well. Every time the denominator is changed, the numerator must be changed in the same way.

For example, in the problem 3/25 x 5/18, the numerator of the first fraction, 3, is a factor of the denominator of the other fraction, 18. Dividing 3 by 3 reduces it to 1 and dividing 18 by 3 reduces it to 6. Similarly, since 5 is a common factor of 25, 5 reduces to 1 and 25 reduces to 5.

The problem then reads 1/5 x 1/6. Multiplying the numerators and the denominators shows that 3/25 x 5/18 equals 1/30. Reducing the fractions prior to multiplying results in an answer that is already reduced.

For example, to add 0.045 and 0.02

align the decimal points in each number. Since 0.02 is shorter than 0.045, insert an additional zero to make the number 0.020. Once both numbers have the same number of decimal places, add the numbers to find 0.065.

Reducing a fraction means expressing the fraction in its simplest form, or smallest numbers. To reduce a fraction, find the

greatest common factor, which is the largest number that can be evenly divided into both numbers. Then divide both the numerator and the denominator by the greatest common factor.

For addition or subtraction problems with both a decimal and a whole number

simply add a decimal and zeros to the whole number. For example, to subtract 3.8 from 12, align the whole numbers by aligning 12 and 3. Since the number 12 is a whole number and does not have a decimal point, add the decimal and a zero. Once the number of decimal places is equal, subtract 3.8 from 12.0 to find 8.2.

Fraction multiplication is different from addition and subtraction. To multiply fractions

simply multiply the numerators, and then multiply the denominators. Finding a common denominator is not necessary when multiplying fractions. However, always reduce the answer if possible.

The same rules apply to subtracting fractions as adding fractions. If both fractions have the same denominator

simply subtract the numerators and keep the same denominator. If the numerator and denominator of the result have a greatest common factor, reduce the answer.

Multiplying fractions effectively creates two individual multiplication problems, one for the numerators, and another for the denominators. The order of numbers in individual multiplication problems does not matter

so the order of numerators and denominators in a multiplication problem also does not matter. This means that it is possible to reduce either numerator in relation to either denominator. Reducing the fractions in this manner can take place before the fractions are multiplied.

Before adding fractions, the fractions must have the same denominator. If both fractions have the same denominator, simply add the numerators together and keep the same denominator. For example, in 4/9 + 3/9

the fractions combine to equal 7 total ninths of the whole number.