Fifth Grade Math Facts

Learning the explanations behind certain 5th grade math skills can improve retention.

In terms of math, fifth grade focuses on learning to apply concepts and skills found in the "real world." A large part of the curriculum usually involves fractions, decimals and measurements. However, extra insight into these types of concepts can help students learn to use them on a day-to-day basis and start to develop the deeper meanings needed for understanding algebra.

Numerators and Denominators

The numerator is the number on the top of the division bar in a fraction. The numerator tells you the "number" of pieces you have. The denominator, on the other hand, is the bottom number and tells you how big each piece is. The bigger the denominator is, the smaller the pieces are. For instance, the fractions 3/7 and 3/9 both have three pieces, but the pieces in the second fraction are smaller.

Decimals

Decimals are really just fractions. Each place to the right of the decimal point represents a different fraction. The first place represents tenths, the second place represents hundredths, and the third replace represents thousands. To turn, a decimal into a fraction, figure out the furthest place it occupies and use that as the denominator. For instance, .329 occupies three places to the right of the decimal point, so you know you are dealing with thousandths. In this example, 329 is the numerator, and 1,000 is the denominator to create 329/1,000.

Inverse Relationship Between Addition and Subtraction

You may have learned that to divide a fraction by another fraction, you multiply by the reciprocal. For instance 2/3 divided by 1/4 is the same as 2/3 x 4/1. This is because multiplication and division are "inverse" operations--the effects they have on numbers are thely opposite of each other. In fact, multiplying by a reciprocal always accomplishes the same thing as dividing, even when there are no fractions. For example, 3 divided by 4 is the same thing as saying 3 x 1/4.

Changing from Meters to Feet

In math, and life, some measurements have English units (like feet) while others have metric units (like meters). However, it is not difficult to convert feet to meters or meters to feet if you remember that a meter is extremely close in size to a yard and that a yard is 3 feet. For instance, 33 feet divided by 3 would change to 11 yards. Because yards are so similar to meters, something that measures 33 feet is about 11 meters long. Likewise, a building measuring 100 meters would be about 300 feet.

Averages

You can find the average or "mean" of a group of numbers by using addition and division. Add together all of the numbers in the group. Then, divide the answer by the number of numbers. For example, if you received an 87, 92, 79 and 91 on four tests and wanted to find your average grade, you would add them to get 87+ 92 + 79 + 91 = 349. You would then divide 349 by 4 because there were 4 tests. This would give you an average grade of 87.25.

Estimating Problems with a Numerous Digits

When faced with numbers having more than two digits, operations often take a long time. To estimate or check an answer quickly, you can perform the operation with the first digits of the numbers and replace all of the other digits with zeros. Round the first digit up if the second digit is bigger than 5. To add 173,248 and 105,283, you would change them to 200,000 and 100,000 and get an estimated answer of 300,000.

References

• AAAmath: Fifth Grade-Topics