5th Grade Math Facts: Overview and Examples

Although curriculums vary, many 5th graders learn math topics such as algebraic thinking, fractions and geometry. Below is an overview of the basic math concepts studied in 5th grade is presented below along with examples.

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What a Fifth Grader Learns in Math

Algebraic Thinking

In 5th grade, students learn to write and use math sentences (equations) that use parentheses and brackets. For instance, students are taught to write a problem such as 'add 9 and 6, then multiply by 3' in the form of an equation: 3 x (9 + 6). They also know that they have to add the numbers in the parenthesis before doing the multiplication.

In addition, students examine number patterns and can generate rules based on these patterns. For example, consider the following two equations: 0 + 4 = 4 and 0 + 8 = 8. From this pattern, students can draw the conclusion that adding any number to 0 equals that number.


Students in 5th grade add and subtract fractions using equivalent denominators. Before solving an equation for fractions with unlike denominators, students must first find a common denominator. For example, 3/4 + 1 1/3 becomes 3/4 + 4/3, which becomes 9/12 + 16/12 = 25/12. This is generalized with the formula a/b + c/d = (ad + bc)/bd.

Another large aspect of fraction instruction is recognizing that a fraction is a division statement. A fraction represents the numerator divided by the denominator (a/b = a ÷b). If the division is performed, the answer may be a whole number or a mixed number.

To multiply fractions, simply multiply the numerators and then the denominators. The problem 3/4 x 5/6 becomes (3 x 5)/(4 x 6) or 12/30. If a whole number is multiplied by a fraction (e.g., 7 x 3/4), the whole number is converted to a fraction and the problem becomes 7/1 x 3/4 or (7 x 3)/(1 x 4). The formula is (a/b) * (c/d) = ac/bd.

To divide a fraction by a whole number greater than 0, students are shown that a problem such as 1/4 ÷ 3 = 1/12 is true because (1/12) x 3 = 1/4. Solve by converting the whole number to a fraction and then inverting it, like this: (1/4) x (1/3).

Long Division and Decimals

In addition, students develop their long-division skills by dividing 4-digit dividends by 2-digit divisors. Students will be shown that keeping numbers in columns relating to place values is vital to accurately solving long-division problems.

Again being aware of place values and keeping them in proper columns as they work, 5th graders will learn to add, subtract, multiply and divide with decimals to the hundredths' place. For instance, to add and subtract, keep the decimal point in a column of its own. To multiply, count the total quantity of numbers after decimals.

Solid Geometry

By using unit cubes, 5th grade students are taught what volume means. They learn to use the terms cubic inch, cubic foot and cubic centimeter. Similarly, students learn to find the volume (V) of right rectangular prisms using the formulas V = l x w x h and V = b x h.

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