Fractions - N

A fraction is "a numerical quantity that is not a whole number (e.g. 1/2, 0.5), as well as "a small or tiny part, amount, or proportion of something."

— Oxford Languages & Dictionary

Quick Overview of Fractions:

There are three parts of addition: the addend, the equal sign, and the sum.

Example problem/equation: $1/4 + 2/3 = 11/12$

Terminology:

• Numerator - this is the number that represents the number of parts out of the whole. This number will always be on the top and, for Fourth Grade, it will always be the smaller number. In the problem above, for$1/4$, the numerator would be 1, and for $2/3$, the numerator would be 2

• Fraction bar - this is the symbol that splits the parts of the whole and the whole itself. In other words, it splits the numerator and denominator. It can be represented as a slash, a straight line, or a whole number

• Denominator - this is the number that represents the total parts of the fraction. This number will always be on the bottom and, for Fourth Grade, it will always be the larger number. In the problem above, for $1/4$, the denominator is 4, and for $2/3$, the denominator is 3

Rules of Fraction:

• Adding fractions - this is the first basic operation with fractions. When adding fractions, you NEED to make sure that the denominators are the same. First, you take the LCM (Least Common Multiple) of the numbers. For example, 2 and 3 share a multiple at 6, which is the smallest multiple they share. Then you multiply the top and bottom of each fraction by the same amount. In the problem above, the LCM of 3 and 4 is 12, so you multiply 4 by 3 and then 1 by 3, to get $3/12$. Then do the same thing for the other fraction to get $8/12$. Then finally you add them together to get $11/12$

• Subtracting fractions - this is the second basic operation with fractions. This is the EXACT same process as adding fractions, except at the end you subtract them. In the problem, $2/3 - 1/4 = ?$, we said that $2/3$is $8/12$, and that $1/4$is $3/12$, so to subtract them we would do $8/12 - 3/12$, to get an answer of $5/12$

• Multiplying Fractions - this is the third basic operation with fractions. This is a lot more straightforward than addition and subtraction. For multiplication, all you have to do is multiply the top numbers by the bottom numbers (or multiply the numerators and multiply the denominators together). In the problem above, $1 * 2 = 2$and $4 * 3 = 12$, so $1/4 * 2/3 = 2/12$or $1/6$

• Dividing fractions - this is the fourth basic operation with fractions. This is the most complicated operation with fractions. If you're given, $1/4 ÷ 2/3$, the first step is to change this to multiplication. To do this you can flip the SECOND fraction, so that $2/3$becomes $3/2$, then your new problem becomes $1/4 * 3/2$, which equals $3/8$. This process can be represented by "copy...change...flip" You copy the problem, change the symbol to multiplication, and then flip the second fraction to solve the problem

Application of Fractions:

Complex Fractions:

Links to resources, videos, and worksheets:

• The Story Of Mathematics (Website)

• Math Is Fun (Website)

• Math Is Fun (Worksheet)

Showing common fractions and their pictorial representation!

Lesson Complete!