## 15 April 2019

Adding integers together is generally the first form of arithmetic that adolescents learn. Once children can count to at least ten and have a solid understanding of these numerical values,  addition is valuable. Other forms of simple arithmetic include subtraction, multiplication, and division. These concepts are easy to maneuver around after years of active learning but can be difficult for first-timers. Experiencing challenges with arithmetic is especially true for young students who are beginning to work with fractions. Teachers often demonstrate adding fractions together first, so children become comfortable in this area.

## Defining Fractions

Fractions are specific portions of an observable whole. Every fraction is made up of a numerator and a denominator. The numerator is the number that appears above the dividing line of the fraction. A numerator represents a particular portion of a given whole. For example, think of a basket of apples that has two green apples and two red apples. When focusing your attention on the red apples, the numerator for that fraction would be two. A denominator, on the other hand, is the number which appears below the dividing line of the fraction. The denominator identifies a given whole value. So, the denominator for this basket example would be four since there are four apples present.

## Adding Two Fractions with the Same Denominator

One of the easiest ways to visualize fractions is to buy a pizza or pie for your child and cut it into equal pieces. If you make one cut that equally divides a pie into two sections, each piece is considered to be one-half. Have your child push these two parts of the pie together again, and this will represent a whole pie. It is essential to teach fractions in a hands-on way to crystallize this information. These two halves can each receive an additional slice to create four quarters. Your child can add two quarters together to recreate one-half. Quarters are commonly used alongside this example to express the fractions of one dollar.

## Adding Two Fractions with Different Denominators

When your child is examining two fractions that have two different denominators, this is when confusion occurs. One of the easiest ways to add two fractions with two different denominators involves something referred to as the least common multiple. A least common multiple between two positive integers is the smallest number by which two values are divisible. Returning to the pie example will help solidify this concept. Assume your child is looking to add one-half of the pie to one-fourth. The denominator for the former is two and four for the latter. The least common multiple for these denominators is four. The entire fraction for one-half of the pie must be multiplied by two to create a denominator of four. Adding these two fractions together will give your child an answer of three-fourths.
An easy way for your child to comprehend this answer of three-fourths is to push three pieces of the pie together. There are four pieces in total, but one part stands alone. With this being the case, three is the numerator, and four equals the denominator for this answer.