Concept

The denominator of a fraction is how many equal parts make up a whole
The numerator of a fraction is now many equal parts there are.

Like fractions are fractions with the same denominator. 

A fraction is said to be in simplest form if its numerator and denominator have no common factors other than 1.

Rule

To add like fractions using a model:
1. On the model, count how many equal parts make up the whole. This is the denominator.
2. Count the number of shaded equal parts. This is the numerator. 

To subtract like fractions using models:
1. On the model, count how many equal parts make up the whole. This is the denominator. 
2. Count the shaded parts of the whole and subtract the shaded parts that have been crossed off.
This is the numerator.

Simplify if needed by dividing numerator and denominator by the greatest common factor.

Example

1) Add.

2) Subtract.

Solution

Example 1:
On the model, count how many equal parts make up the whole. There are 10 equal parts. This is the denominator.

Count the number of shaded equal parts. There are 7 parts shaded blue, and 2 parts shaded yellow, so 9 parts total. This is the numerator.

Answer: 910

Example 2:
1. On the model, count how many equal parts make up the whole. 
There are 10 equal parts. This is the denominator. 

2. Count the shaded parts of the whole and subtract the shaded parts that have been crossed off. There are 7 shaded parts with 2 parts crossed off. This leaves 5 parts left over.
This is the numerator.

Answer: 510

Pre-requisite Skills

Simplify Fractions (5.10.6)

Fractions and Decimal Models - Tenths (4.15.1)