Welcome to fraction operations! A fraction represents parts of a whole. Look at this pizza divided into 4 equal parts. If we take 3 parts, we have 3 out of 4 parts, which we write as three-fourths. The top number shows how many parts we have, and the bottom number shows the total parts.
Now let's learn to add fractions with the same denominator. When fractions have the same bottom number, we simply add the top numbers together. For example, one-fourth plus two-fourths equals three-fourths. We can see this visually: one part plus two parts gives us three parts out of four total parts.
Now let's learn to multiply fractions by whole numbers. When we multiply 3 times one-fourth, we're taking one-fourth three times. This is like adding one-fourth plus one-fourth plus one-fourth, which gives us three-fourths. We multiply the top number by 3 and keep the bottom number the same.
Now let's multiply fractions by fractions using area models. To find one-half times one-third, we create a rectangle and divide it. First, we shade half of the rectangle in red. Then we shade one-third in green. The purple area where they overlap is one-sixth of the whole rectangle. This shows us that one-half times one-third equals one-sixth.
Let's review what we've learned about fraction operations. When adding fractions with the same denominator, we add the numerators and keep the denominator the same. When multiplying a fraction by a whole number, we multiply the numerator. When multiplying fractions together, we can use area models to visualize the result. Keep practicing with visual models to build your understanding!