Welcome to our lesson on calculating fractions. A fraction represents a part of a whole or a division of two numbers. It consists of two parts: the numerator, which is the number above the line, and the denominator, which is the number below the line. In this example, three-fourths means three out of four equal parts, as shown in the circle where three out of four sections are filled.
Now, let's learn how to add and subtract fractions. To add or subtract fractions, we need to follow four steps. First, find a common denominator. Second, convert each fraction to an equivalent fraction with that common denominator. Third, add or subtract the numerators while keeping the common denominator. Finally, simplify the result if possible. Let's look at an example: one-fourth plus two-thirds. We need to find a common denominator, which is 12. Converting one-fourth to three-twelfths and two-thirds to eight-twelfths, we can add the numerators to get eleven-twelfths. The visual representation shows how these fractions combine.
Let's move on to multiplying fractions. Multiplying fractions is actually simpler than addition or subtraction. You just need to follow three steps. First, multiply the numerators together. Second, multiply the denominators together. Third, simplify the result if possible. Let's look at an example: two-thirds times three-fourths. We multiply the numerators: two times three equals six. Then we multiply the denominators: three times four equals twelve. So we get six-twelfths, which simplifies to one-half. The visual representation shows how the areas overlap when we multiply these fractions.
Now let's learn how to divide fractions. Division might seem tricky, but we can convert it to multiplication using a simple trick. Here are the steps: First, keep the first fraction as it is. Second, flip the second fraction to find its reciprocal. Third, change the division sign to multiplication. Fourth, multiply the fractions as we learned earlier. Finally, simplify if possible. Let's look at an example: three-fourths divided by two-thirds. We keep three-fourths as is, and flip two-thirds to get three-halves. Then we multiply three-fourths by three-halves, which gives us nine-eighths, or one and one-eighth. The visual representation shows how this works with the rectangles representing each fraction.
Let's summarize what we've learned about calculating fractions. A fraction represents a part of a whole, with a numerator above the line and a denominator below. To add or subtract fractions, you need to find a common denominator first, then add or subtract the numerators while keeping the common denominator. To multiply fractions, simply multiply the numerators together and the denominators together. To divide fractions, flip the second fraction to find its reciprocal, then multiply. And always remember to simplify your final answer when possible. This table summarizes the four basic operations with fractions and provides examples of each. With practice, calculating fractions will become second nature, allowing you to solve more complex math problems with confidence.