What should be applied to fractions

This is the diagram from Section 7. The easiest way would be to use a pencil and ruler to mark the border of inches from the top, the bottom and the sides of the matting; then measure the width and length of the rectangular hole to ensure that it is very close to the inches width and the inches length you want for the photograph. Now you are ready to cut out the hole.

If you are careful, and use a craft knife and a ruler, you will have a rectangular piece of matting that you can use later for a smaller photograph! Your last step is to buy the frame to put the photograph and matting in.

You must now find the final size of the framed photo. Did you start with the final dimensions of the matting? Did you remember to include the width of the frame? Looking back at the information you collected, you chose the border of the frame to be of an inch all around.

Thus, we must add to each side of the length of the matting. The height we need for the frame is: equation sequence sum with, 3 , summands two divided by three plus two divided by three equals open 15 plus seven divided by 10 close plus two multiplication open two divided by three close equals Then, add to the top and bottom of the matting. The length we need for the frame is: equation sequence sum with, 3 , summands two divided by three plus two divided by three equals open 27 plus 13 divided by 15 close plus two multiplication open two divided by three close equals So, we found that the overall dimensions of the framed photograph are approximately 17 inches by 29 inches.

Now you can decide where you have the space to hang up your beautiful picture. In order to decide where to hang up the picture, you need a space that is at least 17 inches in height and 29 inches in length. When you complete a problem, you should always look back over your work. That could have cost you more money! You should also consider which techniques you may be able to use in future problems. Here, breaking the problem down into small steps, using sketches, and using the real-world context of the problem helped.

Perhaps you even could attempt to carry out this project in your home. Another important strategy is discussing the problem with someone else. By explaining how you have approached the problem in your own words, or having another person provide insight and ask a question or two, you might clarify your thinking enough to find a way to move forward in your work.

Now you just have to decide in which room to hang up your old photograph. Lucky for you, you've already done the math! In this section, we will try to deepen our understanding of the mathematical content that was discussed throughout the unit. If you find a problem difficult, feel free to discuss it with a friend. If you still have your sheet of paper, then use it.

Misplaced it? Try it using your piece of paper. You can then try it using a tissue to compare your results. In theory, you should be able to keep folding your paper in half forever. This is due to the thickness of the paper. Most types of paper get stuck at seven folds. What about yours? Do you think a larger piece of paper could be folded more?

This video investigates it. In this unit, you might have found some portions easier than others. The more you practice, the more your skills improve. It will help to work through the exercises for each section provided below. They were asked about the main reasons they had decided to join the center. A quarter of the group wanted to take advantage of the discounted payment for those joining on the first day, three-eighths were advised to join by their physician and one-fifth were motivated by watching the Olympics.

One-eighth of is 20, so three-eighths of is 20 multiplication three equals One-fifth of is division five equals Therefore, the total number of people who chose one of the three reasons is.

The number of people who gave some other reason was minus equals Take your solution from part a , and express it as a fraction. You should now have. So, of the people joining gave some other reason. Alternatively, you could have worked out the fraction of students that gave some other reason as follows:. A recipe for an iced cake requires pounds of icing.

Two-thirds of the icing is to go on the sides of the cake, with one-third on the top. How much icing should be reserved for the sides of the cake? Give your answer in ounces. There are several ways you can do this calculation. For example, you can calculate two thirds of as follows:. There are 16 ounces in a pound, so pounds is. Alternatively, you might have converted the pounds to ounces.

A Walmart employee is a shelf stacker. His time for stacking shelves is 50 minutes for an average set of shelves. If he is at work for 9 hours, and he has a 40 minute break in that time, how many sets of shelves will he be able to fill? You need to calculate first how many hours he is working, and then divide that by how long it takes him to complete one set of shelves. Alternatively, you could convert the 9 hours to minutes: nine multiplication 60 equals minutes. So he is in the store for minutes.

He has a break of 40 minutes, leaving his working time minus 40 equals minutes. It takes him 50 minutes to stack a set of shelves, so the number of shelves he can stack is sets of shelves. Unit fractions are fractions which have a numerator of 1, for example italic one divided by italic four and italic one divided by italic five. The Ancient Egyptians used only the fraction italic two divided by italic three and unit fractions.

How did you work these out? One way to work these out is to use a diagram split into quarters or eighths, with the required fraction shaded. Alternatively, you can think about the problem practically: three divided by four means '3 divided by 4'. So imagine three bars of chocolate being shared equally among four people. If you broke all the bars in half and gave one half to each person, there would still be two half bars left. These could be broken in half again, and a quarter given to each person.

So each person would get a half and a quarter. Can you use fractions with the denominator of 60 to find a sum of unit fractions which represent the fraction? Now that you have taken the time to work through these sections, try this short quiz! You may find that it will help you to monitor your progress, particularly if you took the quiz at the start of the unit as well.

The quiz does not check all the topics in the unit, but it should give you some idea of the areas you may need to spend more time on.

Click here for the post quiz. Read through the list on the next page and think over all the work you have done in this unit. Remember, your mathematical skills will develop and grow stronger over time. Just keep working at it! You will work with percentages and ratios to improve your understanding of how numbers are used in communication and the business world. Fractions in the real world 5.

Summary 6. Introduction Why should I learn about fractions? Also read: Free Math puzzle with answers on fractions How to add Fractions with different combinations? What are Fractions? Fractions in Mathematics Fractions are an elementary topic in mathematics that act as a building block in many other mathematics topics. Some of the ways fractions are used in mathematics are: We can determine the part of any number using fractions. They are used to attribute a numerical value to the likelihood of the occurrence of an event.

Example What is the likelihood of the number 3 showing up on rolling an unbiased dice? Fractions are used in ratios. These concepts along with others are widely used in mathematics and other sciences to perform calculations. Fractions in the real world Fractions surround our everyday activities.

Here are some examples of fractions in real life: Eating at a restaurant: Think about a time you go to a restaurant with friends and the waitress brings a single bill. Summary The applications of fractions in everyday life are endless; they are of great importance and profoundly impact everything around us.

Where are fractions used in mathematics? Fractions are used in: Determining the part of a number Calculating decimals and percentages Ratio and proportion Probability Algebraic equations. What are some examples of fractions in real life? Here are some applications of fractions in real life: Splitting a bill while eating at a restaurant Calculating the discounted price of an object on sale.

Following a recipe Fractions are frequently used to analyze the performance of a particular player and team. Different fractions of liquids are mixed in the right amounts to make mocktails.

Dividing pizza slices equally amongst everyone requires fractions. The shutter speed of a camera is calculated using fractions. The doctor prescribes different dosages, for people of different sizes based on fractions. In time, Half n hour is a common way of expressing 30 minutes. Thus the improper fraction is the same as 1. On the number line, the line segment from 0 to m is divided into n equal parts, each part has length.

In order to write 10 as an improper fraction, we write:. There are approximately days in a year. Express this mixed numeral as an improper fraction. If two fractions have the same denominator then it is easy to decide which is the larger. It is the one with the larger numerator. One number is greater than another if it lies to the right of that number on the number line.

If the denominators of two fractions are not equal, it is more difficult to see which of the two fractions is larger. In this case, we can use equivalent fractions. To compare and , first find a common denominator. The lowest common denominator is the lowest common multiple of the two denominators, which in this example is What about and? Addition of fractions is straightforward if the denominators are the same. Of course this is exactly the same process as with the whole numbers and the number line.

Thus, when the denominators of the fractions to be added are the same, we add the numerators. When the denominators are different, we use equivalent fractions to express the fractions using a common denominator and then proceed exactly as before:.

We can add mixed numerals together simply by adding together the whole number parts and then adding the fractions. Note that the commutative and associative laws for addition have been used in obtaining the result. Subtracting fractions uses similar ideas to addition of fractions. If the denominators of the two fractions are equal, subtraction is straightforward. When the denominators of the fractions to be subtracted are the same, we subtract the second numerator from the first.

If the denominators are not equal, we use equivalent fractions to find a common denominator. What fraction when added to 4 gives 6? In mathematics, when we are asked, for example, to find of 18 oranges, we take it to mean that we divide the 18 oranges into three equal parts and then take two of these parts. This method can be extended. For example, to find of : we first calculate of and then multiply by 3.

The base is divided into three equal intervals denominators of the first fraction. The height is divided into 4 equal intervals denominators of the second fraction. Each of the rectangles has area equal to. The rectangle with side lengths and is shaded.

You get the same shaded region if you first shade of the square and then shade of the shaded section. We cancelled down the second last fraction to its lowest form, after doing the multiplication. There is a shorthand way of writing this, which often simplifies the process of multiplication. This process is called cancelling. The cancellation can take place because you are doing the same operation to both numerator and denominator which we know gives an equivalent fraction.

What is the total length of 6 pieces of ribbon if each piece is 8 cm? When multiplying two mixed numerals, we can convert both into improper fractions before multiplying. For example,. Dividing a whole number by a whole number. We have considered dividing a whole number by a whole number in a previous section of this module. It was found that dividing a whole number by a whole number gives a fraction. Also note that dividing by 3 gives the same result as multiplying by.

In general, for whole numbers m and n , dividing m by n is the same as multiplying m by. Note that is called the reciprocal of n. Division of a fraction by a whole number. The idea of performing a division by multiplying by the reciprocal can also be used to divide a fraction by a whole number.