Can fractions be equivalent to whole numbers? For example, does 8/8 equal 1?

Remember when we are talking about fractions, we are talking about parts of a whole. Fractions are equivalent, if they represent the same amount of space or distance. I have a pie that is divided into three equal parts and I eat 1 part of the pie. I have eaten 1/3 of the pie. (Shade in 1/3) Now if you have the same size pie but it is divided into 6 equal parts and you eat 2 parts of your pie. You would have eaten 2/6 of your pie. (Shade in 2/6) Did we eat the same amount? If you said, “Yes,” you are right. As you can see 1/3 and 2/6 represent the same amount of the pie. 1/3 and 2/6 are equivalent fractions.

1 2 3 A common mistake is thinking fractions and whole number can not represent the same amount of space or distance. Here we have a number line that shows whole numbers labeled below. This number line is divided into thirds, because there are three equal spaces between each whole number. The fractions are labeled above the number line. Look at the fraction 3/3. It names the same distance or point on the number line as the whole number one.

This is one whole fraction strip This is one whole fraction strip. If I take the same strip and divide it in into four equal parts, the strip would be divided into fourths. Using fraction strips, let’s see how many fourths it takes to equal one whole. It takes, one, two, three, four fourths to equal the same amount of space. We now know that 4/4 is equivalent to 1 because they represent the same amount of space. Notice that in the fraction 4/4 the numerator is four. That means that we are thinking about eight parts. The denominator is 4 that means the whole is divided into 4 parts. So in this fraction we are thinking about 4 out of 4 parts. This means we are thinking of all the parts which means we are thinking of the whole strip. Let’s divide the one whole fraction strip into eight equal parts. It is now divided into eighths. I wonder how many eighths it takes to equal the same amount as one whole strip. Let’s use the eighth fraction strips and count to find out. It takes one, two, three , four, five, six, seven, eight eighths to equal one whole strip. We now know that 8/8 is equal to 1. Notice that in the fraction 8/8 the numerator is eight. That means that we are thinking about eight parts. The denominator is 8 that means the whole is divided into 8 parts. So in this fraction we are thinking about 8 out of 8 parts. This means we are thinking of all the parts which means we are thinking of the whole strip. By using the fractions strips, we were able to see that 1, 4/4, and 8/8 are equivalent because they all represent the same amount of space.

Again we have one whole fraction strip Again we have one whole fraction strip. If I take the same strip and divide it in into six equal parts, the strip would be divided into sixths. Using fraction strips, let’s see how many sixths it takes to equal one whole. It takes, one, two, three, four, five, six sixths to equal the same amount of space. We now know that 6/6 is equivalent to 1 because they represent the same amount of space. Notice that in the fraction 6/6 the numerator is 6. That means that we are thinking about 6 parts. The denominator is 6 hat means the whole is divided into 6 parts. So in this fraction we are thinking about 6 out of 6 parts. This means we are thinking of all the parts which means we are thinking of the whole strip.

In a problem it may look like this In a problem it may look like this. Tatum and Angel shared one whole pizza. Tatum ate 1/3 of the pizza. Angel ate 2/3 of the pizza. Did they eat the whole pizza? I will use my one whole fraction strip to represent the one whole pizza the girls shared. Now the problem says Tatum ate 1/3 of the pizza, so I will use one of my thirds fraction strip to show the amount Tatum ate. Then the problem says Angel at 2/3, so I need two of my thirds fraction strips to show the amount Angel ate. Using my fraction strips, I can see that the answer is yes. Tatum and Angel ate the whole pizza because together they ate 3 parts out of a total of 3 parts.

In this lesson you have learned how to recognize fractions that are equivalent to one by using fraction strips.

Devin, Sam, Lori, and Chuck shared one whole cake Devin, Sam, Lori, and Chuck shared one whole cake. They each ate ¼ of the cake. Did they eat the whole cake? Try to figure this one out on your own. Press the pause button. If you have any trouble or need to see me work the problem press the play button again. I will use my one whole fraction strip to represent the one whole cake the friends shared. Now the problem says each person ate ¼ of the cake, so I will use my fourths fraction strip to show the amount each person ate. Devin ate ¼ of the cake. Sam ate ¼. Lori also ate ¼ of the cake and Chuck at ¼. Using my fraction strips, I can see that the answer is yes. Devin, Same, Lori, and Chuck ate the whole cake because together they ate 4 parts out of a total of 4 parts.

Using your fraction strips to answer the following questions Using your fraction strips to answer the following questions. Illustrate your answers in your math journal. How many fifths equal one whole? How many twelfths equal one whole? How many tenths equal one whole?