At Last....DECIMALS!!!

The time is here were we come to the last post of this blog.  This last post I wanted to focus on a topic that can be difficult to a lot of students. The DECIMAL!!! Some children and adults find the period very intimidating because when multiplying decimals together you are not only trying to figure out the correct numericals, but you also have to know if you can leave the decimal in its place or move the decimal to a different position of the number.





With the example, as a student I would atutomiatically get confused because you have some problems with decimals being multiplied by whole numbers and by other deceimal numbers, but the decimals are lined up together.  So first we have to go over the stepts to multiplying with decimals.

Steps to Multyiplying Decimals:

1. Multiply like whole numbers.

2. Count decimal places in the problem.

3. Put the same number of places beind the decimal in the product.

Here below is an example of how two decimals would be multiplied together.




From the very first problems that was given above the student would have to multiply

a. 4.6                b. 3.9                 c. 14.56
   x  7                  x5.6                    x   2.8

  32.2                   234                    11648
                          1950                    29120
                         21.84                   40.768

Another way to try to figure out where the decimal point goes and that is by rounding the two multiplying numbers to the nearest whole number. After solving the product of those two numbers that is where you will place your decimal point. I found this way by watcing this video that is provided below.

Perform operations with multi-digit whole numbers and with decimals to hundredths.

CCSS.MATH.CONTENT.5.NBT.B.7
Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

Did I Divide That?!?!?

Fractions can come easy or hard to some people when doing it in math class.  For me is was quite simple, but once my teachers tried to teach me that two fractions can be divided by each other I becae the biggest confused person in the classroom.  I needed extra help and once I got the help I had to teach myself that there is one important step that has to be taken before I can complete the problem.  I would always forget to flip the fraction before soloving.  This week I wanted to focus on dividing fractions.

When I was a student and I had saw a similar problem like this I was very confused on what was done and why it was done that way.  Below are some steps to solving a fraction divided by another fraction.

Steps:

1. The problem is given as a division problem.  It must be rewritten to a multiplication problem by simply reversing the fraction recipricol to the divisor.

2. Then you multiply the numerator and the denominator.

3. Then simplify if necessary.

So using the first example given the student(s) would have to solve the problem like this:


1  ➗  1  ͇     1 ✖  4   ͇    4   ͇͇   2
2         4       2       1      2



CCSS.MATH.CONTENT.5.NF.B.7
Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.

Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

CCSS.MATH.CONTENT.6.NS.A.1
Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?.

Fractions X's Whole Numbers

When I was learning about multiplying fractions one conept that used to confuse me was multiplying a fraction by a whole number.  This past class reminded me of that when we the professor gave us an identical example problem.  If I was presented with the problem 3/4 x 7. I knew that I would have to change the 7 into a fraction so I would put 7/7.  The problem with that 7/7 is equaled to 1. So this week I will be focusing on the steps to multiplying a fraction by a whole number.

Above is an example of whole number multiplied by a fraction. Here are the steps that I and students can use in order to solve the problem.

Steps:

1. Rewrite the whole number as a fraction. To rewrite a whole number as a fraction, simply place the whole number over 1. (Any number over one is equaled to itself.)

2. Multiply the numerators of the two fractions. (The numerators are the numbers above the line.)

3. Multiply the denominators of the two fractions. (The denominators are the numbers below the line.)

4. Reduce the answer if possible.  Your answer most likley will become a proper fraction or an imporper fraction, you have to simplify the answer to its lowest terms.  The number in the denominator will have to be divided by the numerator and the denominator to equal your simplified answer.

By using the steps above for the example 3 x 2/15 the answer would be:

 3    x   2   =  6     =    2 

 1        15      15         5

Here is another example of a whole number multiplied by a fraction that is turned into an improper fraction and simplified:

 

Multiplying whole numbers by fractons can also be shown in models because multiplication is nothing more than repeated addition. So below is a model to show how it multiplyng whole numbers by fractions can be used a a different way:

Though some students might not be comfortable with word problems, they should be able to understand and extract the key details that is needed to solve a word problem.  I would provide the students with a fun word problem activity for them to do individually or in pairs.

CCSS.MATH.CONTENT.4.NF.B.4
Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.

CCSS.MATH.CONTENT.4.NF.B.4.A
Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4).

CCSS.MATH.CONTENT.4.NF.B.4.B
Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In general, n × (a/b) = (n × a)/b.)

CCSS.MATH.CONTENT.4.NF.B.4.C
Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?

STOP.....IT'S FRACTION TIME!!!!

So far we have covered multiplying single & double digit numbers, long multiplication, and multiplication including addition.  This week I will be covering mulitplying fractions.  Fractions may can be simple for students when trying to identify a portion of a large quanity. A circle that is divided in half and shaded is equalled to 1/2 and a square that is cut into 4 squares and three of them are shaded is equalled to 3/4. Though that can be easy, some students might find it difficult when they want to find out how much of the shaded areas combined equals up too. Here is a video below to show students how to multiply fractions.

After the students become familarized with the song the students should be presented with the three step process of multiplying fractions.

Steps for Multiplying Fractions:

1. Multiply the numerator.

2. Multiply the denomicator.

3. Reduce the fraction if necessary.





After we revisit the parts of a fraction from the example of above I would then give students an example of how to multiple a fraction by used the three step process.




Below is a work sheet that can be given to students for them to practice on.



For an even fun activity you can group students in to pairs and have them give each other there own fraction multiplication problems by providing them with a blank sheet.

CCSS.MATH.CONTENT.5.NF.B.4
Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction

CCSS.MATH.CONTENT.5.NF.B.4.A
Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd).