Quick! What is 2/3 of 240 6/229?
This is the type of problem that can cause a real dread of math. Just the thought of the process and computations involved is enough to make one frustrated and annoyed. Multiplying fractions and mixed numbers! Ugh! Solving this problem will probably take a little division as well. Double ugh!
Yet there is a much simpler and elegant way to solve this without ever putting pen to the paper. All it requires is a little “number sense.” Let’s use Wholes and Parts and Fractions to answer this question mentally.
Wholes and Parts
One of the best ways to solve a math problem is to break it down into smaller parts. Let’s take this mixed number and break it down into two parts: 240 and 6/229. We can find two-thirds of each part and add the results together.
Most of us have heard of numerators and denominators, but many students do not know why we even use them. The numerator numbers the fraction. The denominator names the fraction.
Just like every food has a name: “bananas,” “doughnuts” or “grapes,” every fraction has a name: thirds, halves, or even two hundred twenty-ninths!
Now that we have some hints, let’s solve our problem!
First: find 2/3 of 240. Divide 240 into three equal parts (each part would be 80) and add together two of those parts (160).
Second: find 2/3 of 6/229. This may seem daunting, until you remember that 229 is simply the “name” of the fraction. The great news is: the name stays the same! If I divide 6 “bananas” into three equal groups, I get 2 “bananas” in each group. If I divide 6 “doughnuts” into three equal groups I get 2 “doughnuts” in each group. So if I divide 6 “two hundred twenty-ninths” into three equal groups I get 2 “two hundred twenty-ninths” (2/229) in each group. And adding together two of those equals 4/229.
Now we add the results together and get the final answer: 160 4/229.
Number sense alone can’t be used to solve all problems; however, developing number sense in a child along with an understanding of the more general mathematical methods, leads to a deeper understanding and appreciation of math.
Mathnasium’s goal is to build number sense and, with it, a deep understanding and lifelong appreciation of mathematics. Our programs help students who are at, above, and below grade level to develop the foundational and advanced skills necessary for success in the classroom.
*See attached PDF for Mental Math Challenge Worksheet
For your chance to receive a $25 discount off your initial Assessment, bring in your student’s answers to these number sense questions! All 2nd- 4th Graders may try Page 1; all 5th Graders and above may try Page 2, 3, 4 or 5. Make sure they show how they got their answer (even though it can all be done mentally) on paper. Students do not need to make a 100% in order to receive a discount!