Today in class we reviewed the 3 techniques we use in order to solve fraction problems for ex. 4/5 + 5/6. The 3 techniques were clocks, money, and double number lines.
We first found all the denominators that could go into 60 since there are 60 minutes in a hour. All the denominators we found were:
60, 2, 3, 4, 5, 6, 10, 12, 15, 20, and 3
We then did one fraction question together only using clocks as our strategy.
3/5 + 2/12 =23/30
We first divded the denominators into 60 to get how much minutes there are in 5ths and 12ths. We then multiplied the answer which was 20 minutes(5ths) and 5 minutes(12ths) to there numerators. This made it 36 minutes(3/5) and 10 minutes(2/12). It look a little bit like this
Mr Harbeck then gave us 3 more questions to work on only using clocks, and they were
2/3 + 1/10=
7/10 + 1/5=
We first found all the denominators that goes into 100 because there are 100 cents in a dollar. The denominators are
100, 2, 4, 5, 10, 25, and 50.
We then did another question as a class only using money as our strategy and the question was
2/5 + 7/10=1 1/10
We first took the denominators and divided them into 100 to get 20 cents(2/5) and 10 cents(7/10). Next we took 20 cents then timesed it by it's numerator 2 to get 40 cents. We also did the same thing to 10 cents so we got 70 cents. We then got the 40 cents (2/5) and 70 cents (7/10) then added them together. When we added them together we got the sum of 1.10 which turned into a mixed fraction would be 1 10/100 then simplified would be 1 1/10. It would have looked like this
Mr Harbeck gave us 3 more questions to only solve them using money and they are
6/10 + 11/25=
2/5 + 3/4=
13/50 + 11/20=
Double Number lines
We first found out all the fractions that you could use this strategy and they are called as "Ugly Fractions".
We worked on a problem as a class only using double number lines to help us and the question was
3/8 x 4/9=
We first tried to find the lowest common denominator so we multiplied 8 and 9 to get 72 so we then knew that the fraction should be out of 72. We then multiplied 3 to 9 because what you do to the bottom number of a fraction you have to do the same to the top and we got 27/72 for the first fraction. To get the second fraction we needed to multiply 4 to 8 because what you do to the bottom number of a fraction you have to do the same to the top then we got 32 and we already know it will be out of 72( 32/72). Now all we neede to do was to add them to gether and since they both have the same denominator all you have to do is add the numerator and we got 59/72. Here is how we did it on a double number line