Today in class, we were each assigned a question for the blog. I'll be doing question 20a, and b.
20a) Kwasi said that he ignored the fractions when he decided that -2 1/5 is smaller than -1 9/10. Explain his thinking.
Well, if you pretend the fractions aren't there and just take a look at the whole numbers they would be -2 and -1. Now, since -2 would be on the left side of -1 on a number line, it would be smaller.
If you put the fractions back, it wouldn't make a difference because the whole numbers would still be the same.
Answer: -1 > -2
b) Naomi said that she ignored the integers -1, when she decided that -1 1/4 is greater than -1 2/7. Explain her thinking.
Since both start with the integer -1, it wouldn't really help if you're trying to figure out, which is greater or which is smaller. So, you just have to focus on the fractions, 1/4 and 2/7. Now, there are many ways of figuring which is greater, but I will show you one way. I'll convert them to decimals by using long division, then compare them.
1/4 = 0.25
2/7 = 0.29
Now that we know 1/4 = 0.25 and 2/7 = 0.29, we cant tell that 2/7 is bigger, but because it's a negative, it's the opposite of that. So, that means -1/4 is bigger than -2/7. If you put the integers back, it wouldn't make a difference, since they are the same, and only the fractions matter in this case.
Answer: -1 1/4 > -1 2/7
(p.s. sorry if it's not colourful, it won't work.)