Jayvee's Textbook Question

2.1 #30

How to get equivalent fractions:
Step 1: Find which part of the fractions are both given (Both denominators/numerators)
Step 2: Find how one number got to the other number (You can either divide/multiply)
Step 3: If you found what was done, do the same thing to the fraction part which is missing.

a) 4/-5 = x/-10
In this case, the other numerator is missing. We have to do the steps on the denominator.
-5 = -10, -5 is multiplied by 2 to get -10
Now we have to do the same thing to the numerator.
We have to multiply 4 by 2 to get the missing numerator.
4x2 = 8
x = 8

b) x/3 = 6/-9
1 Numerator is missing, look at the denominator.
3 = -9, you can also use division
3 = -9, -9 is divided by -3 to get 3 (sign rules)
Do the same thing to the numerator
Divide 6 by -3 to get -2
x = -2

c) 5/x = -20/12
1 Denominator is missing, look at the numerator
5 = -20, let's use division
5 = -20, -20 is divided by -4 to get 5 (remember sign rules)
Do the same thing to the denominator
Divide -12 by -4 to get 3
x = 3

d) -6/-5 = 30/x
1 denominator is missing, look at the numerator
-6 = 30, let's use multiplication this time
-6 = 30, -6 is multiplied by -5 to get 30
Do the same thing to the denominator
Multiply -5 by -5 to get 25
x = 25

Chelsea's Textbook Question

Here is the question that we're going to solve from 2.1, Comparing and Ordering Rational Numbers:

26. Which number in each pair is greater? Explain each answer.

a) 0.4 and 0.44

b) 0. 333... and 0.33

c) -0.7 and -0.77

d) -0.66 and 0.66...

So, in order to figure out which number is greater, we have to put the decimal numbers onto a number line first. Then, you can convert it into a fraction (which you should still remember how to do so):

a)

0.4 = 4/10

0.44 = 44/100

0.44 is greater than 0.4

b)

0.333... = 1/3

0.33 = 33/100

0.333... is greater than 0.33

c)

-0.7 = -7/10

-0.77 = -77/100

-0.7 is the greater number than -0.77.

d)

-0.66 = -66/100

0.66... = 2/3

-0.66 is greater than 0.66...

If I have forgotten anything, please tell me!