Solve -x:y/z: Substituting Values (-3 and -4.4) in Algebraic Expression

Question

Look at the algebraic expression:

x:yz -\frac{x:y}{z}

Substitute and calculate:

  1. x=y,z=3 x=y,z=-3

  2. x=z,y=4.4 x=z,y=-4.4

Video Solution

Solution Steps

00:00 Place and Calculate
00:04 Let's start by placing the first option
00:12 Negative divided by negative is always positive
00:21 Any number divided by itself always equals 1
00:25 Let's substitute in our exercise and continue solving
00:30 This is the solution for option A, now let's calculate option B
00:35 Let's substitute according to option B's data
00:40 Let's reduce what we can
00:50 Let's write division as a fraction
00:55 Negative divided by negative is always positive
01:03 Let's convert from decimal to mixed number
01:13 Let's convert from mixed number to fraction
01:18 Instead of dividing, multiply by the reciprocal
01:22 And this is the solution to the question

Step-by-Step Solution

Let's start with the first option.

Let's substitute the data into the expression:

y:y3= -\frac{y:y}{-3}=

Note that we are dividing between two negative numbers, therefore the result must be a positive number:

=+ \frac{-}{-}=+

+y:y3= +\frac{y:y}{3}=

Let's remember the rule that any number divided by itself equals 1, therefore:

yy=1 \frac{y}{y}=1

Now we have:

13 \frac{1}{3}

Let's continue with the second option.

Let's substitute the data into the expression:

z:4.4z= -\frac{z:-4.4}{z}=

Let's now reduce z z in both numerator and denominator of the fraction to get:

(1:4.4)= -(1:-4.4)=

Let's next write the exercise as a simple fraction:

14.4= -\frac{1}{-4.4}=

Note that we are dividing between two negative numbers, therefore the result must be a positive number:

=+ \frac{-}{-}=+

Let's convert 4.4 into a simple fraction:

+1425= +\frac{1}{4\frac{2}{5}}=

Let's write the denominator fraction as a complex fraction:

+1425=1225= +\frac{1}{4\frac{2}{5}}=\frac{1}{\frac{22}{5}}=

Let's convert the fraction to a multiplication exercise remembering to switch between numerator and denominator:

1225=1×522=522 \frac{1}{\frac{22}{5}}=1\times\frac{5}{22}=\frac{5}{22}

Therefore the final answer is:

1=+13,2=+522 1=+\frac{1}{3},2=+\frac{5}{22}

Answer

1=+13,2=+522 1=+\frac{1}{3},2=+\frac{5}{22}