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

Algebraic Expression Substitution with Sign Changes

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

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:15 First, find the place and calculate.
00:19 Let's start by placing the first option. Ready?
00:27 Remember, a negative divided by a negative is positive!
00:36 Any number divided by itself equals one.
00:40 Insert these into our example and keep solving.
00:45 We've solved option A. Now onto option B.
00:50 Substitute values using option B's information.
00:55 Now, simplify as much as possible.
01:05 Express division as a fraction.
01:10 Again, a negative divided by a negative is positive!
01:18 Change the decimal to a mixed number.
01:28 Now, turn the mixed number into a fraction.
01:33 Instead of dividing, multiply by the reciprocal.
01:37 And that's how we solve this question!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

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

2

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}

3

Final Answer

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

Key Points to Remember

Essential concepts to master this topic
  • Expression Structure: Identify where to substitute each variable correctly
  • Sign Rules: Negative divided by negative equals positive: =+ \frac{-}{-} = +
  • Check Division: Any number divided by itself equals 1: yy=1 \frac{y}{y} = 1

Common Mistakes

Avoid these frequent errors
  • Ignoring sign changes when dividing negatives
    Don't keep negative signs when dividing two negatives = wrong answer! When both numerator and denominator are negative, they cancel out to make positive. Always apply the rule: negative ÷ negative = positive.

Practice Quiz

Test your knowledge with interactive questions

What will be the sign of the result of the next exercise?

\( (-2)\cdot(-4)= \)

FAQ

Everything you need to know about this question

What does the colon (:) mean in the expression?

+

The colon : means division, just like ÷ or /. So x:y x:y is the same as xy \frac{x}{y} .

Why does x = y make the fraction equal to 1?

+

When x = y, you get yy \frac{y}{y} . Any number divided by itself always equals 1! This is a fundamental rule: aa=1 \frac{a}{a} = 1 for any non-zero number.

How do I handle the negative signs correctly?

+

Remember the sign rules: negative ÷ negative = positive and positive ÷ negative = negative. Count your negative signs carefully - if there's an even number, the result is positive!

Why do we convert 4.4 to a fraction?

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Converting 4.4 to 425=225 4\frac{2}{5} = \frac{22}{5} makes division easier. Then 1225=1×522=522 \frac{1}{\frac{22}{5}} = 1 \times \frac{5}{22} = \frac{5}{22} .

What if I substitute the wrong variable values?

+

Always double-check which variable equals what! In part 1: x = y and z = -3. In part 2: x = z and y = -4.4. Mix these up and you'll get completely wrong answers.

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