9. Explain the process of cross-multiplication.
http://www.aaamath.com/rat-prop-crossx.htm
I object!!!! I would never teach cross-multiplication. While it appears to work often, and in the above link as an example, here is where it gets students into trouble...
(x+3)/2=(5/7)+3/1
So many students apply "cross multiplication and get results such as this.
a. x*7=5*2+3 or
b. 7*1(x+3)=13
or many other variants. If you forget about "cross-multiplying", you will never have this issue.
It is so much easier to just take operations wherein you multiply/divide both sides of the equation by the same factors.
example: 7*2(x+3)/2=7*2((5/7)+3/1)
or 7(x+3)=10+14*3/1
which is quite different from the earlier results.
Cross-multiplication is a useful technique for solving equations or comparing ratios. It involves multiplying the numerator of one fraction by the denominator of the other fraction, and then equating the products obtained. Let's break it down into steps:
Step 1: Identify the two fractions you want to compare or equate.
Step 2: Write the fractions in equation form, with an equal sign separating them. For example, if the fractions are A/B and C/D, the equation would be A/B = C/D.
Step 3: Cross-multiply the fractions. Multiply the numerator (A) of the first fraction by the denominator (D) of the second fraction, and vice versa. This gives you A * D and B * C.
Step 4: Set up an equation using the products obtained in step 3. For example, if we have A * D = B * C, we can rewrite the equation as Ad = Bc.
Step 5: Solve the equation for the unknown variable. This may involve simplifying or rearranging the equation, depending on the given problem.
The process of cross-multiplication is especially useful when dealing with proportionality. By cross-multiplying, you can determine if two ratios are equal or find the missing value in a proportion.