Answer :
Sure, let's explore whether it's valid to compare [tex]\(\frac{30}{70}\)[/tex] and [tex]\(\frac{20}{50}\)[/tex] by "cancelling" the zeros and comparing [tex]\(\frac{3}{7}\)[/tex] and [tex]\(\frac{2}{5}\)[/tex] instead.
Step 1: Simplify the fractions
- Start by simplifying [tex]\(\frac{30}{70}\)[/tex]:
Both 30 and 70 can be divided by 10 (the common factor of 10). So, cancel the zeros:
[tex]\[
\frac{30}{70} = \frac{3}{7}
\][/tex]
- Next, simplify [tex]\(\frac{20}{50}\)[/tex]:
Similarly, divide 20 and 50 by their common factor of 10:
[tex]\[
\frac{20}{50} = \frac{2}{5}
\][/tex]
Step 2: Compare the fractions
Now that we have simplified both fractions, let's compare the simplified versions:
- [tex]\(\frac{3}{7}\)[/tex] and [tex]\(\frac{2}{5}\)[/tex] are the results of simplifying the original fractions.
Verification of Validity
To determine if the simplification was correctly done by "cancelling" the zeros, check if the simplified fractions are equivalent to the original fractions:
- The fraction [tex]\(\frac{30}{70} = 0.42857142857142855\)[/tex] when calculated in decimal form.
- The simplified fraction [tex]\(\frac{3}{7} = 0.42857142857142855\)[/tex] in decimal form as well.
- Similarly, [tex]\(\frac{20}{50} = 0.4\)[/tex].
- And, [tex]\(\frac{2}{5} = 0.4\)[/tex].
Both simplified fractions match their respective original fractions in decimal form.
Conclusion
Cancelling the zeros to simplify the fractions [tex]\(\frac{30}{70}\)[/tex] to [tex]\(\frac{3}{7}\)[/tex] and [tex]\(\frac{20}{50}\)[/tex] to [tex]\(\frac{2}{5}\)[/tex] is valid because it does not change the values of the fractions. The simplification reflects the true relationship between the fractions, making it a correct and efficient method to compare these fractions.
Step 1: Simplify the fractions
- Start by simplifying [tex]\(\frac{30}{70}\)[/tex]:
Both 30 and 70 can be divided by 10 (the common factor of 10). So, cancel the zeros:
[tex]\[
\frac{30}{70} = \frac{3}{7}
\][/tex]
- Next, simplify [tex]\(\frac{20}{50}\)[/tex]:
Similarly, divide 20 and 50 by their common factor of 10:
[tex]\[
\frac{20}{50} = \frac{2}{5}
\][/tex]
Step 2: Compare the fractions
Now that we have simplified both fractions, let's compare the simplified versions:
- [tex]\(\frac{3}{7}\)[/tex] and [tex]\(\frac{2}{5}\)[/tex] are the results of simplifying the original fractions.
Verification of Validity
To determine if the simplification was correctly done by "cancelling" the zeros, check if the simplified fractions are equivalent to the original fractions:
- The fraction [tex]\(\frac{30}{70} = 0.42857142857142855\)[/tex] when calculated in decimal form.
- The simplified fraction [tex]\(\frac{3}{7} = 0.42857142857142855\)[/tex] in decimal form as well.
- Similarly, [tex]\(\frac{20}{50} = 0.4\)[/tex].
- And, [tex]\(\frac{2}{5} = 0.4\)[/tex].
Both simplified fractions match their respective original fractions in decimal form.
Conclusion
Cancelling the zeros to simplify the fractions [tex]\(\frac{30}{70}\)[/tex] to [tex]\(\frac{3}{7}\)[/tex] and [tex]\(\frac{20}{50}\)[/tex] to [tex]\(\frac{2}{5}\)[/tex] is valid because it does not change the values of the fractions. The simplification reflects the true relationship between the fractions, making it a correct and efficient method to compare these fractions.
