Answer :
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The product 1/8 times 4/3 is greater than 1/8.
Step-by-step explanation:
The given information is Roxy multiplying two numbers [tex]\frac{1}{8}[/tex] and [tex]\frac{4}{3}[/tex].
We have to find that their product is less then or greater than [tex]\frac{1}{8}[/tex].
Let us find the product first.
=[tex]\frac{1}{8}[/tex]×[tex]\frac{4}{3}[/tex].
=[tex]\frac{1}{6}[/tex].
Let us now compare [tex]\frac{1}{6}[/tex] and [tex]\frac{1}{8}[/tex].
We can compare a fraction when the denominators of the fractions are same. Else we can use LCM to make the denominator same.
Or else we can turn the fraction into decimal to compare.
LCM method:
1) Find the least common denominator(LCM) for the denominators.
⇒ LCM of 6 and 8 is 24.
2) Next let us change the fractions for equal denominators.
For the 1st fraction,
[tex]\frac{1}{6}=\frac{1 \times 4}{6 \times 4}=\frac{4}{24}[/tex].
For the 2nd fraction,
[tex]\frac{1}{8}=\frac{1 \times 3}{8 \times 3}=\frac{3}{24}[/tex].
Now compare the two new numbers.
[tex]\frac{4}{24}>\frac{3}{24}[/tex].
Since the denominators are now the same, the fraction with the bigger numerator is the greater fraction.
Thus [tex]\frac{4}{24}[/tex] is the greater number which means [tex]\frac{1}{6}[/tex] .
i.e. [tex]\frac{1}{6}[/tex] is greater than [tex]\frac{1}{8}[/tex].
Decimal Method:
[tex]\frac{1}{6}[/tex] = 0.167.
[tex]\frac{1}{8}[/tex]= 0.125.
By comparing 0.167 and 0.125,
0.167 > 0.125.
0.167 is greater than 0.125.
Thus [tex]\frac{1}{6}[/tex] is greater than [tex]\frac{1}{8}[/tex].