Sure! Let's go through the problems step-by-step.
### Question 1: How many groups of [tex]$\frac{3}{4}$[/tex] are in 1?
To determine how many groups of \(\frac{3}{4}\) fit into 1, we need to perform the division:
[tex]\[ 1 \div \frac{3}{4} \][/tex]
Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of \(\frac{3}{4}\) is \(\frac{4}{3}\). So:
[tex]\[ 1 \div \frac{3}{4} = 1 \times \frac{4}{3} = \frac{4}{3} \][/tex]
The fraction \(\frac{4}{3}\) can also be expressed as a decimal:
[tex]\[ \frac{4}{3} \approx 1.33333333 \][/tex]
So, there are approximately \(1.333\) groups of \(\frac{3}{4}\) in 1.
Answer:
[tex]\[ \boxed{1.333} \][/tex] groups
### Question 2: Evaluate \( 5 \div \frac{3}{4} \)
Now we need to evaluate \(5 \div \frac{3}{4}\).
Again, dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of \(\frac{3}{4}\) is \(\frac{4}{3}\). So:
[tex]\[ 5 \div \frac{3}{4} = 5 \times \frac{4}{3} \][/tex]
To perform the multiplication, we multiply the numerator by the numerator and the denominator by the denominator:
[tex]\[ 5 \times \frac{4}{3} = \frac{5 \times 4}{1 \times 3} = \frac{20}{3} \][/tex]
To convert \(\frac{20}{3}\) into a decimal:
[tex]\[ \frac{20}{3} \approx 6.66666667 \][/tex]
So, \( 5 \div \frac{3}{4} \approx 6.666 \).
Answer:
[tex]\[ \boxed{6.666} \][/tex]
These are the answers to the given questions.
