QuestionFind the simplest form of the quotient: $\frac{12}{7} \div 3$ .

Studdy Solution

STEP 1

Assumptions1. We are asked to find the quotient of the given fractions and numbers in simplest form. . The given numbers and fractions are $\frac{12}{7}$ , $3$ , $\frac{7}{36}$ , $\frac{4}{7}$ , $1 \frac{3}{4}$ , and $5 \frac{1}{7}$ .

STEP 2

First, we need to convert all the mixed numbers into improper fractions.For $1 \frac{}{4}$ , we multiply the whole number by the denominator of the fraction and add the numerator. This gives us the new numerator. The denominator remains the same.
$1 \frac{}{4} = \frac{1 \times4 +}{4}$ For $5 \frac{1}{7}$ , we do the same.
$5 \frac{1}{7} = \frac{5 \times7 +1}{7}$

STEP 3

Now, calculate the new numerators for the improper fractions.
$1 \frac{3}{} = \frac{1 \times +3}{} = \frac{7}{}$ $5 \frac{1}{7} = \frac{5 \times7 +1}{7} = \frac{36}{7}$

STEP 4

Now, we have all the numbers and fractions as follows $\frac{12}{7}$ , $3$ , $\frac{7}{36}$ , $\frac{4}{7}$ , $\frac{7}{4}$ , and $\frac{36}{7}$ .
We can perform the division operation on these numbers and fractions.Remember that dividing by a fraction is the same as multiplying by its reciprocal.So, we have $\frac{12}{7} \div3 \div \frac{7}{36} \div \frac{4}{7} \div \frac{7}{4} \div \frac{36}{7}$ This is equivalent to $\frac{12}{7} \times \frac{1}{3} \times \frac{36}{7} \times \frac{7}{4} \times \frac{4}{7} \times \frac{7}{36}$

STEP 5

Now, we can simplify the expression by cancelling out the common terms in the numerator and denominator.
$\frac{12}{7} \times \frac{1}{3} \times \frac{36}{7} \times \frac{7}{4} \times \frac{4}{7} \times \frac{7}{36} =1$ So, the quotient of the given numbers and fractions in simplest form is $1$ .

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