Question

find the quotient of the mixed numeral fractions. simplify your answer when possible. (hint: you must convert the mixed numerals to improper fractions! magic c! then you will need k.c.f.) 58.) $6\frac{1}{2} div 3\frac{1}{3}$ = 59.) $4\frac{2}{3} div 1\frac{4}{8}$ = 60.) $2\frac{1}{2} div 3\frac{2}{8}$ = 61.) $8\frac{1}{4} div 3\frac{2}{3}$ =

Explanation:

Problem 58: \( 6\frac{1}{2} \div 3\frac{1}{3} \)

Step 1: Convert to improper fractions

To convert \( 6\frac{1}{2} \) to an improper fraction: Multiply the whole number (6) by the denominator (2) and add the numerator (1). So, \( 6 \times 2 + 1 = 13 \), so \( 6\frac{1}{2} = \frac{13}{2} \).

To convert \( 3\frac{1}{3} \) to an improper fraction: Multiply the whole number (3) by the denominator (3) and add the numerator (1). So, \( 3 \times 3 + 1 = 10 \), so \( 3\frac{1}{3} = \frac{10}{3} \).

Now the problem becomes \( \frac{13}{2} \div \frac{10}{3} \).

Step 2: Apply K.C.F. (Keep, Change, Flip)

Keep the first fraction, change the division to multiplication, and flip the second fraction. So, \( \frac{13}{2} \times \frac{3}{10} \).

Step 3: Multiply the fractions

Multiply the numerators: \( 13 \times 3 = 39 \).

Multiply the denominators: \( 2 \times 10 = 20 \).

So the result is \( \frac{39}{20} \), which can be written as a mixed number \( 1\frac{19}{20} \).

Step 1: Simplify and convert to improper fractions

First, simplify \( 1\frac{4}{8} \) to \( 1\frac{1}{2} \) (since \( \frac{4}{8} = \frac{1}{2} \)).

Convert \( 4\frac{2}{3} \) to an improper fraction: \( 4 \times 3 + 2 = 14 \), so \( 4\frac{2}{3} = \frac{14}{3} \).

Convert \( 1\frac{1}{2} \) to an improper fraction: \( 1 \times 2 + 1 = 3 \), so \( 1\frac{1}{2} = \frac{3}{2} \).

Now the problem becomes \( \frac{14}{3} \div \frac{3}{2} \).

Step 2: Apply K.C.F.

Keep \( \frac{14}{3} \), change division to multiplication, flip \( \frac{3}{2} \) to \( \frac{2}{3} \). So, \( \frac{14}{3} \times \frac{2}{3} \).

Step 3: Multiply the fractions

Numerators: \( 14 \times 2 = 28 \).

Denominators: \( 3 \times 3 = 9 \).

Result: \( \frac{28}{9} = 3\frac{1}{9} \).

Step 1: Simplify and convert to improper fractions

Simplify \( 3\frac{2}{8} \) to \( 3\frac{1}{4} \) (since \( \frac{2}{8} = \frac{1}{4} \)).

Convert \( 2\frac{1}{2} \) to an improper fraction: \( 2 \times 2 + 1 = 5 \), so \( 2\frac{1}{2} = \frac{5}{2} \).

Convert \( 3\frac{1}{4} \) to an improper fraction: \( 3 \times 4 + 1 = 13 \), so \( 3\frac{1}{4} = \frac{13}{4} \).

Now the problem becomes \( \frac{5}{2} \div \frac{13}{4} \).

Step 2: Apply K.C.F.

Keep \( \frac{5}{2} \), change division to multiplication, flip \( \frac{13}{4} \) to \( \frac{4}{13} \). So, \( \frac{5}{2} \times \frac{4}{13} \).

Step 3: Multiply and simplify

Numerators: \( 5 \times 4 = 20 \).

Denominators: \( 2 \times 13 = 26 \).

Simplify \( \frac{20}{26} \) by dividing numerator and denominator by 2: \( \frac{10}{13} \).

Answer:

\( 1\frac{19}{20} \) (or \( \frac{39}{20} \))

Problem 59: \( 4\frac{2}{3} \div 1\frac{4}{8} \)