Question

multiplying mixed numbers
change mixed numbers into improper fractions then multiply as before.
ex. 1:
$2\frac{1}{2} \times 3\frac{1}{3} = \frac{5}{2} \times \frac{10}{3} = \frac{25}{3} = 8\frac{1}{3}$
change the mixed numbers to improper fractions by:
$2\frac{1}{2} = \frac{2 \times 2 + 1}{2} = \frac{4 + 1}{2} = \frac{5}{2}$

1. multiplying the bottom number by the whole number
2. add the top number
3. keep the bottom number.

cancel top and bottom. multiply. improper fractions simplify by dividing.
ex.2:
$4\frac{1}{4} \times 6 = \frac{17}{4} \times \frac{6}{1} = \frac{51}{2} = 25\frac{1}{2}$ change the mixed number into an improper fraction. change the whole number into an improper fraction. cancel. multiply. simplify to get the quotient.
exercise 2 (answers on page 40)
multiply these fractions. cancel and simplify if necessary.

1. $1\frac{1}{2} \times 1\frac{3}{4} =$
2. $2\frac{1}{3} \times 5\frac{2}{5} =$
3. $4\frac{1}{3} \times 1\frac{7}{8} =$
4. $\frac{1}{2} \times 2\frac{1}{8} =$
5. $3\frac{1}{4} \times \frac{7}{8} =$
6. $5\frac{5}{7} \times \frac{14}{15} =$
7. $7 \times 1\frac{3}{8} =$
8. $2\frac{4}{5} \times 5 =$
9. $6\frac{2}{3} \times 9 =$
10. $1\frac{8}{9} \times 1\frac{5}{6} =$
11. $7\frac{1}{7} \times 8\frac{2}{5} =$
12. $1\frac{1}{7} \times 9\frac{1}{3} =$

created by mlc

Explanation:

Let's solve each problem step by step. We'll take problem 2 as an example: \( 2\frac{1}{3} \times 5\frac{2}{5} \)

Step 1: Convert mixed numbers to improper fractions

For \( 2\frac{1}{3} \):
Multiply the whole number (2) by the denominator (3), then add the numerator (1). So, \( 2 \times 3 + 1 = 7 \). The improper fraction is \( \frac{7}{3} \).

For \( 5\frac{2}{5} \):
Multiply the whole number (5) by the denominator (5), then add the numerator (2). So, \( 5 \times 5 + 2 = 27 \). The improper fraction is \( \frac{27}{5} \).

Step 2: Multiply the improper fractions

Now, multiply \( \frac{7}{3} \times \frac{27}{5} \). First, we can simplify before multiplying. The 27 and 3 have a common factor of 3. Divide 27 by 3 to get 9, and divide 3 by 3 to get 1. So now we have \( \frac{7}{1} \times \frac{9}{5} \).

Multiply the numerators: \( 7 \times 9 = 63 \)
Multiply the denominators: \( 1 \times 5 = 5 \)

So the result is \( \frac{63}{5} \), which can be converted back to a mixed number: \( 12\frac{3}{5} \)

Step 1: Convert mixed numbers to improper fractions

For \( 4\frac{1}{3} \):
\( 4 \times 3 + 1 = 13 \), so the improper fraction is \( \frac{13}{3} \).

For \( 1\frac{7}{8} \):
\( 1 \times 8 + 7 = 15 \), so the improper fraction is \( \frac{15}{8} \).

Step 2: Multiply the improper fractions

\( \frac{13}{3} \times \frac{15}{8} \). Simplify first: 15 and 3 have a common factor of 3. Divide 15 by 3 to get 5, divide 3 by 3 to get 1. Now we have \( \frac{13}{1} \times \frac{5}{8} \).

Multiply numerators: \( 13 \times 5 = 65 \)
Multiply denominators: \( 1 \times 8 = 8 \)

The result is \( \frac{65}{8} \), which is \( 8\frac{1}{8} \) as a mixed number.

Step 1: Convert the mixed number to an improper fraction

For \( 2\frac{1}{8} \):
\( 2 \times 8 + 1 = 17 \), so the improper fraction is \( \frac{17}{8} \).

Step 2: Multiply the fractions

Now, multiply \( \frac{1}{2} \times \frac{17}{8} \).

Multiply numerators: \( 1 \times 17 = 17 \)
Multiply denominators: \( 2 \times 8 = 16 \)

The result is \( \frac{17}{16} \), which is \( 1\frac{1}{16} \) as a mixed number.

Answer:

\( 12\frac{3}{5} \)

Let's solve problem 3: \( 4\frac{1}{3} \times 1\frac{7}{8} \)