Answer :
Sure! Let's solve each of these multiplication problems step by step.
### Problem 1: [tex]\( 6 \times \frac{5}{12} \)[/tex]
To multiply a whole number by a fraction, multiply the numerator (top part) of the fraction by the whole number and keep the denominator (bottom part) unchanged:
[tex]\[ 6 \times \frac{5}{12} = \frac{6 \times 5}{12} = \frac{30}{12} \][/tex]
Now, simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (which is 6 in this case):
[tex]\[ \frac{30}{12} = \frac{30 \div 6}{12 \div 6} = \frac{5}{2} \][/tex]
[tex]\[ \frac{5}{2} = 2.5 \][/tex]
So, the result is [tex]\( 2.5 \)[/tex].
### Problem 2: [tex]\( \frac{7}{8} \times 24 \)[/tex]
Multiply the fraction by the whole number. Treat the whole number as a fraction (in this case, 24 is equivalent to [tex]\( \frac{24}{1} \)[/tex]):
[tex]\[ \frac{7}{8} \times 24 = \frac{7}{8} \times \frac{24}{1} = \frac{7 \times 24}{8 \times 1} = \frac{168}{8} \][/tex]
Now simplify the fraction:
[tex]\[ \frac{168}{8} = 21 \][/tex]
So, the result is [tex]\( 21.0 \)[/tex].
### Problem 3: [tex]\( \frac{4}{9} \times 27 \times \frac{1}{2} \)[/tex]
First, multiply the fractions step by step. Start with [tex]\( \frac{4}{9} \times 27 \)[/tex], treating 27 as [tex]\( \frac{27}{1} \)[/tex]:
[tex]\[ \frac{4}{9} \times 27 = \frac{4}{9} \times \frac{27}{1} = \frac{4 \times 27}{9 \times 1} = \frac{108}{9} \][/tex]
Now simplify:
[tex]\[ \frac{108}{9} = 12 \][/tex]
Now, multiply the result by [tex]\( \frac{1}{2} \)[/tex]:
[tex]\[ 12 \times \frac{1}{2} = \frac{12 \times 1}{2} = \frac{12}{2} = 6 \][/tex]
So, the result is [tex]\( 6.0 \)[/tex].
### Problem 4: [tex]\( 8 \frac{2}{5} \times 18 \frac{1}{3} \)[/tex]
First, convert the mixed numbers to improper fractions:
[tex]\[ 8 \frac{2}{5} = 8 + \frac{2}{5} = \frac{40}{5} + \frac{2}{5} = \frac{42}{5} \][/tex]
[tex]\[ 18 \frac{1}{3} = 18 + \frac{1}{3} = \frac{54}{3} + \frac{1}{3} = \frac{55}{3} \][/tex]
Now multiply the improper fractions:
[tex]\[ \frac{42}{5} \times \frac{55}{3} = \frac{42 \times 55}{5 \times 3} = \frac{2310}{15} \][/tex]
Simplify the fraction:
[tex]\[ \frac{2310}{15} = 154 \][/tex]
So, the result is [tex]\( 154.0 \)[/tex].
### Problem 5: [tex]\( 6 \times \frac{2}{3} \times 2 \frac{1}{2} \)[/tex]
First, convert the mixed number to an improper fraction:
[tex]\[ 2 \frac{1}{2} = 2 + \frac{1}{2} = \frac{4}{2} + \frac{1}{2} = \frac{5}{2} \][/tex]
Now, multiply step by step:
[tex]\[ 6 \times \frac{2}{3} = \frac{6 \times 2}{3} = \frac{12}{3} = 4 \][/tex]
Now, multiply the result by [tex]\( \frac{5}{2} \)[/tex]:
[tex]\[ 4 \times \frac{5}{2} = \frac{4 \times 5}{2} = \frac{20}{2} = 10 \][/tex]
So, the result is [tex]\( 10.0 \)[/tex].
In summary, the answers are:
1. [tex]\( 2.5 \)[/tex]
2. [tex]\( 21.0 \)[/tex]
3. [tex]\( 6.0 \)[/tex]
4. [tex]\( 154.0 \)[/tex]
5. [tex]\( 10.0 \)[/tex]
### Problem 1: [tex]\( 6 \times \frac{5}{12} \)[/tex]
To multiply a whole number by a fraction, multiply the numerator (top part) of the fraction by the whole number and keep the denominator (bottom part) unchanged:
[tex]\[ 6 \times \frac{5}{12} = \frac{6 \times 5}{12} = \frac{30}{12} \][/tex]
Now, simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (which is 6 in this case):
[tex]\[ \frac{30}{12} = \frac{30 \div 6}{12 \div 6} = \frac{5}{2} \][/tex]
[tex]\[ \frac{5}{2} = 2.5 \][/tex]
So, the result is [tex]\( 2.5 \)[/tex].
### Problem 2: [tex]\( \frac{7}{8} \times 24 \)[/tex]
Multiply the fraction by the whole number. Treat the whole number as a fraction (in this case, 24 is equivalent to [tex]\( \frac{24}{1} \)[/tex]):
[tex]\[ \frac{7}{8} \times 24 = \frac{7}{8} \times \frac{24}{1} = \frac{7 \times 24}{8 \times 1} = \frac{168}{8} \][/tex]
Now simplify the fraction:
[tex]\[ \frac{168}{8} = 21 \][/tex]
So, the result is [tex]\( 21.0 \)[/tex].
### Problem 3: [tex]\( \frac{4}{9} \times 27 \times \frac{1}{2} \)[/tex]
First, multiply the fractions step by step. Start with [tex]\( \frac{4}{9} \times 27 \)[/tex], treating 27 as [tex]\( \frac{27}{1} \)[/tex]:
[tex]\[ \frac{4}{9} \times 27 = \frac{4}{9} \times \frac{27}{1} = \frac{4 \times 27}{9 \times 1} = \frac{108}{9} \][/tex]
Now simplify:
[tex]\[ \frac{108}{9} = 12 \][/tex]
Now, multiply the result by [tex]\( \frac{1}{2} \)[/tex]:
[tex]\[ 12 \times \frac{1}{2} = \frac{12 \times 1}{2} = \frac{12}{2} = 6 \][/tex]
So, the result is [tex]\( 6.0 \)[/tex].
### Problem 4: [tex]\( 8 \frac{2}{5} \times 18 \frac{1}{3} \)[/tex]
First, convert the mixed numbers to improper fractions:
[tex]\[ 8 \frac{2}{5} = 8 + \frac{2}{5} = \frac{40}{5} + \frac{2}{5} = \frac{42}{5} \][/tex]
[tex]\[ 18 \frac{1}{3} = 18 + \frac{1}{3} = \frac{54}{3} + \frac{1}{3} = \frac{55}{3} \][/tex]
Now multiply the improper fractions:
[tex]\[ \frac{42}{5} \times \frac{55}{3} = \frac{42 \times 55}{5 \times 3} = \frac{2310}{15} \][/tex]
Simplify the fraction:
[tex]\[ \frac{2310}{15} = 154 \][/tex]
So, the result is [tex]\( 154.0 \)[/tex].
### Problem 5: [tex]\( 6 \times \frac{2}{3} \times 2 \frac{1}{2} \)[/tex]
First, convert the mixed number to an improper fraction:
[tex]\[ 2 \frac{1}{2} = 2 + \frac{1}{2} = \frac{4}{2} + \frac{1}{2} = \frac{5}{2} \][/tex]
Now, multiply step by step:
[tex]\[ 6 \times \frac{2}{3} = \frac{6 \times 2}{3} = \frac{12}{3} = 4 \][/tex]
Now, multiply the result by [tex]\( \frac{5}{2} \)[/tex]:
[tex]\[ 4 \times \frac{5}{2} = \frac{4 \times 5}{2} = \frac{20}{2} = 10 \][/tex]
So, the result is [tex]\( 10.0 \)[/tex].
In summary, the answers are:
1. [tex]\( 2.5 \)[/tex]
2. [tex]\( 21.0 \)[/tex]
3. [tex]\( 6.0 \)[/tex]
4. [tex]\( 154.0 \)[/tex]
5. [tex]\( 10.0 \)[/tex]
