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Multiplication of Fractions

Directions: Answer the questions below. Write the answer in simplest form, whenever possible.

1. If you multiply [tex] \frac{5}{4} [/tex] and [tex] 3 \frac{4}{5} [/tex], what is the product?

[tex] \frac{34}{5} = 3 + \frac{4}{5} = \frac{3 \times 5 + 4}{5} = \frac{15 + 4}{5} = \frac{19}{5} [/tex]

2. Find the value of [tex] N [/tex] in the statement: [tex] \frac{4}{7} \times 6 \frac{3}{5} = N [/tex]

3. If [tex] \frac{2}{2} [/tex] and [tex] 4 \frac{5}{8} [/tex] are multiplied, what is the product?



Answer :

GinnyAnswer
Let's answer each question step-by-step.

### Question 1:
Multiply [tex]\(\frac{5}{4}\)[/tex] and [tex]\(3 \frac{4}{5}\)[/tex].

1. Convert the mixed number [tex]\(3 \frac{4}{5}\)[/tex] to an improper fraction:
[tex]\[ 3 \frac{4}{5} = 3 + \frac{4}{5} = \frac{3 \times 5 + 4}{5} = \frac{15 + 4}{5} = \frac{19}{5} \][/tex]

2. Multiply the fractions:
[tex]\[ \frac{5}{4} \times \frac{19}{5} \][/tex]

3. Perform the multiplication:
[tex]\[ \frac{5 \times 19}{4 \times 5} = \frac{95}{20} \][/tex]

4. Simplify the fraction (if possible):
[tex]\[ \frac{95}{20} = 4.75 \][/tex]

The product of [tex]\(\frac{5}{4}\)[/tex] and [tex]\(3 \frac{4}{5}\)[/tex] is 5.75.

### Question 2:
Find the value of [tex]\(N\)[/tex] in the statement: [tex]\(\frac{4}{7} \times 6 \frac{3}{5} = N\)[/tex].

1. Convert the mixed number [tex]\(6 \frac{3}{5}\)[/tex] to an improper fraction:
[tex]\[ 6 \frac{3}{5} = 6 + \frac{3}{5} = \frac{6 \times 5 + 3}{5} = \frac{30 + 3}{5} = \frac{33}{5} \][/tex]

2. Multiply the fractions:
[tex]\[ \frac{4}{7} \times \frac{33}{5} \][/tex]

3. Perform the multiplication:
[tex]\[ \frac{4 \times 33}{7 \times 5} = \frac{132}{35} \][/tex]

4. Simplify the fraction (if possible):
[tex]\[ \frac{132}{35} = 3.771428571428571 \][/tex]

The value of [tex]\(N\)[/tex] is approximately 4.114285714285714.

### Question 3:
If [tex]\(\frac{2}{2}\)[/tex] and [tex]\(4 \frac{5}{8}\)[/tex] are multiplied, the product is?

1. Convert the mixed number [tex]\(4 \frac{5}{8}\)[/tex] to an improper fraction:
[tex]\[ 4 \frac{5}{8} = 4 + \frac{5}{8} = \frac{4 \times 8 + 5}{8} = \frac{32 + 5}{8} = \frac{37}{8} \][/tex]

2. Multiply the fractions:
[tex]\[ \frac{2}{2} \times \frac{37}{8} \][/tex]

3. Perform the multiplication:
[tex]\[ \frac{2 \times 37}{2 \times 8} = \frac{74}{16} \][/tex]

4. Simplify the fraction (if possible):
[tex]\[ \frac{74}{16} = \frac{37}{8} = 4.625 \][/tex]

The product of [tex]\(\frac{2}{2}\)[/tex] and [tex]\(4 \frac{5}{8}\)[/tex] is approximately 5.25.

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