Question Complete the multiplication pattern with fractions to find the missing values.
$\frac{1}{2} \times \frac{1}{5} = \frac{1}{10}$ $\frac{1}{3} \times \frac{1}{5} = \frac{1}{15}$ $\frac{1}{4} \times \frac{1}{5} = \frac{1}{20}$ $\frac{1}{5} \times \frac{1}{5} = \frac{1}{25}$
Describe the relationship between the factors and products.

Studdy Solution

STEP 1

Assumptions
1. The pattern involves multiplying a fraction by $\frac{1}{5}$ .
2. The products are fractions in their simplest form.
3. We are to continue the pattern by filling in the missing values in the chart.

STEP 2

Observe the pattern in the multiplication of the fractions.
The first row shows that $1 \times \frac{1}{5} = \frac{1}{5}$ .

STEP 3

Calculate the product for the second row.
$\frac{1}{2} \times \frac{1}{5} = \frac{1}{2} \times \frac{1}{5} = \frac{1 \times 1}{2 \times 5} = \frac{1}{10}$

STEP 4

Calculate the product for the third row.
$\frac{1}{3} \times \frac{1}{5} = \frac{1}{3} \times \frac{1}{5} = \frac{1 \times 1}{3 \times 5} = \frac{1}{15}$

STEP 5

Identify the pattern in the denominators of the products.
The denominators are multiples of 5: $5, 10, 15, \ldots$

STEP 6

Use the pattern to fill in the missing numerator in the fourth row.
Given that $\square \times \frac{1}{5} = \frac{1}{20}$ , we need to find the numerator that, when multiplied by $\frac{1}{5}$ , gives $\frac{1}{20}$ .

STEP 7

Solve for the missing numerator in the fourth row.
$\square \times \frac{1}{5} = \frac{1}{20}$
$\square = \frac{1}{20} \div \frac{1}{5}$
$\square = \frac{1}{20} \times \frac{5}{1}$
$\square = \frac{5}{20}$
$\square = \frac{1}{4}$

STEP 8

Use the pattern to fill in the missing numerator in the fifth row.
Given that $\square \times \frac{1}{5} = \frac{1}{25}$ , we need to find the numerator that, when multiplied by $\frac{1}{5}$ , gives $\frac{1}{25}$ .

STEP 9

Solve for the missing numerator in the fifth row.
$\square \times \frac{1}{5} = \frac{1}{25}$
$\square = \frac{1}{25} \div \frac{1}{5}$
$\square = \frac{1}{25} \times \frac{5}{1}$
$\square = \frac{5}{25}$
$\square = \frac{1}{5}$

STEP 10

Complete the pattern in the chart with the found values.
$\begin{array}{l} 1 \times \frac{1}{5}=\frac{1}{5} \\ \frac{1}{2} \times \frac{1}{5}=\frac{1}{10} \\ \frac{1}{3} \times \frac{1}{5}=\frac{1}{15} \\ \frac{1}{4} \times \frac{1}{5}=\frac{1}{20} \\ \frac{1}{5} \times \frac{1}{5}=\frac{1}{25} \end{array}$

STEP 11

Describe the pattern observed.
The factors on the left side of the multiplication are consecutive fractions with a numerator of 1 and increasing denominators starting from 1. The products are fractions with denominators that are multiples of 5, increasing by 5 each time.

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Studdy Solution

STEP 1

Assumptions
1. The pattern involves multiplying a fraction by $\frac{1}{5}$ .
2. The products are fractions in their simplest form.
3. We are to continue the pattern by filling in the missing values in the chart.

STEP 2

Observe the pattern in the multiplication of the fractions.
The first row shows that $1 \times \frac{1}{5} = \frac{1}{5}$ .

STEP 3

Calculate the product for the second row.
$\frac{1}{2} \times \frac{1}{5} = \frac{1}{2} \times \frac{1}{5} = \frac{1 \times 1}{2 \times 5} = \frac{1}{10}$

STEP 4

Calculate the product for the third row.
$\frac{1}{3} \times \frac{1}{5} = \frac{1}{3} \times \frac{1}{5} = \frac{1 \times 1}{3 \times 5} = \frac{1}{15}$

STEP 5

Identify the pattern in the denominators of the products.
The denominators are multiples of 5: $5, 10, 15, \ldots$

STEP 6

Use the pattern to fill in the missing numerator in the fourth row.
Given that $\square \times \frac{1}{5} = \frac{1}{20}$ , we need to find the numerator that, when multiplied by $\frac{1}{5}$ , gives $\frac{1}{20}$ .

STEP 7

Solve for the missing numerator in the fourth row.
$\square \times \frac{1}{5} = \frac{1}{20}$
$\square = \frac{1}{20} \div \frac{1}{5}$
$\square = \frac{1}{20} \times \frac{5}{1}$
$\square = \frac{5}{20}$
$\square = \frac{1}{4}$

STEP 8

Use the pattern to fill in the missing numerator in the fifth row.
Given that $\square \times \frac{1}{5} = \frac{1}{25}$ , we need to find the numerator that, when multiplied by $\frac{1}{5}$ , gives $\frac{1}{25}$ .

STEP 9

Solve for the missing numerator in the fifth row.
$\square \times \frac{1}{5} = \frac{1}{25}$
$\square = \frac{1}{25} \div \frac{1}{5}$
$\square = \frac{1}{25} \times \frac{5}{1}$
$\square = \frac{5}{25}$
$\square = \frac{1}{5}$

STEP 10

STEP 11

Describe the pattern observed.
The factors on the left side of the multiplication are consecutive fractions with a numerator of 1 and increasing denominators starting from 1. The products are fractions with denominators that are multiples of 5, increasing by 5 each time.

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Studdy Solution

STEP 1

Assumptions1. The pattern involves multiplying a fraction by 15\frac{1}{5}51​.2. The products are fractions in their simplest form.3. We are to continue the pattern by filling in the missing values in the chart.

STEP 2

Observe the pattern in the multiplication of the fractions.The first row shows that 1×15=151 \times \frac{1}{5} = \frac{1}{5}1×51​=51​.

STEP 3

Calculate the product for the second row.12×15=12×15=1×12×5=110\frac{1}{2} \times \frac{1}{5} = \frac{1}{2} \times \frac{1}{5} = \frac{1 \times 1}{2 \times 5} = \frac{1}{10}21​×51​=21​×51​=2×51×1​=101​

STEP 4

Calculate the product for the third row.13×15=13×15=1×13×5=115\frac{1}{3} \times \frac{1}{5} = \frac{1}{3} \times \frac{1}{5} = \frac{1 \times 1}{3 \times 5} = \frac{1}{15}31​×51​=31​×51​=3×51×1​=151​

STEP 5

Identify the pattern in the denominators of the products.The denominators are multiples of 5: 5,10,15,…5, 10, 15, \ldots5,10,15,…

STEP 6

Use the pattern to fill in the missing numerator in the fourth row.Given that □×15=120\square \times \frac{1}{5} = \frac{1}{20}□×51​=201​, we need to find the numerator that, when multiplied by 15\frac{1}{5}51​, gives 120\frac{1}{20}201​.

STEP 7

STEP 8

Use the pattern to fill in the missing numerator in the fifth row.Given that □×15=125\square \times \frac{1}{5} = \frac{1}{25}□×51​=251​, we need to find the numerator that, when multiplied by 15\frac{1}{5}51​, gives 125\frac{1}{25}251​.

STEP 9

STEP 10

STEP 11

Describe the pattern observed.The factors on the left side of the multiplication are consecutive fractions with a numerator of 1 and increasing denominators starting from 1. The products are fractions with denominators that are multiples of 5, increasing by 5 each time.

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Assumptions
1. The pattern involves multiplying a fraction by $\frac{1}{5}$ .
2. The products are fractions in their simplest form.
3. We are to continue the pattern by filling in the missing values in the chart.

Observe the pattern in the multiplication of the fractions.
The first row shows that $1 \times \frac{1}{5} = \frac{1}{5}$ .

Calculate the product for the second row.
$\frac{1}{2} \times \frac{1}{5} = \frac{1}{2} \times \frac{1}{5} = \frac{1 \times 1}{2 \times 5} = \frac{1}{10}$

Calculate the product for the third row.
$\frac{1}{3} \times \frac{1}{5} = \frac{1}{3} \times \frac{1}{5} = \frac{1 \times 1}{3 \times 5} = \frac{1}{15}$

Identify the pattern in the denominators of the products.
The denominators are multiples of 5: $5, 10, 15, \ldots$

Use the pattern to fill in the missing numerator in the fourth row.
Given that $\square \times \frac{1}{5} = \frac{1}{20}$ , we need to find the numerator that, when multiplied by $\frac{1}{5}$ , gives $\frac{1}{20}$ .

Use the pattern to fill in the missing numerator in the fifth row.
Given that $\square \times \frac{1}{5} = \frac{1}{25}$ , we need to find the numerator that, when multiplied by $\frac{1}{5}$ , gives $\frac{1}{25}$ .

Describe the pattern observed.
The factors on the left side of the multiplication are consecutive fractions with a numerator of 1 and increasing denominators starting from 1. The products are fractions with denominators that are multiples of 5, increasing by 5 each time.