Solved on Dec 10, 2023

Find common denominator for $\frac{5}{6}$ and $\frac{7}{10}$ .

STEP 1

Assumptions
1. We have two fractions: $\frac{5}{6}$ and $\frac{7}{10}$ .
2. We need to find a common denominator for these fractions.
3. A common denominator is a shared multiple of the denominators of the fractions.

STEP 2

Identify the denominators of the given fractions.
The denominators are 6 and 10 for the fractions $\frac{5}{6}$ and $\frac{7}{10}$ , respectively.

STEP 3

Find the least common multiple (LCM) of the denominators, which will be the common denominator.
The LCM of 6 and 10 can be found by listing the multiples of each number until we find a common multiple.

STEP 4

List the first few multiples of 6: 6, 12, 18, 24, 30, ...

STEP 5

List the first few multiples of 10: 10, 20, 30, 40, ...

STEP 6

Identify the least common multiple from the lists.
The LCM of 6 and 10 is 30, as it is the smallest multiple that appears in both lists.

STEP 7

Now that we have the common denominator (30), we can write each fraction with this denominator.
To convert each fraction to an equivalent fraction with the common denominator, we need to find a number to multiply the numerator and the denominator of each fraction by, such that the denominator becomes 30.

STEP 8

For the fraction $\frac{5}{6}$ , determine what number to multiply the denominator by to get 30.
$6 \times 5 = 30$
So, we need to multiply both the numerator and the denominator by 5.

STEP 9

Convert the fraction $\frac{5}{6}$ to an equivalent fraction with a denominator of 30.
$\frac{5}{6} \times \frac{5}{5} = \frac{25}{30}$

STEP 10

For the fraction $\frac{7}{10}$ , determine what number to multiply the denominator by to get 30.
$10 \times 3 = 30$
So, we need to multiply both the numerator and the denominator by 3.

STEP 11

Convert the fraction $\frac{7}{10}$ to an equivalent fraction with a denominator of 30.
$\frac{7}{10} \times \frac{3}{3} = \frac{21}{30}$

STEP 12

Now we have both fractions with the common denominator of 30.
The fractions $\frac{5}{6}$ and $\frac{7}{10}$ can be written with a common denominator as $\frac{25}{30}$ and $\frac{21}{30}$ , respectively.
The option that shows the fractions written with a common denominator of 30 is:
$\frac{25}{30} \text{ and } \frac{21}{30}$

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Find common denominator for $\frac{5}{6}$ and $\frac{7}{10}$ .

STEP 1

Assumptions
1. We have two fractions: $\frac{5}{6}$ and $\frac{7}{10}$ .
2. We need to find a common denominator for these fractions.
3. A common denominator is a shared multiple of the denominators of the fractions.

STEP 2

Identify the denominators of the given fractions.
The denominators are 6 and 10 for the fractions $\frac{5}{6}$ and $\frac{7}{10}$ , respectively.

STEP 3

Find the least common multiple (LCM) of the denominators, which will be the common denominator.
The LCM of 6 and 10 can be found by listing the multiples of each number until we find a common multiple.

STEP 4

List the first few multiples of 6: 6, 12, 18, 24, 30, ...

STEP 5

List the first few multiples of 10: 10, 20, 30, 40, ...

STEP 6

Identify the least common multiple from the lists.
The LCM of 6 and 10 is 30, as it is the smallest multiple that appears in both lists.

STEP 7

STEP 8

For the fraction $\frac{5}{6}$ , determine what number to multiply the denominator by to get 30.
$6 \times 5 = 30$
So, we need to multiply both the numerator and the denominator by 5.

STEP 9

Convert the fraction $\frac{5}{6}$ to an equivalent fraction with a denominator of 30.
$\frac{5}{6} \times \frac{5}{5} = \frac{25}{30}$

STEP 10

For the fraction $\frac{7}{10}$ , determine what number to multiply the denominator by to get 30.
$10 \times 3 = 30$
So, we need to multiply both the numerator and the denominator by 3.

STEP 11

Convert the fraction $\frac{7}{10}$ to an equivalent fraction with a denominator of 30.
$\frac{7}{10} \times \frac{3}{3} = \frac{21}{30}$

STEP 12

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Find common denominator for 56\frac{5}{6}65​ and 710\frac{7}{10}107​.

STEP 1

Assumptions1. We have two fractions: 56\frac{5}{6}65​ and 710\frac{7}{10}107​.2. We need to find a common denominator for these fractions.3. A common denominator is a shared multiple of the denominators of the fractions.

STEP 2

Identify the denominators of the given fractions.The denominators are 6 and 10 for the fractions 56\frac{5}{6}65​ and 710\frac{7}{10}107​, respectively.

STEP 3

Find the least common multiple (LCM) of the denominators, which will be the common denominator.The LCM of 6 and 10 can be found by listing the multiples of each number until we find a common multiple.

STEP 4

List the first few multiples of 6: 6, 12, 18, 24, 30, ...

STEP 5

List the first few multiples of 10: 10, 20, 30, 40, ...

STEP 6

Identify the least common multiple from the lists.The LCM of 6 and 10 is 30, as it is the smallest multiple that appears in both lists.

STEP 7

STEP 8

For the fraction 56\frac{5}{6}65​, determine what number to multiply the denominator by to get 30.6×5=306 \times 5 = 306×5=30So, we need to multiply both the numerator and the denominator by 5.

STEP 9

Convert the fraction 56\frac{5}{6}65​ to an equivalent fraction with a denominator of 30.56×55=2530\frac{5}{6} \times \frac{5}{5} = \frac{25}{30}65​×55​=3025​

STEP 10

For the fraction 710\frac{7}{10}107​, determine what number to multiply the denominator by to get 30.10×3=3010 \times 3 = 3010×3=30So, we need to multiply both the numerator and the denominator by 3.

STEP 11

Convert the fraction 710\frac{7}{10}107​ to an equivalent fraction with a denominator of 30.710×33=2130\frac{7}{10} \times \frac{3}{3} = \frac{21}{30}107​×33​=3021​

STEP 12

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Find common denominator for $\frac{5}{6}$ and $\frac{7}{10}$ .

Assumptions
1. We have two fractions: $\frac{5}{6}$ and $\frac{7}{10}$ .
2. We need to find a common denominator for these fractions.
3. A common denominator is a shared multiple of the denominators of the fractions.

Identify the denominators of the given fractions.
The denominators are 6 and 10 for the fractions $\frac{5}{6}$ and $\frac{7}{10}$ , respectively.

Find the least common multiple (LCM) of the denominators, which will be the common denominator.
The LCM of 6 and 10 can be found by listing the multiples of each number until we find a common multiple.

Identify the least common multiple from the lists.
The LCM of 6 and 10 is 30, as it is the smallest multiple that appears in both lists.

For the fraction $\frac{5}{6}$ , determine what number to multiply the denominator by to get 30.
$6 \times 5 = 30$
So, we need to multiply both the numerator and the denominator by 5.

Convert the fraction $\frac{5}{6}$ to an equivalent fraction with a denominator of 30.
$\frac{5}{6} \times \frac{5}{5} = \frac{25}{30}$

For the fraction $\frac{7}{10}$ , determine what number to multiply the denominator by to get 30.
$10 \times 3 = 30$
So, we need to multiply both the numerator and the denominator by 3.

Convert the fraction $\frac{7}{10}$ to an equivalent fraction with a denominator of 30.
$\frac{7}{10} \times \frac{3}{3} = \frac{21}{30}$