Math / Numbers & Operations

Question $\frac{4}{5}+\frac{9}{11}=$

Studdy Solution

STEP 1

What is this asking? We need to add two fractions with different denominators! Watch out! Don't just add the numerators and denominators directly.
We need a common denominator!

STEP 2

1. Find the Least Common Denominator (LCD)
2. Express each fraction with the LCD
3. Add the fractions

STEP 3

Since $5$ and $11$ are prime numbers and share no common factors other than $1$ , their least common multiple, and therefore our least common denominator, is simply their product: $5 \cdot 11 = \mathbf{55}$ .

STEP 4

To express $\frac{4}{5}$ with a denominator of $55$ , we need to multiply the denominator by $11$ .
To keep the fraction's value the same, we must also multiply the numerator by $11$ .
This is equivalent to multiplying by $\frac{11}{11}$ , which is equal to $1$ , and multiplying by $1$ doesn't change the value!
So, we have $\frac{4}{5} \cdot \frac{11}{11} = \frac{4 \cdot 11}{5 \cdot 11} = \frac{\mathbf{44}}{\mathbf{55}}$ .

STEP 5

Similarly, for $\frac{9}{11}$ , we multiply both the numerator and denominator by $5$ : $\frac{9}{11} \cdot \frac{5}{5} = \frac{9 \cdot 5}{11 \cdot 5} = \frac{\mathbf{45}}{\mathbf{55}}$ .
We're multiplying by $\frac{5}{5}$ which is just $1$ , so the value stays the same!

STEP 6

Now that both fractions have the same denominator, we can add them by adding their numerators and keeping the common denominator: $\frac{44}{55} + \frac{45}{55} = \frac{44 + 45}{55} = \frac{\mathbf{89}}{\mathbf{55}}$ .

STEP 7

Our final answer is $\frac{89}{55}$ !

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Question $\frac{4}{5}+\frac{9}{11}=$

Studdy Solution

STEP 1

What is this asking? We need to add two fractions with different denominators! Watch out! Don't just add the numerators and denominators directly.
We need a common denominator!

STEP 2

1. Find the Least Common Denominator (LCD)
2. Express each fraction with the LCD
3. Add the fractions

STEP 3

Since $5$ and $11$ are prime numbers and share no common factors other than $1$ , their least common multiple, and therefore our least common denominator, is simply their product: $5 \cdot 11 = \mathbf{55}$ .

STEP 4

STEP 5

Similarly, for $\frac{9}{11}$ , we multiply both the numerator and denominator by $5$ : $\frac{9}{11} \cdot \frac{5}{5} = \frac{9 \cdot 5}{11 \cdot 5} = \frac{\mathbf{45}}{\mathbf{55}}$ .
We're multiplying by $\frac{5}{5}$ which is just $1$ , so the value stays the same!

STEP 6

Now that both fractions have the same denominator, we can add them by adding their numerators and keeping the common denominator: $\frac{44}{55} + \frac{45}{55} = \frac{44 + 45}{55} = \frac{\mathbf{89}}{\mathbf{55}}$ .

STEP 7

Our final answer is $\frac{89}{55}$ !

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Question45+911=\frac{4}{5}+\frac{9}{11}=54​+119​=

Studdy Solution

STEP 1

What is this asking? We need to add two fractions with different denominators! Watch out! Don't just add the numerators and denominators directly.We need a common denominator!

STEP 2

1. Find the Least Common Denominator (LCD)2. Express each fraction with the LCD3. Add the fractions

STEP 3

Since 555 and 111111 are **prime numbers** and share no common factors other than 111, their least common multiple, and therefore our **least common denominator**, is simply their product: 5⋅11=555 \cdot 11 = \mathbf{55}5⋅11=55.

STEP 4

STEP 5

STEP 6

Now that both fractions have the same denominator, we can add them by adding their numerators and keeping the common denominator: 4455+4555=44+4555=8955\frac{44}{55} + \frac{45}{55} = \frac{44 + 45}{55} = \frac{\mathbf{89}}{\mathbf{55}}5544​+5545​=5544+45​=5589​.

STEP 7

Our final answer is 8955\frac{89}{55}5589​!

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Question $\frac{4}{5}+\frac{9}{11}=$

What is this asking? We need to add two fractions with different denominators! Watch out! Don't just add the numerators and denominators directly.
We need a common denominator!

1. Find the Least Common Denominator (LCD)
2. Express each fraction with the LCD
3. Add the fractions

Since $5$ and $11$ are prime numbers and share no common factors other than $1$ , their least common multiple, and therefore our least common denominator, is simply their product: $5 \cdot 11 = \mathbf{55}$ .

Now that both fractions have the same denominator, we can add them by adding their numerators and keeping the common denominator: $\frac{44}{55} + \frac{45}{55} = \frac{44 + 45}{55} = \frac{\mathbf{89}}{\mathbf{55}}$ .

Our final answer is $\frac{89}{55}$ !