Math / Numbers & Operations

QuestionWhich sign makes the statement true? $\frac{2}{3} ? \frac{8}{12}$

Studdy Solution

STEP 1

What is this asking? We need to figure out if $\frac{2}{3}$ is greater than, less than, or equal to $\frac{8}{12}$ . Watch out! Don't be tricked just because the numbers look different!
We need to compare them fairly.

STEP 2

1. Simplify the Fractions
2. Compare the Fractions

STEP 3

Alright, let's simplify $\frac{8}{12}$ !
We want to make it easier to compare with $\frac{2}{3}$ .
To simplify a fraction, we find the greatest common divisor (GCD) of the numerator and the denominator and divide both by it.
The GCD of 8 and 12 is 4.

STEP 4

So, let's divide both the numerator and the denominator by 4: $\frac{8}{12} = \frac{8 \div 4}{12 \div 4} = \frac{2}{3}$ Look at that! $\frac{8}{12}$ simplifies to $\frac{2}{3}$ .

STEP 5

Now, our problem is comparing $\frac{2}{3}$ to $\frac{2}{3}$ .
They are the same!

STEP 6

The equal sign makes the statement true: $\frac{2}{3} = \frac{8}{12}$

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QuestionWhich sign makes the statement true? $\frac{2}{3} ? \frac{8}{12}$

Studdy Solution

STEP 1

What is this asking? We need to figure out if $\frac{2}{3}$ is greater than, less than, or equal to $\frac{8}{12}$ . Watch out! Don't be tricked just because the numbers look different!
We need to compare them fairly.

STEP 2

1. Simplify the Fractions
2. Compare the Fractions

STEP 3

Alright, let's simplify $\frac{8}{12}$ !
We want to make it easier to compare with $\frac{2}{3}$ .
To simplify a fraction, we find the greatest common divisor (GCD) of the numerator and the denominator and divide both by it.
The GCD of 8 and 12 is 4.

STEP 4

So, let's divide both the numerator and the denominator by 4: $\frac{8}{12} = \frac{8 \div 4}{12 \div 4} = \frac{2}{3}$ Look at that! $\frac{8}{12}$ simplifies to $\frac{2}{3}$ .

STEP 5

Now, our problem is comparing $\frac{2}{3}$ to $\frac{2}{3}$ .
They are the same!

STEP 6

The equal sign makes the statement true: $\frac{2}{3} = \frac{8}{12}$

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QuestionWhich sign makes the statement true? 23?812\frac{2}{3} ? \frac{8}{12}32​?128​

Studdy Solution

STEP 1

What is this asking? We need to figure out if 23\frac{2}{3}32​ is greater than, less than, or equal to 812\frac{8}{12}128​. Watch out! Don't be tricked just because the numbers look different!We need to compare them fairly.

STEP 2

1. Simplify the Fractions2. Compare the Fractions

STEP 3

Alright, let's **simplify** 812\frac{8}{12}128​!We want to make it easier to compare with 23\frac{2}{3}32​.To simplify a fraction, we find the **greatest common divisor** (GCD) of the numerator and the denominator and divide both by it.The GCD of 8 and 12 is **4**.

STEP 4

So, let's divide both the numerator and the denominator by **4**: 812=8÷412÷4=23 \frac{8}{12} = \frac{8 \div 4}{12 \div 4} = \frac{2}{3} 128​=12÷48÷4​=32​ Look at that! 812\frac{8}{12}128​ simplifies to 23\frac{2}{3}32​.

STEP 5

Now, our problem is comparing 23\frac{2}{3}32​ to 23\frac{2}{3}32​.They are the *same*!

STEP 6

The equal sign makes the statement true: 23=812 \frac{2}{3} = \frac{8}{12} 32​=128​

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QuestionWhich sign makes the statement true? $\frac{2}{3} ? \frac{8}{12}$

What is this asking? We need to figure out if $\frac{2}{3}$ is greater than, less than, or equal to $\frac{8}{12}$ . Watch out! Don't be tricked just because the numbers look different!
We need to compare them fairly.

1. Simplify the Fractions
2. Compare the Fractions

Alright, let's simplify $\frac{8}{12}$ !
We want to make it easier to compare with $\frac{2}{3}$ .
To simplify a fraction, we find the greatest common divisor (GCD) of the numerator and the denominator and divide both by it.
The GCD of 8 and 12 is 4.

So, let's divide both the numerator and the denominator by 4: $\frac{8}{12} = \frac{8 \div 4}{12 \div 4} = \frac{2}{3}$ Look at that! $\frac{8}{12}$ simplifies to $\frac{2}{3}$ .

Now, our problem is comparing $\frac{2}{3}$ to $\frac{2}{3}$ .
They are the same!

The equal sign makes the statement true: $\frac{2}{3} = \frac{8}{12}$