Math

Question Determine if the statement 1248=28\frac{12}{48} = \frac{2}{8} is true. Show your work.

Studdy Solution

STEP 1

Assumptions
1. We are given two ratios: 1248\frac{12}{48} and 28\frac{2}{8}.
2. We need to determine if the two ratios are equivalent.

STEP 2

To determine if two ratios are equivalent, we can simplify both ratios to their lowest terms and then compare them.

STEP 3

First, simplify the ratio 1248\frac{12}{48} by finding the greatest common divisor (GCD) of the numerator and the denominator.

STEP 4

The GCD of 12 and 48 is 12.

STEP 5

Divide both the numerator and the denominator of the ratio 1248\frac{12}{48} by the GCD to simplify it.
12÷1248÷12\frac{12 \div 12}{48 \div 12}

STEP 6

Perform the division to obtain the simplified ratio.
12÷1248÷12=14\frac{12 \div 12}{48 \div 12} = \frac{1}{4}

STEP 7

Now, simplify the ratio 28\frac{2}{8} by finding the GCD of the numerator and the denominator.

STEP 8

The GCD of 2 and 8 is 2.

STEP 9

Divide both the numerator and the denominator of the ratio 28\frac{2}{8} by the GCD to simplify it.
2÷28÷2\frac{2 \div 2}{8 \div 2}

STEP 10

Perform the division to obtain the simplified ratio.
2÷28÷2=14\frac{2 \div 2}{8 \div 2} = \frac{1}{4}

STEP 11

Now that we have both ratios simplified, we can compare them to see if they are equivalent.

STEP 12

The simplified form of the first ratio is 14\frac{1}{4} and the simplified form of the second ratio is also 14\frac{1}{4}.

STEP 13

Since both simplified ratios are equal, the original ratios 1248\frac{12}{48} and 28\frac{2}{8} are equivalent.
The statement that 1248=28\frac{12}{48}=\frac{2}{8} is True.

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