Find an equivalent ratio in simplest terms: 110:42 :

Find GCD: To find an equivalent ratio in simplest terms, we need to find the greatest common divisor (GCD) of 110 and 42. This will allow us to divide both numbers by the GCD to simplify the ratio.List Factors: First, we list the factors of 110 and 42 to find the GCD. The factors of 110 are 1, 2, 5, 10, 11, 22, 55, 110. The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42.Identify GCD: Looking at the factors of both numbers, we see that the largest common factor is 2. Therefore, the GCD of 110 and 42 is 2.Divide by GCD: Now, we divide both terms of the ratio by the GCD. So, we divide 110 by 2 and 42 by 2. 110 ÷ 2 = 55 42 ÷ 2 = 21Simplify Ratio: After dividing both numbers by the GCD, we get the simplified ratio of 55:21.

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Find an equivalent ratio in simplest terms:

110:42
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Find an equivalent ratio in simplest terms: $\newline$ $110: 42$ $\newline$ $\square$ : $\square$

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Math Problems

Grade 7

Write an equivalent ratio

Full solution

Q. Find an equivalent ratio in simplest terms:

\newline

110: 42

\newline

\square

\square

Find GCD: To find an equivalent ratio in simplest terms, we need to find the greatest common divisor (GCD) of $110$ and $42$ . This will allow us to divide both numbers by the GCD to simplify the ratio.
List Factors: First, we list the factors of $110$ and $42$ to find the GCD. The factors of $110$ are $1$ , $2$ , $5$ , $10$ , $11$ , $22$ , $55$ , $110$ . The factors of $42$ are $1$ , $2$ , $42$ $4$ , $42$ $5$ , $42$ $6$ , $42$ $7$ , $42$ $8$ , $42$ .
Identify GCD: Looking at the factors of both numbers, we see that the largest common factor is $2$ . Therefore, the GCD of $110$ and $42$ is $2$ .
Divide by GCD: Now, we divide both terms of the ratio by the GCD. So, we divide $110$ by $2$ and $42$ by $2$ . $\newline$ $110 \div 2 = 55$ $\newline$ $42 \div 2 = 21$
Simplify Ratio: After dividing both numbers by the GCD, we get the simplified ratio of $55:21$ .