Classwork. Write the rat io in its simplest form a) \( 24: 144 \) (b) \( 1276 \mathrm{~cm} A B ; A C: B C \) \( = \)

To simplify the ratios, we will follow these steps: 1. **For the first ratio \( 24:144 \)**: - Find the greatest common divisor (GCD) of 24 and 144. - Divide both numbers by their GCD to simplify the ratio. 2. **For the second ratio \( 1276 \mathrm{~cm} A B : A C : B C \)**: - We will first express the ratios in a standard form and then simplify them if necessary. Let's start with the first ratio \( 24:144 \). ### Step 1: Simplifying \( 24:144 \) 1. Find the GCD of 24 and 144. - The factors of 24 are \( 1, 2, 3, 4, 6, 8, 12, 24 \). - The factors of 144 are \( 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144 \). - The GCD is \( 24 \). 2. Divide both numbers by their GCD: \[ \frac{24}{24} : \frac{144}{24} = 1 : 6 \] So, the simplified form of the ratio \( 24:144 \) is \( 1:6 \). ### Step 2: Simplifying \( 1276 \mathrm{~cm} A B : A C : B C \) Assuming \( A B, A C, \) and \( B C \) are segments of a triangle or line, we will express them in a ratio format. However, we need to know the lengths of \( A C \) and \( B C \) to simplify the ratio. If we assume \( A C \) and \( B C \) are also \( 1276 \) cm, then the ratio would be: \[ 1276 : 1276 : 1276 \] To simplify: 1. Divide each term by \( 1276 \): \[ \frac{1276}{1276} : \frac{1276}{1276} : \frac{1276}{1276} = 1 : 1 : 1 \] Thus, the simplified form of the ratio \( 1276 \mathrm{~cm} A B : A C : B C \) is \( 1:1:1 \). ### Final Answers: a) \( 24:144 = 1:6 \) b) \( 1276 \mathrm{~cm} A B : A C : B C = 1:1:1 \)