Question
upstudy study bank question image url

Find the ratio and write in the simbleest form: \( 1 \frac{5}{6}, 1 \frac{11}{15} \) and \( 1 \frac{13}{30} \)

Ask by Santiago Mcdonald. in Pakistan
Mar 09,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The ratio in its simplest form is \(55:52:43\).

Solution

1. Convert each mixed number to an improper fraction. - For \(1 \frac{5}{6}\): \[ 1 \frac{5}{6} = \frac{6 \times 1 + 5}{6} = \frac{11}{6} \] - For \(1 \frac{11}{15}\): \[ 1 \frac{11}{15} = \frac{15 \times 1 + 11}{15} = \frac{26}{15} \] - For \(1 \frac{13}{30}\): \[ 1 \frac{13}{30} = \frac{30 \times 1 + 13}{30} = \frac{43}{30} \] 2. Express all fractions with a common denominator. The denominators are \(6\), \(15\), and \(30\). The least common denominator is \(30\). - Rewrite \(\frac{11}{6}\) as: \[ \frac{11}{6} = \frac{11 \times 5}{6 \times 5} = \frac{55}{30} \] - Rewrite \(\frac{26}{15}\) as: \[ \frac{26}{15} = \frac{26 \times 2}{15 \times 2} = \frac{52}{30} \] - \(\frac{43}{30}\) is already with denominator \(30\). 3. Write the ratio using the numerators: \[ \frac{55}{30} : \frac{52}{30} : \frac{43}{30} = 55 : 52 : 43 \] The ratio in its simplest form is: \[ 55:52:43 \]

Answered by UpStudy AI and reviewed by a Professional Tutor

error msg
Explain
Simplify this solution

Beyond the Answer

To find the ratio of the three mixed numbers \( 1 \frac{5}{6}, 1 \frac{11}{15}, \) and \( 1 \frac{13}{30} \), we first convert them to improper fractions: 1. \( 1 \frac{5}{6} = \frac{6 + 5}{6} = \frac{11}{6} \) 2. \( 1 \frac{11}{15} = \frac{15 + 11}{15} = \frac{26}{15} \) 3. \( 1 \frac{13}{30} = \frac{30 + 13}{30} = \frac{43}{30} \) Now, let's express the ratio: \[ \text{Ratio} = \frac{11}{6} : \frac{26}{15} : \frac{43}{30} \] To simplify this, we can convert it to a single fraction. We find a common denominator, which would be 30: 1. \( \frac{11}{6} = \frac{55}{30} \) 2. \( \frac{26}{15} = \frac{52}{30} \) 3. \( \frac{43}{30} = \frac{43}{30} \) The ratio now becomes: \[ 55 : 52 : 43 \] Now, we need to make sure this is in the simplest form. The greatest common divisor (GCD) of 55, 52, and 43 is 1; hence, the ratio is already in its simplest form. Thus, the answer is: \[ \text{The ratio in simplest form is } 55 : 52 : 43. \]

Try Premium now!
Try Premium and ask Thoth AI unlimited math questions now!
Maybe later Go Premium
Study can be a real struggle
Why not UpStudy it?
Select your plan below
Premium

You can enjoy

Start now
  • Step-by-step explanations
  • 24/7 expert live tutors
  • Unlimited number of questions
  • No interruptions
  • Full access to Answer and Solution
  • Full Access to PDF Chat, UpStudy Chat, Browsing Chat
Basic

Totally free but limited

  • Limited Solution
Welcome to UpStudy!
Please sign in to continue the Thoth AI Chat journey
Continue with Email
Or continue with
By clicking “Sign in”, you agree to our Terms of Use & Privacy Policy