$
\begin{array}{l}
a:b = 3:5 \\
b:c = 10:11
\end{array}
$

Work out \( a:c \).

Give your answer in its simplest form.

Optional working: \(\square\)

Answer: [tex]\( a:c = \)[/tex] [tex]\(\square\)[/tex]



Answer :

To determine the ratio \( a : c \) given the ratios \( a : b = 3 : 5 \) and \( b : c = 10 : 11 \), we can follow these steps:

1. Understand the given ratios:
- The ratio \( a : b \) is given as \( 3 : 5 \).
- The ratio \( b : c \) is given as \( 10 : 11 \).

2. Convert these ratios into fractions:
- \( a : b = \frac{a}{b} = \frac{3}{5} \)
- \( b : c = \frac{b}{c} = \frac{10}{11} \)

3. Find the product of the fractions to determine \( a : c \):
[tex]\[ \frac{a}{c} = \frac{a}{b} \times \frac{b}{c} = \frac{3}{5} \times \frac{10}{11} \][/tex]

4. Multiply the numerators and the denominators:
[tex]\[ \frac{a}{c} = \frac{3 \times 10}{5 \times 11} = \frac{30}{55} \][/tex]

5. Simplify the fraction \(\frac{30}{55}\) to its simplest form:
- The greatest common divisor (GCD) of 30 and 55 is 5.
- Divide both the numerator and the denominator by the GCD:
[tex]\[ \frac{30 \div 5}{55 \div 5} = \frac{6}{11} \][/tex]

Therefore, the ratio \( a : c \) in its simplest form is:
\(
a : c = 6 : 11
\)

Optional working

Answer: [tex]\( a : c = 6 : 11 \)[/tex]