We are tasked with solving the expression:
\[
\frac{3}{5} \times \frac{4}{9} \times \frac{15}{24}
\]
Step 1: Write down the expression
The given expression is:
\[
\frac{3}{5} \times \frac{4}{9} \times \frac{15}{24}
\]
Step 2: Multiply the fractions
When multiplying fractions, we multiply the numerators together and the denominators together. So, we have:
\[
\frac{3 \times 4 \times 15}{5 \times 9 \times 24}
\]
Step 3: Simplify before multiplying
To simplify the calculation, we can cancel out common factors between the numerator and the denominator.
#### Numerator:
The numerator is \(3 \times 4 \times 15\).
#### Denominator:
The denominator is \(5 \times 9 \times 24\).
Let's break down the factors:
-
Numerator: \(3 \times 4 \times 15 = 3 \times 4 \times (3 \times 5)\)
-
Denominator: \(5 \times 9 \times 24 = 5 \times (3 \times 3) \times (8 \times 3)\)
Now, write the full expression with these factorizations:
\[
\frac{3 \times 4 \times 3 \times 5}{5 \times 3 \times 3 \times 8 \times 3}
\]
#### Cancel common factors:
1.
Cancel one \(3\) from the numerator and one \(3\) from the denominator:
\[
\frac{\cancel{3} \times 4 \times 3 \times 5}{5 \times \cancel{3} \times 3 \times 8 \times 3}
\]
2.
Cancel another \(3\) from the numerator and one \(3\) from the denominator:
\[
\frac{4 \times \cancel{3} \times 5}{5 \times \cancel{3} \times 3 \times 8 \times 3}
\]
3.
Cancel the \(5\) in the numerator and the \(5\) in the denominator:
\[
\frac{4 \times 1}{1 \times 3 \times 8 \times 3}
\]
4.
Simplify the remaining terms:
\[
\frac{4}{3 \times 8 \times 3} = \frac{4}{72}
\]
Step 4: Simplify the fraction \(\frac{4}{72}\)
The greatest common divisor (GCD) of \(4\) and \(72\) is \(4\). Divide both the numerator and the denominator by \(4\):
\[
\frac{4 \div 4}{72 \div 4} = \frac{1}{18}
\]
Final Answer:
\[
\boxed{\frac{1}{18}}
\]
Parent Tip: Review the logic above to help your child master the concept of multiplying 3 fractions worksheet.
