Question Calculate the value of $15 \cdot \frac{24}{1600}$ .

Studdy Solution

STEP 1

Assumptions
1. We are given the mathematical expression $15 \cdot \frac{24}{1600}$ .
2. We need to simplify the expression to find its value.

STEP 2

First, we will write down the expression that we need to simplify.
$15 \cdot \frac{24}{1600}$

STEP 3

We can simplify the expression by performing the multiplication. However, it is often easier to simplify the fraction first before multiplying to make the numbers smaller and easier to work with.

STEP 4

We can simplify the fraction $\frac{24}{1600}$ by finding the greatest common divisor (GCD) of the numerator and the denominator and then dividing both by the GCD.

STEP 5

The GCD of 24 and 1600 is 8. We will divide both the numerator and the denominator by 8.
$\frac{24}{1600} = \frac{24 \div 8}{1600 \div 8}$

STEP 6

Perform the division to simplify the fraction.
$\frac{24 \div 8}{1600 \div 8} = \frac{3}{200}$

STEP 7

Now we have a simplified fraction, and we can proceed with the multiplication.
$15 \cdot \frac{3}{200}$

STEP 8

Multiply the numerator of the fraction by the whole number.
$15 \cdot 3 = 45$

STEP 9

Now the expression looks like this:
$\frac{45}{200}$

STEP 10

We can simplify this fraction further by finding the GCD of 45 and 200. The GCD is 5.

STEP 11

Divide both the numerator and the denominator by the GCD to simplify the fraction.
$\frac{45 \div 5}{200 \div 5}$

STEP 12

Perform the division.
$\frac{45 \div 5}{200 \div 5} = \frac{9}{40}$

STEP 13

The fraction $\frac{9}{40}$ is already in its simplest form, so this is the final answer.
The value of $15 \cdot \frac{24}{1600}$ is $\frac{9}{40}$ .

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