Question Video: Finding the Product of Rational Numbers Given in Different Forms | Nagwa Question Video: Finding the Product of Rational Numbers Given in Different Forms | Nagwa

# Question Video: Finding the Product of Rational Numbers Given in Different Forms Mathematics • First Year of Preparatory School

## Join Nagwa Classes

Find the value of the product of 20 × (3/4) × 0.18 to the nearest 2 decimal places.

03:20

### Video Transcript

Find the value of the product of 20 times three-quarters times 0.18 to the nearest two decimal places.

In this question, we are asked to evaluate the product of three rational numbers and give our answer to the nearest two decimal places.

To answer this question, we can start by recalling that the multiplication of rational numbers is associative and commutative. So, we can rearrange the product and evaluate the product in any order. Next, we can also recall that it is often easiest to multiply rational numbers together when they are all written as fractions.

So, we will start by writing all of the factors as fractions. It is not necessary to rewrite 20 as 20 over one, since 20 will just be a factor in the numerator. However, we will convert anyway. We can also note that 0.18 is equal to 18 over 100 to obtain the following product. We can now multiply the fractions by recalling that we multiply two fractions by multiplying their numerators and denominators together separately.

In general, we could multiply fractions by recalling that 𝑎 over 𝑏 times 𝑐 over 𝑑 is equal to 𝑎𝑐 over 𝑏𝑑. This result extends to the product of any number of fractions. So, we have 20 times three times 18 divided by one times four times 100. We could now evaluate the products in the numerator and denominator. However, it is easier to cancel the shared factors first. We can see that there is a shared factor of four in the numerator and denominator. We can cancel this factor as shown.

We could now continue to cancel shared factors. However, we are told to give our answer to two decimal places. We know that a fraction with a denominator of 100 is easy to convert into a decimal. So, we will leave the denominator as 100. Evaluating the product in the numerator, we have that five times three is 15. And then we can calculate that 15 times 18 is equal to 270. So, we have 270 divided by 100.

We can then convert 270 over 100 into a decimal by moving the decimal point over two spaces to the left to obtain 2.70. It is worth noting that the exact value of this product is 2.7. However, since we are asked for two decimal places of accuracy, we will give the answer of 2.70.

## Join Nagwa Classes

Attend live sessions on Nagwa Classes to boost your learning with guidance and advice from an expert teacher!

• Interactive Sessions
• Chat & Messaging
• Realistic Exam Questions