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Chapter 4: Problem 79

Calculate. \(\frac{4}{5} \times 384.8+24.8 \div \frac{8}{3}\)

Short Answer

Expert verified
317.14

Step by step solution

01

- Multiply the fraction with the number

First, calculate \(\frac{4}{5} \times 384.8 \). Multiply the numerator by the number: \[ 4 \times 384.8 = 1539.2 \]. Then divide by the denominator: \[ \frac{1539.2}{5} = 307.84 \]
02

- Divide the number by the fraction

Next, calculate \(24.8 \div \frac{8}{3} \). Dividing by a fraction is the same as multiplying by its reciprocal: \[ 24.8 \div \frac{8}{3} = 24.8 \times \frac{3}{8} \]. Simplify: \[ 24.8 \times 0.375 = 9.3 \]
03

- Add the two results

Finally, add the results from Step 1 and Step 2: \[ 307.84 + 9.3 = 317.14 \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Multiplication of Fractions
Multiplying fractions sounds tricky, but it鈥檚 quite simple! When multiplying a fraction by a number, follow these two easy steps:

First, multiply the numerator (top number) of the fraction by the whole number. In our example, we have \( \frac{4}{5} \times 384.8 \). So, multiply 4 by 384.8 which equals 1539.2.

Second, divide this product by the denominator (bottom number) of the fraction. Here, we divide 1539.2 by 5, giving us 307.84.

Remember these steps, and multiplying fractions will be a breeze!
Division by Fractions
Dividing by a fraction can seem confusing, but there's a neat trick to simplify it: multiply by the reciprocal!

The reciprocal of a fraction is just switching its numerator and denominator. So, when we need to compute \( 24.8 \div \frac{8}{3} \), we instead multiply 24.8 by \frac{3}{8}\.

Start by converting the division into multiplication. Now, it鈥檚 \( 24.8 \times \frac{3}{8} \).

Next, simplify the fraction part: \( \frac{3}{8} \) converts to 0.375. Now, multiply 24.8 by 0.375, which results in 9.3.

With these steps, you can quickly handle division by fractions!
Addition of Decimals
Adding decimals requires careful alignment of the decimal points.

To add 307.84 and 9.3, align the decimals vertically to ensure each digit is in the correct column. It may help to add a trailing zero to the number with fewer decimal places for easier alignment: hence, think of 9.30 instead of just 9.3.

Now add them column-by-column starting from the right:
  • 4 + 0 = 4
  • 8 + 3 = 11 (write 1 and carry over 1 to the next column)
  • 7 + 9 + 1 (from the carry-over) = 17 (write 7 and carry over 1)
  • 0 + 0 + 1 (from the carry-over) = 1
  • Finally, bring down the 3
So, 307.84 + 9.3 equals 317.14.

Simple alignment and step-by-step addition will make sure you get the correct result!

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