/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 90 Perform the indicated operations... [FREE SOLUTION] | 91影视

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Chapter 5: Problem 90

Perform the indicated operations. Round the answer to the nearest hundredth when necessary. $$(4.6)\left(\frac{7}{6}\right)$$

Short Answer

Expert verified
5.37

Step by step solution

01

Write the problem

The problem given is \[ (4.6) \left( \frac{7}{6} \right) \]
02

Perform the multiplication

Multiply the decimal number by the fraction: \[ 4.6 \times \frac{7}{6} \]
03

Convert the decimal to a fraction

Convert 4.6 to a fraction to make multiplication easier: \[ 4.6 = \frac{46}{10} \]
04

Multiply the fractions

Multiply \( \frac{46}{10} \) by \( \frac{7}{6} \): \[ \frac{46}{10} \times \frac{7}{6} = \frac{46 \times 7}{10 \times 6} = \frac{322}{60} \]
05

Simplify the fraction

Simplify \( \frac{322}{60} \) by dividing both the numerator and the denominator by their greatest common divisor (2): \[ \frac{322 \div 2}{60 \div 2} = \frac{161}{30} \]
06

Convert the fraction to a decimal

Convert \( \frac{161}{30} \) to a decimal by performing the division: \[ \frac{161}{30} \approx 5.3667 \]
07

Round to the nearest hundredth

Round 5.3667 to the nearest hundredth: \[ 5.3667 \approx 5.37 \]

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Key Concepts

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

Decimal Multiplication
Multiplying decimals is an essential math skill. The key is to ignore the decimal points initially and multiply the numbers as if they were whole numbers. Afterward, count the total number of decimal places from both of the original numbers. Place the decimal in the product by counting from the rightmost digit. For example, when you multiply 4.6 and 7, you get 32.2 because there is one decimal place in the number 4.6.
Fraction Multiplication
Multiplying fractions might seem tricky at first, but it鈥檚 straightforward once you get the hang of it. First, multiply the numerators (top numbers) together, then the denominators (bottom numbers). Simplify the resulting fraction if possible. For instance, multiplying \( \frac{46}{10} \) by \( \frac{7}{6} \) involves multiplying 46 by 7 to get 322 and 10 by 6 to get 60, resulting in \( \frac{322}{60} \).
Rounding Numbers
Rounding is a method of approximating a number to make it simpler but still close to the original value. To round a number to the nearest hundredth (two decimal places), look at the third decimal place. If it is 5 or greater, round the second decimal place up. If it is less than 5, keep the second decimal place as is. For example, rounding 5.3667 gives you 5.37.
Converting Decimals to Fractions
Converting decimals to fractions is useful in making some operations easier, like multiplication. Start by writing the decimal as a fraction with a denominator of 10, 100, 1000, etc., depending on the number of decimal places. For instance, 4.6 can be written as \( \frac{46}{10} \). Once you have the fraction, simplify it if possible. Converting decimals makes fraction operations more consistent and manageable.

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