/*! 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 67 Calculate. \(\frac{7}{8} \time... [FREE SOLUTION] | 91影视

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Chapter 4: Problem 67

Calculate. \(\frac{7}{8} \times 12.64\)

Short Answer

Expert verified
11.06

Step by step solution

01

Understand the Problem

You need to multiply the fraction \(\frac{7}{8}\) by the decimal number 12.64.
02

Convert the Fraction to Decimal (if needed)

Although it is not necessary here, note that \(\frac{7}{8}\) as a decimal is 0.875. You can use either form for multiplication.
03

Perform the Multiplication

Multiply the fraction \(\frac{7}{8}\) by 12.64. \[ \frac{7}{8} \times 12.64 = 7 \times \frac{12.64}{8} = 7 \times 1.58 = 11.06 \]

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Key Concepts

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

fraction multiplication
Multiplying fractions is an important skill in mathematics that is easy to master with practice. For example, to multiply \(\frac{7}{8}\) by a number, follow a simple rule: multiply the numerators (top numbers) together and the denominators (bottom numbers) together. In our case, since we're multiplying a fraction by a decimal, we can first convert the decimal to a fraction if it makes the multiplication easier. However, it's not always necessary. Let's see a practical step-by-step approach to solving multiplication involving fractions and decimals.
decimal multiplication
When working with decimal multiplication, remember to align the numbers by their decimal points, multiply as if they were whole numbers, and then place the decimal point in the product. For instance, multiplying 12.64 by \(\frac{7}{8}\) is simpler if you turn the fraction into a decimal first. You can convert \(\frac{7}{8}\) to 0.875. Now, the problem is just 0.875 * 12.64. Perform the multiplication: \( \begin{aligned} & 12.64 \times 0.875=\ & 11.06. \ \end{aligned} \)
conversion between fractions and decimals
Converting between fractions and decimals is a useful technique, especially when dealing with complex operations. A fraction like \(\frac{7}{8}\) can be converted to a decimal by dividing the numerator (7) by the denominator (8), giving 0.875. Conversely, to turn a decimal into a fraction, write the decimal as a fraction with 1 in the denominator, then multiply the numerator and the denominator by 10 for each digit after the decimal point. Finally, simplify the fraction if necessary.
simplification
Simplification makes complex problems easier to handle. When multiplying fractions, after converting and multiplying, always check if the answer can be simplified. For the fraction \(\frac{7}{8}\), when multiplied by 12.64, you may not need to simplify the fraction. Yet, converting it into easiest forms, like turning it into a decimal first, can make calculations straightforward. Always look for ways to reduce fractions by finding the greatest common divisor (GCD) of the numerator and denominator and dividing both by this number. Simplification helps to keep your answers neat and less cumbersome.

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Most popular questions from this chapter

Fence Posts. A zoo plans to construct a fence around a proposed exhibit featuring animals of the Great Plains. The perimeter of the area to be fenced is \(1760 \mathrm{ft}\). Estimate the number of wooden fence posts needed if the posts are placed \(8.625 \mathrm{ft}\) apart.

Subtract. $$ 36.2-16.28 $$

Peggy filled her van's gas tank and noted that the odometer read 26,342.8 . After the next fill-up, the odometer read 26,736.7 . It took 19.5 gal to fill the tank. How many miles per gallon did the van get between fill-ups?

Petra bought gasoline when the odometer read 14,296.3 . At the next gasoline purchase, the odometer read 14,515.8 . How many miles had been driven?

Estimate by rounding as directed. $$ \begin{aligned} &198.67432-24.5007\\\ &\text { nearest ten } \end{aligned} $$
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