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Chapter 2: Problem 49

Write the mixed number or whole number as an improper fraction. $$4 \frac{7}{12}$$

Short Answer

Expert verified
The mixed number \(4 \frac{7}{12}\) as an improper fraction is \(\frac{55}{12}\).

Step by step solution

01

Identify the numbers

Firstly, identify the whole number, the numerator and the denominator. In the mixed number \(4 \frac{7}{12}\), '4' is the whole number, '7' is the numerator and '12' is the denominator.
02

Multiply the whole number and the denominator

Secondly, multiply the whole number by the denominator. So here, \(4 \times 12 = 48\).
03

Add the product to the numerator

Next, add the product resulted from step 2 to the numerator. Therefore, \(48 + 7 = 55\).
04

Write the improper fraction

Finally, write the sum from step 3 as the new numerator and put it over the original denominator. Thus, the mixed number \(4 \frac{7}{12}\) can be written as the improper fraction \(\frac{55}{12}\).

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Key Concepts

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

Mixed Numbers
Mixed numbers are a combination of whole numbers and fractions. They are used to express quantities that are greater than a whole but involve fractional parts. For instance, in the mixed number \(4 \frac{7}{12}\), the '4' represents the whole number, while the \(\frac{7}{12}\) is the fractional part.

To convert a mixed number to an improper fraction, you multiply the whole number by the denominator of the fractional part, then add the numerator. This process reflects how much of the whole is encompassed in the fraction, and it helps in simplifying calculations involving addition, subtraction, multiplication, or division of fractions and mixed numbers.
Numerator
The numerator is a term that represents the top part of a fraction. It indicates how many parts of the whole are being considered. In the fraction \(\frac{7}{12}\), '7' is the numerator.

When working with mixed numbers, the role of the numerator becomes significant when converting these numbers to improper fractions. By calculating \(4 \times 12 + 7 = 55\), the combined number '55' becomes the new numerator in the improper fraction, showing how many total fraction parts there are in the whole and the fractional part together.
Denominator
The denominator is the bottom part of a fraction that shows into how many equal parts the whole is divided. In the fraction \(\frac{7}{12}\), the number '12' is the denominator.

It remains unchanged when you convert mixed numbers to improper fractions. The denominator holds the entire fraction stable, defining the size of the fractional parts. By maintaining the denominator at '12', we see the consistency of division across the whole parts and the fractional parts in \(\frac{55}{12}\), the improper fraction equivalent of \(4 \frac{7}{12}\).
Whole Numbers
Whole numbers are integers without fractions or decimals, representing entire units. In mixed numbers, whole numbers represent the complete units before adding any fractional parts. For instance, the '4' in \(4 \frac{7}{12}\) is a whole number.

These whole numbers are crucial when converting mixed numbers to improper fractions. They determine how many complete sets of the denominator there are. By multiplying the whole number by the denominator \(4 \times 12\), you establish the foundation of the improper fraction, before integrating the fractional "leftover" represented by the initial numerator.

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Most popular questions from this chapter

Convert the decimal to a fraction. $$4.55$$

Find 0.82 times \(10^{2}\)

Write an equivalent fraction with the given denominator. $$\frac{1}{4}=\frac{}{20}$$

Simplify. $$\left(\frac{1}{4}\right)^{2} \div\left(2 \frac{1}{2}-\frac{3}{4}\right)+\frac{5}{7}$$

Convert the decimal to a fraction. $$0.6$$
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