Question

Change the following improper fractions to mixed numbers, and reduce to lowest terms. \(\frac{59}{14}=\) ______

Short answer

The mixed number is 4\(\frac{3}{14}\).

Step-by-step solution

Divide the Numerator by the Denominator

We start by dividing the numerator (59) by the denominator (14). Perform the division: 59 ÷ 14 to determine how many whole numbers we can extract from the fraction. 59 divided by 14 equals 4, with a remainder.

Determine the Whole Number Part

The whole number part of the mixed number is the quotient obtained from the division; here, it is 4.

Calculate the Remainder

Compute the remainder from the division in Step 1. Multiply 4 (the quotient) by 14 (the divisor) to find the closest multiple of 14 that is less than 59. This product is 56. Subtract 56 from 59 to find the remainder: 59 - 56 = 3.

Write the Remainder as a Fraction

The remainder becomes the numerator of the fractional part, and the denominator stays the same. This gives us the fraction \(\frac{3}{14}\).

Combine Whole Numbers with Fraction

Form the mixed number by placing the whole number and the fractional part together. The mixed number is 4\(\frac{3}{14}\).

Simplify the Fraction (if necessary)

Check if the fraction \(\frac{3}{14}\) can be simplified. Since the GCD of 3 and 14 is 1, the fraction is already in its lowest terms.

Key concepts

Understanding Fractions

Fractions are essential components in mathematics that represent a part of a whole. They consist of two parts: the numerator and the denominator. The numerator is the top number, indicating how many parts you have. The denominator is the bottom number, showing the number of equal parts the whole is divided into.

When dealing with fractions, you may come across improper ones, where the numerator is larger than the denominator. This indicates that the fraction is more than one whole. To make improper fractions easier to understand and use, they can be converted into mixed numbers.

• Improper fractions, like \(\frac{59}{14}\), have a numerator greater than their denominator.
• A mixed number combines a whole number with a fraction.

Learning to convert fractions between these forms is a valuable skill in mathematics education.

Converting Improper Fractions to Mixed Numbers

Mixed numbers represent both a whole part and a fractional part, making them easy to grasp. To convert an improper fraction to a mixed number, you will follow a simple process.

Start by dividing the numerator by the denominator to find the whole number part of the mixed number. The quotient from this division gives the whole number. In our original exercise, dividing \(59\) by \(14\) gives \(4\), which is the whole number of the mixed number.

Next, calculate the remainder of the division. This remainder becomes the numerator of the fraction part. For example, \(59 - (4 \times 14) = 3\), so the fractional part is \(\frac{3}{14}\).

• The fraction \(\frac{3}{14}\) cannot be simplified further, as its greatest common divisor with 14 is 1.
• Finally, combine the whole number and fraction to form the mixed number \(4\frac{3}{14}\).

Understanding how to perform these steps will help you successfully convert improper fractions to mixed numbers.

The Role of Mathematics Education in Learning Fractions

Mathematics education plays a crucial role in helping students understand concepts such as fractions and mixed numbers. Fractions are foundational elements in math that appear across various topics, including ratios, proportions, and even algebra.

By teaching students how to convert improper fractions to mixed numbers, educators help them develop a more concrete understanding of quantities larger than one whole. This is important for grasping more complex mathematical ideas later on.

• Proper understanding of fractions supports learning in other areas of math.
• Education in fractions builds critical thinking and problem-solving skills.
• Fractions are core to everyday mathematical applications and real-world problems.

Effective mathematics education that emphasizes hands-on practice with fractions can significantly improve students' confidence and performance in math.