Question

Can i please have an answer. Thank you​

Answer 1

`3\frac14 = \frac{13}4`, refer to the step-by-step explanation.

Explanation:

Let's break down the procedure for converting a mixed number into a fraction step by step and explain the "why" behind each step along with a "real world example":

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Step 1: You have a mixed number, which is a combination of a whole number and a fraction. For example, 3 1/4 is a mixed number because it has a whole number part, "3," and a fraction part, "1/4."

• Imagine you have a pizza that is divided into 4 equal slices, and you want to know how much pizza you have in total. A mixed number, like 3 1/4, tells us how many whole pizzas we have (3) and how many additional slices we have (1/4).

Step 2: To convert this mixed number into a fraction, we need to make it all a part of the fraction. We do this by imagining the whole number part as a fraction with the same denominator as the fraction part. In our example, the denominator is 4 because the fraction part is 1/4.

• To find out the total amount of pizza in terms of slices, we need to make sure we're using the same-sized slices for the whole pizzas and the additional slices. We do this by converting the whole number part (3) into slices. Since each pizza has 4 slices, we multiply the number of whole pizzas (3) by the number of slices in each pizza (4). This gives us 3 x 4 = 12 slices.

Step 3: Now, let's focus on the whole number part, "3." To turn it into a fraction with the same denominator as the fraction part, "4," we multiply the whole number, "3," by the denominator, "4." This gives us 3 × 4 = 12.

• Now, we add the number of additional slices (1/4) to the 12 slices we got from the whole number part. To add the fraction part, we need to make sure we're using the same-sized slices, which is why we use the common denominator of 4. In this case, 1/4 is already in terms of 4 slices, so we can add it directly.

Step 4: Next, we add the numerator of the fraction part, "1," to the result we got from Step 3. So, we add 1 to 12, which gives us 13.

• Adding the 1 to the 12 slices gives us a total of 13 slices.

Step 5: Finally, we place the result from Step 4, "13," over the original denominator, "4," to form the final fraction: 13/4.

• Now, we want to express this total as a single fraction. To do that, we put the 13 slices over the original denominator of 4 to get the final answer: 13/4.

Thus,

`3\frac14 =(3 * 4 +1)/(4) = \boxed{\frac{13}4}`

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Let me explain the "why" behind the procedure in a more explicit manner:

The reason we convert a mixed number into a fraction using this procedure is to make it easier to work with fractions in different mathematical operations. Fractions represent parts of a whole, and they are essential in many real-life situations like cooking, sharing, measuring, and more. Converting mixed numbers into fractions allows us to handle them in a consistent way, just like we do with whole numbers.


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Additional terminology:

Mixed Number: A mixed number is a combination of a whole number and a proper fraction. It represents a quantity that is made up of both whole units and a fractional part.

Fraction: A fraction represents a part of a whole. It consists of two numbers separated by a horizontal line, with the number above the line called the numerator and the number below the line called the denominator. The numerator indicates how many parts we have, and the denominator indicates the total number of equal parts that make up the whole.

Numerator: The numerator is the top number in a fraction. It represents the number of equal parts that are being considered or counted.

Denominator: The denominator is the bottom number in a fraction. It represents the total number of equal parts that make up a whole.