2. Multiplication of mixed numbers by an integer.

Deepen your knowledge with an interactive video lesson on this topic in our app. Quizzes and pauses will help you better absorb the material!

Let's explore the topic: Multiplying a mixed number by a whole number. Imagine three friends each have two and a half candies. How can we calculate the total number of candies? First, we multiply the two whole candies by three. This gives us six candies. Then we multiply the half candy by three. This equals three half candies or one and a half candies. Altogether, we have seven and a half candies. But here's how the mathematical calculation looks, and the magic is that we don’t have to draw candies, apples, or elephants to count them; we simply work with numbers! Two and a half times three is: Six candies. Three halves are: Seven and a half. Calculation in numbers. Remember: How many times the denominator fits into the numerator is the whole part, and the remainder is the fractions. For instance, we have one whole and two sixths of a pizza, and we want to multiply it by four. We start with the whole parts of the pizza and multiply them by four, and similarly, we multiply the numerator by four to see the result. But eight sixths is a lot of parts and is an improper fraction; how to convert it to proper? It's easy: we simply count how many times six (which is our denominator or how many parts make up a whole) fits into eight. It’s one time and two as a remainder. The result is five wholes and two-sixths of a pizza. 17/5, 17:5 = 3 with a remainder of 2, so 3 and 2/5 Pizza and two-sixths. 1,2/6 x 5 = (1x5) 2x5 and so on. Six whole and 4/6 of a pizza. For convenience, when multiplying a mixed number by a whole, we can simplify this expression to reduce the numbers we work with. For instance, multiplying two wholes and eight fifteenths by five. We multiply the two wholes by five and multiply the numerator by five; for convenience, we'll simplify the multiplier with the denominator, and we see that the multiplier fits the denominator three times, so we reduce the multiplier to one and the denominator to three. What's the result? Keep watching as soon as you’ve calculated. The result is ten wholes and eight-thirds, which we convert to proper fractions, that is – we divide the denominator by the numerator, and in total, we have twelve whole and two-thirds. Voilà! It's that simple!

Mastering Mixed Numbers Multiplication with Integers: A Student Guide

Unlocking the Secrets of Multiplying Mixed Numbers by An Integer

Have you ever wondered how everyday scenarios, like dividing pizza slices among friends, utilize mathematics? It's pretty amazing when you think about it. This article delves deep into the world of multiplying mixed numbers by an integer, a key concept that helps us solve numerous real-life problems. Our objective is not to replicate the lessons from the video but to expand your understanding with additional insights and examples.

Why Is Multiplying Mixed Numbers Important?

Multiplication of mixed numbers by integers comes in handy in various situations. Whether you're cooking and need to adjust a recipe, dividing goods, or even when playing sports and calculating scores, understanding this concept is crucial. And the beauty lies in its simplicity once you grasp the basics!

A Step-By-Step Guide

Let’s take a practical example to understand this better. Suppose you are helping out in organizing a school play and you need to calculate the amount of fabric required to make costumes. If one costume requires one and three-fourths yards of fabric, and you need to make eight costumes, how much fabric is needed in total?

First, you divide this problem into smaller parts. Multiply the whole number (1 yard) by the total number of costumes (8), which equals 8 yards. Next, multiply the fractional part (three-fourths of a yard) by the same number, resulting in 24 fourths, or 6 yards when simplified. Add these two results together to get 14 yards in total. It’s that simple!

Additional Tip: Simplification Before Multiplication

In some cases, simplifying your numbers before starting the multiplication process can save you a lot of time and reduce the chance of errors. This technique is especially useful when dealing with larger numbers or when the numbers can be easily simplified by a common factor.

Remember, the goal is to make the problem easier to solve, without changing the outcome. Practice with different numbers, and soon, you’ll find this method incredibly helpful.

In conclusion, multiplying mixed numbers by an integer might seem daunting at first, but with practice and the right approach, it becomes an invaluable tool in solving everyday problems. So, take this knowledge, apply it, and always be on the lookout for how math illuminates the world around us.