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Multiplying Improper Fractions Worksheets

When a fractions denominator is smaller than its numerator, we call this fraction improper. You will often see improper fractions represented as mixed number (whole number with a proper fraction). Having a solid understanding on how to multiply whole numbers by improper fractions is something we would hope you have achieved. It gets a bit more complicated when you are trying to multiply improper fraction by one another. The basic premise applies here regardless. You multiple the numerators by each other and follow that same procedure for the denominators. The last thing you may need to do is simplify the fraction or mixed number into the lowest available form. This lesson and worksheet series shows you how to multiply top heavy fractions with whole numbers.

Aligned Standard: Grade 5 Fractions - 5.NF.5

  • Answer Keys - These are for all the unlocked materials above.

Homework Sheets

This will get students into the basic rhythm of these types of problems. Multiply the numerator and reduce into a mixed number.

  • Homework 1 - To multiply a fraction by a whole number, write the whole number as a fraction with same numerator and 1 as the denominator.
  • Homework 2 - If we divide the numerator and denominator by the fraction, we can determine the missing parts.
  • Homework 3 - Multiply the numerators then multiply the denominators.

Practice Worksheets

You are introduced to find the missing piece of the fraction.

Math Skill Quizzes

This quiz is loaded with tons of problems that were on the recent New York State and Texas grade 5 assessment.

  • Quiz 1 - Find the products and fill in any empty sections along the way.
  • Quiz 2 - These will require you to think at a higher level.
  • Quiz 3 - Some pretty hefty fractions are here.

How to Find the Products of Improper Fractions and Integers

When learning fractions, there are three types that kids have to understand. The first one that kids learn about are the proper fractions. The denominator of proper fractions is greater than the numerator of the fraction. 1/4, 15/27, and 2/3 are examples of proper fractions. The second type fractions are the improper fractions that are also known as "top-heavy" fractions. Here the denominator of the fraction is smaller than the numerator of the fractions. 12/7, 5/3, and 7/4 are all examples of top-heavy fractions. The third type are mixed numbers, which can be written as a whole number coupled with either a proper or improper fractions. 3 1/4, 1 1/2 are examples of mixed numbers.

Once a student grasps the concepts of improper fractions easily, they can easily multiply the improper fractions with integers.

Example: Find the product of 18/7 × 3.

Step 1: Convert the Integer into a Fraction - The first step is to convert the integer into a fraction with one as its denominator. This means that you place the numerator of the integer over the denominator of 1. We would rewrite this problem as: 18/7 × 3/1

Step 2: Multiply the Numerators and the Denominators - (18×3)/(7×1) = 54/7

The resulting fraction is the answer; you can write it as a mixed number, and where possible, you can simplify the fraction. In this case (54/7 = 7 R 5) as a mixed number we would write this as 7 5/7.

When Will You Use This Skill in Real Life?

Top heavy fractions often will make simple calculation much quicker and even accurate. For example, the other day I was in my kitchen and was making my famous banana muffins. My son and daughter asked if I would send each of them a half-dozen muffins and my husband also wanted some for-work snacks. This means that I needed to triple the recipe. Everything in the recipe was in round numbers, except the amount of flour needed. Which means I just has to multiple all the whole numbers by 3. It required 1 1/3 cups of flour, which complicated things a bit. I was able to make this calculation in my head because I remembered that 1 1/3 = 4/3. When I multiple that by 3(4/3) I get 12/3 or 4. So I needed 4 cups of flour to triple the recipe. Bakers and chefs run into this problem on a daily basis.

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