Multiplying fractions and whole numbers

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Intros
Lessons
  1. How to convert a whole number to a fraction?
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Examples
Lessons
  1. Multiplying Fractions and Whole Numbers Involving Single-digit Numbers
    Calculate.
    1. 2×152 \times \frac{1}{5}
    2. 4×234 \times \frac{2}{3}
    3. 3×543 \times \frac{5}{4}
    4. 2×352 \times \frac{3}{5}
  2. Word Problems: Application of Multiplying Fractions and Whole Numbers
    A pizza had 12 slices, and 34\frac{3}{4} of it was eaten in a party. How many slices of pizza were eaten during the party?
    1. Three quarters of the trees in a park are maple trees. If there are 100 trees in the park, how many of them are maple trees?
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      Topic Notes
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      We learned previously that whole numbers can be written We learned previously that whole numbers can be written as fractions with 1 as the denominator and the whole number as the numerator. To make the calculation easier, we can first make the whole numbers into fraction when we multiply whole numbers with fractions. By doing so, we turn the questions into multiplying fractions only.

      What is a whole number

      You've encountered lots of whole numbers before now. Whole numbers are numbers that aren't fractions—they are integers. For example, 2,122, 12, and 5050 would all be whole numbers.

      On the other hand, numbers that aren't whole numbers would look something like 1.251.25 or 45\frac{4}{5}. Although a fraction is a rational number, it is not a whole number. Knowing the difference will be important in this lesson

      How to multiply fractions with whole numbers

      When you're given a question that requires you to deal with multiplying fractions with whole numbers, there's 44 main steps you'll have to carry out.

      Firstly, rewrite the question so that the whole number is turned into a fraction. As you probably already know, when you have a whole number, turning it into a fraction just requires you to put it over 11. So for example, if you wanted to convert 88 into a fraction, it'll be rewritten as 81\frac{8}{1}.

      Secondly, multiply the two numerators in the two respective fractions. This just means taking the two numbers on top of each of the fractions and then multiplying them with one another.

      For the third step, do the same as step two but now you're using the two numbers in the denominators in the fractions. You'll end up with a new fraction after doing steps two and three!

      Lastly, you'll just have to simplify the fraction you've gotten after solving the problem. You have to show your answer in the lowest terms possible, or you may get marks deducted for not having completely finished the question. Let's take a look at some examples and put the four steps into use to help you with multiplying fractions and whole numbers.

      Practice problems

      Question 1:

      Calculate

      2×152 \times \frac{1}{5}

      Solution:

      First, we can express 22 as a fraction:

      21\frac{2}{1}

      Our question will then be converted to something that looks like this:

      21×15\frac{2}{1} \times \frac{1}{5}

      We multiply these fractions, first tackling the top numbers (2×12 \times 1) and then doing the bottom ones (1×51 \times 5). Then we'll get our final number, which is a new fraction.

      21×15=25\frac{2}{1} \times \frac{1}{5} = \frac{2}{5}

      Since 25\frac{2}{5} is already the most simplified form of the fraction, this will be your final answer.

      Most simplified form of a fraction
      Simplified form of the fraction

      Question 2:

      A pizza had 1212 slices, and 34\frac{3}{4} of it was eaten in a party. How many slices of pizza were eaten during the party?

      Solution:

      There were 1212 slices and 34\frac{3}{4} were eaten. So we multiply 1212 and 34\frac{3}{4} to get the answer. Let's express 1212 as a fraction.

      121×34\frac{12}{1} \times \frac{3}{4}

      Before doing multiplication, we can simplify the question first and get this:

      31×31\frac{3}{1} \times \frac{3}{1}

      How to simplify a fraction
      Simplify a fraction

      Now, do the multiplication. We've got 99 as the final answer

      31×31=91=9\frac{3}{1} \times \frac{3}{1} = \frac{9}{1} = 9

      Simplify the fraction and get the final answer
      Simplify and get the answer

      If you're ever unsure about your answer in questions involving the multiplication of whole numbers and fractions, use this calculator to help you double check your work.

      Good lessons to review and move forward with to help you understand this lesson better includes finding common factors, comparing rational numbers, and solving problems with rational numbers in fraction form. These will eventually lead you into the more advanced problems of solving two-step linear equations.

      In this lesson, we will learn:
      • Multiplying Fractions and Whole Numbers Involving Single-digit Numbers
      • Word Problems: Application of Multiplying Fractions and Whole Numbers
      • Multiplying Fractions and Whole Numbers Involving Multiple-digit Numbers