Estimating Products & Quotients of Fractions & Mixed Numbers

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  • 0:01 Fraction Product & Quotient
  • 1:12 Estimating Fractions
  • 3:18 Example 1
  • 3:58 Example 2
  • 4:51 Lesson Summary
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Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

You will be able to quickly estimate the answer to a multiplication or division problem involving fractions after watching this video lesson. Learn how to estimate the fraction for the best estimate.

Fraction Product & Quotient

If you are a chef or an architect, then you will be dealing with fractions. As a chef, you deal with fractions when you cook or bake and you need an exact amount of ingredients for your dish. As an architect, your measurements need to be exact so that your building comes out correctly when it is built. You will use both fractions and mixed numbers.

Fractions are the division of two whole numbers, and mixed numbers are a whole number followed by a fractional part. As a chef or architect, you might see fractions like 1/3, 1/2, 3/4, 7/8 and mixed numbers like 2 3/4, 1 1/64, 10 1/2. You might also have to make calculations with these fractions, such as multiplication and division, to get the answers that you need for your project. For example, you might need to multiply (14/19)*(4 1/8) or divide (5 6/7)/(2 3/21).

Estimating Fractions

While you do need to be exact in your answers when you start your project, you can estimate your answers in the beginning so that you know roughly what to expect. How do you estimate fractions? Well, since it is easy to work with 0, 1, and 1/2, we will round or estimate our fractions to one of these three numbers. There are three rules for us to follow, one for each number.

1. Round to 0 if the numerator of the fraction is much smaller than the denominator.

For example, you would round the fraction 1/8 to 0 because the numerator, the 1, is much smaller than the denominator, the 8. The same goes for 1/3. Because the 1 is much smaller than the 3, you would round it to 0.

2. Round to 1/2 if the numerator is close to half of the denominator.

For example, you would round 9/16 to 1/2 because the numerator, the 9, is close to half of the denominator, the 16. Half of 16 is 8, and 9 is very close to that. You would also round 5/12 to 1/2 because the numerator is close to half of the denominator. Half of the denominator in this case is 12/2 = 6, and 5 is close to 6.

3. Round to 1 if the numerator is close to the denominator.

For example, you would round 7/8 to 1 because the numerator is close to the denominator. The 7 is very close to 8. The same goes for 15/16 or even 14/16. Both the numerators are close to the denominators.

When working with mixed numbers, remember that you have an invisible plus in between your whole number and fractional part. So 1 3/4 is actually 1 + 3/4. To round mixed numbers, round the fractional part and then perform the addition. For 1 3/4, you would round the 3/4 to 1. You then have 1 + 1, which turns into 2. So 1 3/4 rounds to 2.

Now, let's look at two estimating problems.

Example 1

Estimate (14/19)*(4 1/8).

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