Question

Select all the expressions with a product less than 2/3.
4 and 1/8 x 2/3
2/3 x 2/3
2/3 x 2
5/6 x 2/3

Answer 1

The expressions with a product less than 2/3 are:

2/3 × 2/3 and 5/6 × 2/3 ⇒ 2nd and 4th

Step-by-step explanation:

Let us revise some fact about the product of two numbers

• If x is multiplied by y where y > 1, then the product is greater than x (Ex: if x is 3/4 and y is 2, then xy = (3/4)(2) = 3/2 which is greater than 3/4)
• If x is multiplied by y where 0 < y < 1, then the product is less than x (Ex: if x = 2/5 and y = 1/3, then xy = (2/5)(1/3) = 2/15 which is less than 2/5)

We need to select all the expressions with a product less than 2/3

∵ 4 and 1/8 × 2/3

- 4 and 1/8 means mixed number $4\frac{1}{8}$

∵ $4\frac{1}{8}$ > 1

- That means the product of it and 2/3 will be greater than 2/3

   as the first fact above

∴ $4\frac{1}{8}$ × $\frac{2}{3}$ > $\frac{2}{3}$

∵ $\frac{2}{3}$ × $\frac{2}{3}$

∵ $\frac{2}{3}$ is between 0 and 1

- That means the product of it and 2/3 will be less than 2/3

   as the second fact above

∴ $\frac{2}{3}$ × $\frac{2}{3}$ < $\frac{2}{3}$

∵ $\frac{2}{3}$ × 2

∵ 2 > 1

- That means the product of it and 2/3 will be greater than 2/3

   as the first fact above

∴ $\frac{2}{3}$ × 2 > $\frac{2}{3}$

∵ $\frac{5}{6}$ × $\frac{2}{3}$

∵ $\frac{5}{6}$ is between 0 and 1

- That means the product of it and 2/3 will be less than 2/3

   as the second fact above

∴ $\frac{5}{6}$ × $\frac{2}{3}$ < $\frac{2}{3}$

The expressions with a product less than 2/3 are:

2/3 × 2/3 and 5/6 × 2/3

Learn more:

You can learn more about the fractions in brainly.com/question/1312102

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