Answer and Explanation:
First, we can list whole number factor pairs of 60:
- (1, 60)
- (2, 30)
- (3, 20)
- (4, 15)
- (5, 12)
- (6, 10)
Then, we can select the pairs whose larger number divides nicely into 1—that doesn't create a non-repeating decimal:
For the next step, we have to understand that dividing by a fraction is the same thing as multiplying by its reciprocal:
[tex]A \div \dfrac{B}{C} = A \times \dfrac{C}{B}[/tex]
This means that if B = 1, then:
[tex]A \div \dfrac{1}{C} = A\times C[/tex]
We can use this knowledge to represent our factor pairs:
- [tex]3\times 20 = 60[/tex]
- [tex]6 \times 10 = 60[/tex]
as division of:
- a whole number greater than 1 — the smaller factor
- and a decimal (fraction) less than 1 — the larger factor
So, first we can rewrite multiplying by the larger factors as dividing by their reciprocals:
[tex]3 \times 20 = 3 \div \dfrac{1}{20}[/tex]
[tex]6 \times 10 = 6 \div \dfrac{1}{10}[/tex]
Next, we can rewrite the fractions as decimals:
[tex]3 \div \dfrac{1}{20} = 3 \div 0.05[/tex]
[tex]6 \times 10 = 6 \div 0.1[/tex]
And there we have two expressions with an integer greater than 1 and a decimal smaller than 1 that multiply to 60:
[tex]\huge\boxed{3\div 0.05=60}[/tex]
[tex]\huge\boxed{6\div 0.1 = 60}[/tex]
