We are asked to select all the equations that are true.
& 1/3 Ă· 3 = 1/3 Ă· 3/1=1/3* 1/3 [1em]
& 4/5 Ă· 5=4/5Ă· 5/1=4/5* 1/5 [1em]
& 7/8 Ă· 8 = 7/8Ă· 1/8=7/8* 8/1 [1em]
& 2/3Ă· 6=2/3Ă· 6/1 =2/3* 1/6 [1em]
& 4/9Ă· 4=4/9Ă· 1/4=4/9* 4/1 [1em]
Notice that all of these equations describe the steps that are necessary to divide a fraction by a whole number.
True or False?
Expression
Step 1
Step 2
1/3Ă· 3
1/3Ă· 3/1
1/3* 1/3
4/5Ă· 5
4/5Ă· 5/1
4/5* 1/5
7/8Ă· 8
7/8Ă· 1/8
7/8* 8/1
2/3Ă· 6
2/3Ă· 6/1
2/3* 1/6
4/9Ă· 4
4/9Ă· 1/4
4/9* 4/1
The first step is to write the whole number as fraction.
a=a/1
Let's see which of the given equations this step was done correctly in.
True or False?
Expression
Write Whole Number as Fraction
1/3Ă· 3
1/3Ă· 3/1
4/5Ă· 5
4/5Ă· 5/1
*
7/8Ă· 8
7/8Ă· 1/8
2/3Ă· 6
2/3Ă· 6/1
*
4/9Ă· 4
4/9Ă· 1/4
We can see that there is a mistake in the third and fifth expressions. The whole number should be in the numerator, not the denominator! Therefore, we can already say that the second and fifth equations are false. Next, let's recall how to divide by a fraction.
When you divide by a fraction, you get the same result as when you multiply by its reciprocal.
Let's see if this step was done correctly.
True or False?
Expression
Write Whole Number as Fraction
Multiply by the Reciprocal of the Fraction
âś“
1/3Ă· 3
1/3Ă· 3/1
1/3* 1/3
âś“
4/5Ă· 5
4/5Ă· 5/1
4/5* 1/5
*
7/8Ă· 8
7/8Ă· 1/8
7/8* 8/1
âś“
2/3Ă· 6
2/3Ă· 6/1
2/3* 1/6
*
4/9Ă· 4
4/9Ă· 1/4
4/9* 4/1
The last step was done correctly in each expression. This means that the first, second, and fourth equations are true!
