Place these fraction in the ascending order of magnitude

Question

ScanSolve AI Tutor · Accepted Answer

To arrange these mixed numbers in ascending order, we first compare their whole number parts. Since all the whole number parts are 4, we need to compare their fractional parts.

Identify the fractional parts of the mixed numbers.
The mixed numbers are $4\frac{2}{3}, 4\frac{1}{2}, 4\frac{3}{5}$ .
The fractional parts are $\frac{2}{3}, \frac{1}{2}, \frac{3}{5}$ .
Find the least common multiple (LCM) of the denominators of the fractional parts.
The denominators are 3, 2, and 5.
The LCM of 3, 2, and 5 is $3 \times 2 \times 5 = 30$ .
Convert each fractional part to an equivalent fraction with the common denominator of 30.
For $\frac{2}{3}$ :
$\frac{2}{3} = \frac{2 \times 10}{3 \times 10} = \frac{20}{30}$
For $\frac{1}{2}$ :
$\frac{1}{2} = \frac{1 \times 15}{2 \times 15} = \frac{15}{30}$
For $\frac{3}{5}$ :
$\frac{3}{5} = \frac{3 \times 6}{5 \times 6} = \frac{18}{30}$
Compare the numerators of the equivalent fractional parts.
The equivalent fractional parts are $\frac{20}{30}, \frac{15}{30}, \frac{18}{30}$ .
Arranging the numerators in ascending order: 15, 18, 20.
Write the original mixed numbers in ascending order based on their fractional parts.
The order of the fractional parts from smallest to largest is $\frac{15}{30}, \frac{18}{30}, \frac{20}{30}$ .
This corresponds to the original fractions:
$4\frac{1}{2}$ (since $\frac{1}{2} = \frac{15}{30}$ )
$4\frac{3}{5}$ (since $\frac{3}{5} = \frac{18}{30}$ )
$4\frac{2}{3}$ (since $\frac{2}{3} = \frac{20}{30}$ )

The fractions in ascending order are:
$4\frac{1}{2}, 4\frac{3}{5}, 4\frac{2}{3}$

Place these fraction in the ascending order of magnitude

Answer

Step-by-step solution

Identify the fractional parts of the mixed numbers.

Find the least common multiple (LCM) of the denominators of the fractional parts.

Convert each fractional part to an equivalent fraction with the common denominator of 30.

Compare the numerators of the equivalent fractional parts.

Write the original mixed numbers in ascending order based on their fractional parts.

Try one yourself

Still stuck on this one?

More Mathematics Questions