Solve: 5.25 × 2/3 × 7/21 - Decimal and Fraction Multiplication

Question

$5.25\cdot\frac{2}{3}\cdot\frac{7}{21}=\text{?}$

00:00 Solve

00:03 Convert from numeric representation to mixed number representation

00:12 Now convert from mixed number to fraction

00:15 Multiply the whole number by denominator, add to numerator and combine with fraction

00:22 This is the representation of the entire number as a fraction

00:36 Let's arrange the exercise so it's easier to solve

00:40 Reduce what we can

00:48 Make sure to multiply numerator by numerator and denominator by denominator

00:57 Break down 14 into 12 plus 2

01:01 Break down the fraction into whole number and remainder

01:07 And this is the solution to the question

We rewrite the decimal fraction in the form of a mixed fraction:

$5.25=5\frac{1}{4}$

Now we get the exercise:

$5\frac{1}{4}\cdot\frac{2}{3}\cdot\frac{7}{21}=$

We write the mixed fraction as a simple fraction:

$5\frac{1}{4}=\frac{4\times5+1}{4}=\frac{20+1}{4}=\frac{21}{4}$

Now we obtain:

$\frac{21}{4}\cdot\frac{2}{3}\cdot\frac{7}{21}=$

We simplify the 21 and obtain:

$\frac{7}{4}\cdot\frac{2}{3}=\frac{14}{12}=\frac{12+2}{12}=1\frac{2}{12}=1\frac{1}{6}$

$1\frac{1}{6}$