Question Rewrite $1 \frac{3}{4} - \frac{4}{5}$ using twentieths and simplify.

Studdy Solution

STEP 1

Assumptions
1. We are given a mixed number $1 \frac{3}{4}$ and a fraction $\frac{4}{5}$ .
2. We want to rewrite the expression using a common denominator, which in this case will be twentieths (20) since it is the least common multiple of 4 and 5.

STEP 2

First, we convert the mixed number into an improper fraction. To do this, we multiply the whole number by the denominator of the fractional part and add the numerator of the fractional part.
$1 \frac{3}{4} = \frac{4 \times 1 + 3}{4}$

STEP 3

Now, perform the calculation to find the improper fraction.
$1 \frac{3}{4} = \frac{4 + 3}{4} = \frac{7}{4}$

STEP 4

Next, we need to rewrite both fractions with the common denominator of 20. We start by finding the equivalent fraction for $\frac{7}{4}$ .
$\frac{7}{4} = \frac{7 \times 5}{4 \times 5}$

STEP 5

Perform the multiplication to find the equivalent fraction.
$\frac{7}{4} = \frac{35}{20}$

STEP 6

Now, we find the equivalent fraction for $\frac{4}{5}$ with the denominator of 20.
$\frac{4}{5} = \frac{4 \times 4}{5 \times 4}$

STEP 7

Perform the multiplication to find the equivalent fraction.
$\frac{4}{5} = \frac{16}{20}$

STEP 8

Now that we have both fractions with the common denominator of 20, we can subtract them.
$\frac{35}{20} - \frac{16}{20}$

STEP 9

Subtract the numerators while keeping the common denominator.
$\frac{35}{20} - \frac{16}{20} = \frac{35 - 16}{20}$

STEP 10

Perform the subtraction to find the result.
$\frac{35 - 16}{20} = \frac{19}{20}$
The expression $1 \frac{3}{4}-\frac{4}{5}$ rewritten using twentieths is $\frac{19}{20}$ .

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